Ages and Profit & Loss

Ganesh bought a watch for Rs.3200 and sold it at a loss of 15%. To find the selling price, we need to calculate 85% of the cost price. 85% of Rs.3200 is Rs.2720. Therefore, Ganesh sold the watch for Rs.2720.

Let the cost price of the machine be x. According to the question, selling price at a profit of 10% is x + 0.1x = 1.1x. If it had been sold for Rs 40 less, the selling price would be 1.1x - 40. This selling price would result in a loss of 10% which can be written as 0.9(1.1x - 40). Equating this to the cost price x, we get 0.9(1.1x - 40) = x. Solving this equation, we find x = 200. Therefore, the cost price of the machine is Rs.200.

The shopkeeper initially sells 1 kg of apples for Rs. 160 at a loss of 20%. This means that he is selling the apples for only 80% of their cost price. To calculate the cost price of 1 kg of apples, we divide Rs. 160 by 0.8, which gives us Rs. 200. To gain a 20% profit, the shopkeeper needs to sell the apples for 120% of their cost price. So, to calculate the selling price, we multiply Rs. 200 by 1.2, which gives us Rs. 240. Therefore, the shopkeeper should sell a kg of apples for Rs. 240 to gain a 20% profit.

If a person sells a property for Rs 45,000 and incurs a loss of 10%, it means that the selling price is 90% of the cost price. To find the selling price to gain a profit of 15%, we need to calculate 115% of the cost price. By setting up a proportion, we can find that 90% is to Rs 45,000 as 115% is to the selling price. Solving this proportion, we find that the selling price is Rs 57,500. Therefore, the correct answer is 57500.

When Ayesha was born, her father was 38 years old. When her brother, who is four years younger than her, was born, her mother was 36 years old. This means that the age difference between Ayesha's parents is 2 years (38 - 36).

Six years ago, Vipin was thrice as old as Ruchi, which means that Vipin's age was 3 times Ruchi's age minus 6. In the future, 6 years from now, Vipin will be 5/3 times as old as Ruchi, which means that Vipin's age will be 5/3 times Ruchi's age plus 6. By setting up these two equations, we can solve for Ruchi's age.

John bought the car for Rs.1,80,000 and spent Rs.20,000 on repairs, making his total investment Rs.2,00