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If each dimension of a cuboid is increased by \( 20 \% \), what is the percentage increase in its volume?

At the beginning of the year, a man takes out a loan of Rs 6000 with a \(5\%\) interest rate on a diminishing balance. He pays back Rs 1200 at the end of every year. Determine the outstanding loan balance in Rs at the start of the third year.

Given \( \frac{a}{b}=\frac{1}{3}, \frac{b}{c}=2, \frac{c}{d}=\frac{1}{2}, \frac{d}{e}=3 \), and \( \frac{e}{f}=\frac{1}{4} \), determine the value of \( \frac{a b c}{d e f} \).

When a 20-year-old is replaced by another individual in a group of 23 people, the group's average age rises by 4 months. What is the age of this new individual?

Gunpowder consists of 75% nitre, 10% sulphur, and the remainder is charcoal by weight. If the total weight of the gunpowder is 24 kg, what is the weight of the charcoal?

A cellphone can be purchased for Rs. 39,000 upfront, or with an initial cash payment of Rs. 6,000 followed by 4 equal monthly installments. These installments include compound interest at an annual rate of 24% compounded monthly. Determine the amount of each installment.

Calculate the net profit or loss percentage when the entire purchase is sold to a customer with a markup of \( 10\% \).

the actual weight. Driven by further greed, he mixes in \( 20\% \) impurities into the product. What is the dealer's net profit percentage?

Given the ratios \(a - b : b - c : c - d = 1 : 2 : 3\), what is the ratio of \((a + d) : c\)?

Ramesh got the scores of \(78, 92, 83,\) and 99 in his math tests. What must be his score in the next test to achieve an average score of 90 across all five tests?

15. In a class of 60 students, the average age is 12 years. If the number of girls increases by three-fourths and the number of boys decreases by half, the total number of students remains constant, and the average age of either group does not change either.

The average age of a team of officers decreases from 58 years to 56 years when an older member is substituted with a younger one. Given that the age gap between these two members is 30 years, what is the total number of members in the group?

The age of a student in the class remained the same. The total ages of the 6 students who either left or joined the class was 72 years. Determine the value of A.

the boys or the girls age changes. However, the overall average age becomes 13.5 years. The boys' average age is

In a 120 L mixture, milk and water are in a ratio of \(2:3\). After replacing 30 L of this mixture with 18 L of milk and 12 L of water, the new milk to water ratio is

The dimensions of a cuboid change as follows: length increases by 10%, breadth decreases by 5%, and height increases by 20%. What is the net percentage change in its volume?

Assertion (A): For a small percentage change p, the approximate percentage change in the volume of a cuboid when all three dimensions are increased by p% is about 3p%. Reason (R): Volume is proportional to the product of three linear dimensions, and for small x, \((1+x)^3 \approx 1 + 3x\). Which of the following is correct?

By what equal percentage p% should each dimension of a cuboid be increased so that its volume becomes exactly double?

In an election involving two candidates, the one receiving \( 30\% \) of the total votes is defeated by a margin of 15,000 votes. The total number of votes cast for the victorious candidate is

Rehman purchases some apples at a rate of 15 apples per rupee and an equal quantity at 20 apples per rupee. He combines these two batches and sells the mixture at 35 apples for 2 rupees. What is his percentage of profit or loss?

Given that \(\frac{a}{b} = \frac{2}{3}\), \(\frac{b}{c} = \frac{3}{5}\), and \(\frac{c}{d} = \frac{5}{6}\), find the value of \(\frac{3a + 2b + 4c + d}{3d + 4c}\).

When a person with a height of 184 cm is replaced by someone else, the average height of the group of 13 decreases by 2 cm. What is the height of this new individual?

In what proportion should a \( 30\% \) Phenyl Alcohol solution be combined with a \( 60\% \) Phenyl Alcohol solution to achieve a final solution with \( 50\% \) Phenyl Alcohol content?

If the sides of a square are increased by \( 30\% \), what is the percentage increase in its area?

A merchant set the price of his merchandise \(20\%\) above the cost price. He proceeds to sell \(\tfrac{1}{4}\) of his inventory with a \(10\%\) discount, half of the inventory at the marked price, and the remainder with a \(25\%\) discount. Calculate his percentage profit.

Given that \( \frac{a}{2} = \frac{b}{3} = \frac{c}{4} = \frac{2a - 3b + 5c}{k} \), and where \(a\), \(b\), and \(c\) are non-zero values, determine the value of 'k'.

In a class of 24 students, the average score in a subject with a maximum of 100 marks is 89. If 3 students exit the class, by how much can the average potentially increase?

A combination of liquids A and B is created with a ratio of \(3:2\), and this blend is sold at Rs. 11 per litre, yielding a \(10\%\) profit. Given that the cost of liquid A is Rs. 2 per litre higher than that of liquid B, determine the cost per litre of liquid A.

A vendor sells 30% of his fruits and discards 40% of the leftover fruits. The following day, he sells half of the remaining fruits and discards the remainder. What percentage of the fruits does the vendor discard?

The total price for 2 apples, 3 mangoes, and 4 oranges exceeds the total price for 1 apple, 2 mangoes, and 2 oranges by Rs. 6. Meanwhile, the total price for 1 apple, 2 mangoes, and 1 orange falls Rs. 8 short of the total price for 3 apples, 3 mangoes, and 5 oranges. If the listed price for 3 apples, 1 mango, and 6 oranges is Rs. 12, what percentage discount should be applied on their sale to achieve a net profit of 5%?

The monthly earnings of X and Y have a ratio of \( 1:3 \), while their spending follows a ratio of \( 19:40 \). X saves Rs. 18,860 less compared to Y, and together, their savings amount to Rs. 36,020. What are the respective incomes of X and Y?

A shipping clerk is handling five boxes, each with a distinct but unspecified weight, all under 100 kg. The clerk records the weights by weighing them in pairs, resulting in these measurements: 110, 112, 113, 114, 115, 116, 117, 118, 120, and 121 kg. What is the weight of the heaviest box?

In a 105 L mixture, the milk to water ratio is \(8:7\). If a portion of the mixture is taken out, including 14 L of water, and then 5 L of water is added back to the remaining mixture, what will the new ratio of milk to water be?

If the cost of a bicycle experiences successive hikes of \( 9.09\% \), \( 8.33\% \), and \( 7.7\% \), its final price is Rs. 1,274. What was the bicycle's initial price?

Mr. Alphonso purchases two batches of mangoes. The first batch is priced at Rs. 30 per dozen, while the second batch costs Rs. 50 per dozen. He sells all the mangoes at a rate of Rs. 40 per dozen. If the expenditure on each batch is identical, determine his profit or loss percentage.

A class consists of 40 boys, one of whom weighs 100 kg and leaves. Simultaneously, a new boy becomes part of the class. As a result, the average weight of the boys rises by 0.25 kg. Determine the weight of the new boy.

A milkman combines 20 liters of water with 80 liters of milk. After selling a quarter of this mixture, he adds more water to restore the volume he sold. What is the present ratio of water to milk?

Vaibhav was taking the CAT exam, which included four passages with equal word counts. These passages had 5, 8, 8, and 6 questions, respectively. Vaibhav can complete 12 questions in the time it takes him to read any one of these four passages. His pace for reading and answering questions is consistent across all passages. By what percentage should Vaibhav enhance his reading speed to reduce his overall time by 10%?

A retail bookseller purchases books at 58% of the listed price and aims to secure at least a 20% net profit based on the selling price. What is the highest possible discount he can provide to his customers?

The teachers of classes \( X, Y, \) and \( Z \) administered an algebra test to their students. The average scores were 83 for class \( X \), 76 for class \( Y \), and 85 for class \( Z \). The combined average score for students in classes \( X \) and \( Y \) is 79, while for classes \( Y \) and \( Z \), it is 81. What is the overall average score for students from all three classes?

A container holds a mixture of two liquids, A and B, in a \(7:5\) ratio. After removing \(9\) liters of the mixture and then refilling the container with liquid B, the new ratio of A to B changes to \(7:9\). How many liters of liquid A were originally in the container?

The cost per item of a product drops by \( 4 \% \), and the quantity consumed (in units) also reduces by \( 8 \% \). Consequently, the overall expenditure will decline by

If a retailer gives a \(20\%\) discount on a washing machine's listed price, they earn a \(12\%\) profit. What would be the percentage profit or loss if the retailer provides a \(25\%\) discount on the listed price?

The current age ratio of a mother to her daughter is \( 9: 4 \). A decade ago, the age ratio was \( 7: 2 \). What are their ages now?

In a class of ' \( n \)' students, the average age is ' \( A \)' years. Two students have exited the class, while four new students have joined. Interestingly, the average...

Gold is 18 times denser than water, while copper is 8 times denser. To create a mixture that is 15 times denser than water, in what proportion should copper and gold be combined?

In a class, boys make up \( 70 \% \) of the students, and \( 14 \% \) of the students are cricket players. Given that \( 10 \% \) of the boys participate in cricket, what fraction of the cricket players are boys?

By selling 72 oranges, a person experiences a loss equivalent to the selling price of 12 oranges. What is his loss percentage?

Chinta and Mani currently have an age ratio of 14 to 19. The average age of Suknaya, Chinta, and Mani is 43 years. Given that the ratio of Suknaya's current age to Chinta's is 5:7, determine Mani's current age in years.

The mean rainfall for Monday, Tuesday, and Wednesday is 4.3 cm, while for Friday, Saturday, and Sunday, it is 3.9 cm. Given that the average rainfall for the entire week is 3.7 cm, how much rainfall was recorded on Thursday?

In a collection of products made by three machines, M1, M2, and M3, 40% are produced by M1, 30% by M2, and the remainder by M3. Of those, 3% created by M1 are faulty, 1% from M2 are defective, and 95% from M3 are free of defects. What percentage of the entire stockpile is defective?

A television set priced at Rs. 3,200 is sold to a retailer with consecutive discounts of \(25\%\) and \(15\%\). What is the final amount that the retailer pays for the television set?

The proportion of chocolates that Munni and Chameli have is \( 3: 2 \). If Chameli possesses 5 fewer chocolates than Sheela, and Sheela has three more chocolates than Munni, calculate the combined total of chocolates among all three.

The average age of the five committee members remains unchanged from what it was three years prior due to the replacement of an older member with a new one. What is the age gap between the former member and the new member?

Two iron alloys each contain different iron percentages. The first alloy has a mass of 6 kg, while the second weighs 12 kg. Equal portions were removed from each alloy. The portion from the first alloy was combined with the remaining section of the second alloy, and the portion from the second alloy was mixed with the remaining part of the first alloy. This mixing resulted in the iron percentage being equal in both mixtures. How much did each cut-out portion weigh?

ABC & Company manufactures nuts for FGH Ltd. During the first month of the quarter, the rejection rate for the nuts was 4%, while it increased to 8% in the following month of the quarter. The overall monthly rejection rate averaged out to 7%. Consequently, the production ratio between the first and second quarters was:

Two horses were each sold for Rs. 12,000, with one incurring a \(20\%\) loss and the other realizing a \(20\%\) gain. The overall outcome of this transaction was

In an organization, the male-to-female ratio is \(4:3\). If the male population increases by \(10\%\) and the female population increases by \(20\%\), what will be the new male-to-female ratio?

During the initial 5 hours, the train's average speed was 63 km/h. For the subsequent 3 hours, the speed was \( 58 \mathrm{~km/h} \), and for the final 2 hours, it traveled at \( 72 \mathrm{~km/h} \). What was the train's average speed across the whole journey?

A container initially filled with pure alcohol is gradually drained. When \(1/4\) of the contents remain, the container is refilled with water. This process is repeated when the container is half empty, adding water once more, and again when it is \(3/4\) empty, refilling it with water. Determine the current percentage of alcohol in the container.

The prices of houses A and B were in the ratio of \(4:5\) last year. This year, the price of house A rose by 25%, while the price of house B increased by Rs 50,000. Currently, the prices are in the ratio of \(9:10\). What was the price of house A last year?

A man sells an item with a \( 20\% \) profit. If he had purchased it at \( 20\% \) less and sold it for Rs. 5 less, his profit would have been \( 25\% \). Determine the cost price (in Rs.) of the item.

In two different alloys, the copper-to-zinc ratios are \(4:1\) and \(1:3\) respectively. When 10 kg of the first alloy and 16 kg of the second alloy are combined with a certain amount of pure copper, the resulting alloy displays a copper-to-zinc ratio of \(3:2\). Determine the total weight of the new alloy in kilograms.

A decade ago, the combined ages of the eight members in a joint family totaled 231 years. Three years after that, one member passed away at the age of 60, and a child was born in the same year. Three years later, another member died at the age of 60, and a child was again born during that year. The present average age of this eight-member joint family is closest to

An alloy (A) consists of silver and copper. When a specific amount of this alloy is combined with 15 kg of pure silver and melted, it forms a new alloy (B) which is 90% silver. If alloy (A) is mixed with 10 kg of another alloy that is 90% silver, the resultant alloy (C) has 84% silver content. Determine the percentage of silver present in alloy (A).

A candidate receives \( 39 \% \) of the total possible marks and misses passing by 58 marks. Meanwhile, another candidate who earns \( 55 \% \) of the total possible marks exceeds the passing requirement by 22 marks. Determine the maximum marks for the examination.

When the selling price of 5 articles equals the cost price of 4 articles, determine the percentage of profit or loss.

The current ages of a father and his son are in the ratio of 9 to 4. Eight years from now, the ratio of the father's age to what the son's age was two years ago is \( 8 : 3 \). Determine the son's current age in years.

The average score for the candidates who passed the exam is 60, while those who failed have an average score of 25. The overall average score of all candidates who took the exam falls between more than 43 and up to 49. The proportion of candidates who passed, relative to the total candidates who took the exam, can never be represented as a fraction that is

There are two copper and aluminum alloys with respective ratios of \( 7: 2 \) and \( 7: 11 \). When equal amounts of these two alloys are combined to create a third alloy, determine the copper to aluminum ratio in the newly formed alloy.

The combined weight of two lumps, each consisting of a mix of gold and silver, is 20 kg. One lump has \( 75\% \) gold content and includes 31.25 grams of silver per kilogram. The other lump comprises \( 85\% \) gold with 30 grams of silver per kilogram. Together, the lumps contain a total of 617.5 grams of silver. If the lumps are melted into a single mass, what percentage of gold will it contain?

The production cost of an item went up by \( 20 \% \). A retailer, who kept the selling price constant, observed that his profit decreased by Rs. 20. What was the initial cost price (in Rs.)?

Three friends, A, B, and C, went on a picnic. A brought 5 apples, B brought 3 apples, and C had Rs. 80 with him. They shared the apples equally among themselves, and C gave his entire Rs. 80 to A and B as compensation for their contributions. How should the Rs. 80 be distributed between A and B?

An alloy made of copper and zinc initially consists of \(82\%\) copper. Upon adding 18 kg of zinc to this mixture, the copper percentage decreases to \(70\%\). What are the respective quantities of copper and zinc in this revised alloy?

A and B are friends, both possessing at least one rupee. If A transfers Rs. 20 to B, A then holds 40% of B's new amount. Conversely, if B transfers Rs. 40 to A, B will retain 40% of A's new total. What is the initial amount (in Rs.) that A has?

A man acquires shares at a Rs. \( x \) discount. Subsequently, he sells all except 10 of these shares at a Rs. \( x \) premium. His total investment was Rs. 4,500, and the earnings from the sale amounted to Rs. 6,250. How many shares did he initially purchase? [Consider the nominal value of the shares to be Rs. 100.]

When two out of a class of 40 students were expelled, the average age of the class remained unchanged. One of these students was 14 years old, and

Beaker A and Beaker B hold methanol, ethanol, and phenyl in the proportions of \( 1: 3: 2 \) and \( 2: 1: 5 \), respectively. Portions of the solutions from Beaker A and Beaker B are thoroughly combined and transferred into another Beaker C. Which

The college has already collected \( 75 \% \) of the required funds for a new building, with an average donation of Rs. 600 from those who have been approached so far. These solicited individuals account for \( 60 \% \) of the total number of people the college plans to solicit for donations. To ensure the exact amount needed for the new building is raised, what should be the average donation (in Rs.) from the remaining individuals who have yet to be asked?

A shopkeeper sets an item’s sale price at Rs. 850 and offers a 20% discount on it. The wholesale purchase cost of the item to the shopkeeper was Rs. 500. What percentage profit does the shopkeeper make?

A student obtained marks in a ratio of \(5:4:6:8:7\) across five subjects, each with the same maximum marks. Overall, he achieved 50% of the total possible marks across all subjects. How many subjects did he earn more than 55% of the maximum marks in?

The initial average age of students at the institute was 15 years. When 10 students with an average age of 12 years joined, the overall average age of the students at the institute shifted to 14.8 years. How many students were originally at the institute?

In a particular town, individuals are classified as either married or single. Likewise, they are either employed or unemployed. Of the entire population, 37% were married, and among those married individuals, 76% were employed. Additionally, 54% of the single individuals were employed. Given that the total number of employed individuals was 124,280, determine the total population of the town.

The Santabil shop has a promotion where you receive a free T-shirt with the purchase of three T-shirts. However, the shop increases the price of the T-shirts by 60%. If a customer purchases three T-shirts, what is the store's profit or loss percentage?

Four numbers add up to a total of 253. The proportion of the first to the second number is \(2:3\), while the second to the third number is \(5:6\). Additionally, the third to the fourth number is in the ratio of \(8:9\). What is the average of the second and third numbers?

The monthly earnings of individuals \(A\) and \(B\) are in the proportion of \(3:5\). Upon each receiving an additional Rs. 250, the proportion shifts to \(2:3\). What were their original salaries prior to the increase?

An alloy (A) composed of silver and copper is combined with 15 kg of pure silver and melted to form a new alloy (B), which is \(90\%\) silver. When alloy (A) is mixed with 10 kg of an alloy containing \(90\%\) silver and melted, the resulting alloy (C) has \(84\%\) silver. Calculate the silver percentage in alloy (A).

Considering that the price of 10 oranges matches the price of 1 kg of apples, and the cost of 12 apples is equivalent to the price of 1 kg of oranges, if the selling price of 15 oranges is the same as that of 1 kg of apples, then the selling price of 1 kg of oranges will be equal to the selling price of (assuming all apples are identical, as well as the oranges).

When three juice brands are blended in the ratios of \(3:4:5\) and \(4:5:6\), the resulting cost prices for these two mixtures are Rs. 20 per litre and Rs. 25 per litre, respectively. Determine the cost price per litre for a mixture where the three original juice brands are combined in a \(6:7:8\) ratio.

Ramesh examined the monthly salary numbers for five vice presidents at his company, all expressed as integers. The average and median salaries are both Rs 5 lakh, and Rs 8 lakh is the sole mode. Which of the following options represents the sum (in Rs lakh) of the highest and lowest salaries?

An amount of money, when compounded annually, grows to Rs. 625 in 2 years and to Rs. 675 in 3 years. What is the annual interest rate?

When a shopkeeper offers 3 complimentary pencils with the purchase of every 5 pens, he gains a profit of \(20\%\). Conversely, when he provides 6 free pencils with the purchase of 2 pens, he incurs a \(25\%\) loss. Determine the approximate profit percentage for the shopkeeper when 4 pencils are given free with every purchase of 6 pens, assuming all pencils and pens are identical.

The worth of a diamond increases in direct proportion to the square of its weight. When a diamond weighing 4 kg is divided into two pieces, its overall value reduces by 37.5%. The weights of these two pieces are:

Ramu takes six separate exams in his semester, with each exam having a maximum score of 50. The scores he achieved are in the ratio \(8: 9: 10: 13: 14: 15\). Combined, his total score is less than \(50\%\) of the overall possible marks. How many more points does Ramu need to score, at a minimum, to reach \(50\%\) of the total, assuming his scores in each exam are whole numbers?

The difference between compound interest and simple interest on a certain amount over two years is Rs. 160. If the total simple interest amounts to Rs. 2,880, determine the rate of interest.

A merchant possesses 100 kg of sugar, some of which is sold for a \(7\%\) profit, while the remainder is sold for a \(17\%\) profit. The overall profit is \(10\%\). How much sugar is sold at a \(17\%\) profit?

In a family made up of a father, mother, son, and daughter, the ratio of the father's weight to the son's weight is \(3:2\). The son's weight compared to the mother's is in a \(5:6\) ratio. The daughter weighs 35 kg, which is half the weight of the father. Determine how much the mother weighs.

If the average age of seven consecutive natural numbers is \( K \), what would be the average of the subsequent seven consecutive natural numbers?

In approximately how many years would a loan amount become double the principal if the principal is lent at a 20% annual interest rate, compounded semi-annually?

A company was offering its pianos at a 20% discount off the marked price of Rs. 325. In order to boost sales, they opted to provide an extra discount, enabling a piano to be sold for Rs. 234. What was this second discount?

The income and expenditure ratios for Aishwarya, Babita, and Charu are \(7: 9: 12\) and \(8: 9: 15\) respectively. Assuming Aishwarya saves a quarter of her income, their savings ratio is

If the difference between the compound interest and the simple interest after 2 years is Rs. 100, what is the principal amount? The annual interest rate is \( 5\% \) for both situations. (Assume the principal amount is the same for both scenarios.)

A merchant uses a weight of 0.85 kg instead of 1 kg to sell potatoes. Suppose his real percentage profit or loss is 'm' when he acts as if he is selling his items at a 5% loss, and 'n' when he acts as if he's selling his items at a 5% gain. Determine the value of (m+n).

A year ago, Harsha's and Mandar's salaries were in a \( 3: 5 \) ratio. The individual salary growth ratios from last year to this year for Harsha and Mandar are \( 2: 3 \) and \( 4: 5 \), respectively. Given that their combined salary is now Rs.86,000, determine the current salary of Harsha.

A, B, and C each invested Rs. 2,000, Rs. 5,000, and Rs. 4,000, respectively, in a business. The total profit for the year amounted to 1,210 and was distributed based on their investment ratios. Consequently, the profit earned by A, B, and C, respectively, is

The compound interest on a specific amount over 2 years at an annual rate of 10% is Rs. 420. The simple interest on the same principal, with the same rate and duration, will be

I purchased 5 pens, 7 pencils, and 4 erasers. Rajan purchased 6 pens, 8 erasers, and 14 pencils, spending an amount that was 50% higher than what I paid. What percentage of my total expenditure was allocated to the pens?

A man offers chocolates packaged in whole or half boxes. A customer purchases half of all the boxes the man has, plus an additional half box. Another customer then buys half of the remaining boxes along with half a box. As a result, the seller ends up with no chocolate boxes. How many chocolate boxes did the seller initially possess before the first customer arrived?

X, Y, and Z are business partners having a combined capital of Rs. 3,300. The annual profit amounts to Rs. 1,500 and is shared according to their capital contributions. X's profit share is Rs. 450, while Y's is Rs. 550. Determine the amount of Z's capital.

Bhawna loaned a portion of Rs. 10,000 to her friend Myra at an interest rate of 8% simple interest (SI) for a period of 4 years. She put the rest of the money into an investment at 12% simple interest. The total interest earned after 4 years amounted to Rs. 3,800. How much money (in Rs.) was lent to Myra?

A machine outputs 50 articles per hour. Each article sells for Rs. 100, with a production cost of Rs. 40 per piece. Unfortunately, \(20\%\) of these items are defective and, therefore, unsellable. It's possible to boost the machine's production rate, but for each additional \(x\) units per hour, the production cost rises by \(2x\%\), and defective items would increase to \((20 + 1.5x)\%\). What is the greatest production increase possible without leading to losses?

In January, the students in Batch A and Batch B were in a ratio of \( 2:3 \), changing to \( 5:8 \) in February. Between February and March, the growth rates for students in Batch A and Batch B were two and three times, respectively, of the growth rates from January to February. Given that the overall ratio of students in the two batches between February and January was \( 26:5 \), determine the ratio of students in Batch A to Batch B in March.

A represents the mean of a sequence of \( n \) consecutive odd numbers beginning with \( x \), while \( B \) signifies the mean of \( n \) consecutive odd numbers starting at \( x+4 \). The difference between \( B \) and \( A \) is given by \( B - A \).

Narayan and Murthy put some money into investments at annual simple interest rates of 6% and 7%, respectively. After 2 years, they discovered that their combined interest amounted to Rs. 354. Additionally, one-fourth of Narayan's initial investment is equal to one-fifth of Murthy's investment. Determine the total amount of money they invested.

A shopkeeper sold two products for the same price. He incurred a loss on one item while he gained a profit on the other. The percentages of profit and loss on these items are 10% and 20%, though the order is not specified. Determine the overall profit percentage for the shopkeeper considering he achieved an overall profit from the transaction.

An individual purchases a certain quantity of apples and mangoes from the market. The cost price for a mango is double that of an apple, while its selling price is three times that of an apple. By selling an apple at twice its original cost, the individual earns a 150% profit overall. Determine the ratio of the number of mangoes to the number of apples bought from the market.

Three individuals, A, B, and C, formed a partnership with an investment ratio of \( \frac{1}{2}: \frac{1}{3}: \frac{1}{4} \). They invested their money for different periods in the ratio of 1: \( \frac{1}{2}: \frac{1}{4} \). The profits were distributed in direct proportion to their respective investments and the duration of those investments. Given that A's profit amounted to Rs. 30,000, determine the amount that B received.

A sum of money, compounded annually at an interest rate of \( r \% \), grows to Rs. 1,440 in 2 years and to Rs. 1,728 in 3 years. Determine the value of \( r \).

A book was sold at a certain price, resulting in a \( 20\% \) loss. If the selling price had been Rs. 3 higher, there would have been a \( 30\% \) profit. If the book had been sold for Rs. 6.60, what would the profit or loss percentage have been?

The total costs of operating a boarding house consist of both fixed expenses and expenses that increase linearly with the number of residents. When there are 25 residents, the average cost per resident is Rs. 700, and when there are 50 residents, it is Rs. 600. What is the average cost per resident if there are 100 residents?

A started a business by investing Rs. 4,500 and later, B became a partner with an investment of Rs. 5,400. If the profits at the year's end were shared in the ratio \(2:1\), determine how long after A started the business did B join.

Rs. 2,189 is split into three segments so that their values after 1, 2, and 3 years are identical. If the annual simple interest rate is 4% in each case, the smallest segment is

The various categories of expenses related to manufacturing a product include material, manpower, and overhead costs. These costs are proportioned as \(9:5:11\). The profit generated from the product is \(20\%\) of the overall cost. What is the ratio of the manpower cost to the profit?

A is directly proportional to B, and B is inversely proportional to C. Meanwhile, C is directly proportional to the square of D, and D is directly proportional to the cube root of E. Given that all variables are positive integers, as A increases, E also increases.

In a business collaboration between A, B, C, and D, the profit distribution is set up as follows:\[\frac{\text{Share of A}}{\text{Share of B}}=\frac{\text{Share of B}}{\text{Share of C}}=\frac{\text{Share of C}}{\text{Share of D}}=\frac{1}{3}\]If the overall profit amounts to Rs. 4,00,000, what is C's portion?

Rohit plans to deposit a specific amount of cash into a bank savings account that offers a \(20\%\) annual compound interest rate, with the intention of keeping it there for two years. How much money should Rohit deposit initially to ensure he obtains Rs. 200 after the first year and Rs. 400 after the second year?

The trader's spring balance measured 800 g as 1 kg. What is the actual outcome if he asserts that he sells at the cost price?

Santosh's height varies directly with the square root of his age. If Santosh is 4 feet tall at age 9, what will his height be at age 16?

Ajay initiated a business with an investment of Rs. 28,000. Five months later, Boman became a partner by contributing Rs. 40,000. Chirag joined as the third partner, investing Rs. 56,000, seven months after the business started. By the end of the year, the firm generated a profit of Rs. 32,000. What portion of the profit does Boman receive?

A sum of Rs. 7,000 was split into two equal portions. The first portion was placed in a bank earning simple interest at a rate of 8% per annum for three years. Meanwhile, the second portion was invested in a different bank offering an annual compound interest rate of 10% for two years. What is the difference between the interests accrued from these two investments?

A shopkeeper visits the wholesale market to purchase his goods. The wholesaler possesses a weighing scale that shows 1,100 grams as one kilogram. The shopkeeper then sells the

The pressure of a gas varies directly with its temperature and inversely with its volume. Initially, the pressure is 150 pascals, the volume is \(20\ \mathrm{cu}.\mathrm{m}\), and the temperature is \(100^{\circ}\) Kelvin. Determine the final temperature if the gas has a final volume of \(8\ \mathrm{cu}.\mathrm{m}\) and maintains a pressure of 150 pascals under identical conditions.

A, B, and C invested in a ratio of \(3:6:7\). Given that their total investment amounted to Rs. 80,000 and the profit was \(40\%\) of the investment, what is the combined profit share received by B and C?

A deceptive dealer asserts that he sells a product at its cost price. However, he utilizes a fake weight that is \(20\%\) lighter than the actual weight.

A container holds a mixture of two liquids, A and B, in a ratio of \( 7:5 \). After \( 9 \, \text{L} \) of the mixture is removed and replaced with liquid B, the new ratio of A to B becomes \( 7:9 \). How much liquid A was originally in the container?

Abhishek and Rani initiated a partnership by investing Rs. 1 crore and Rs. 2 crores, respectively, at the start of the year. They proceeded to withdraw one-fourth of their investments at the conclusion of each quarter until the end of the second quarter. After this, Susmita and Randeep entered the partnership with investments of Rs. 50 lakh and Rs. 1 crore, respectively. Randeep withdrew his full investment after three months. By the year's end, the total profit amounted to Rs. 41 lakhs. The combined profit share for Abhishek and Rani is: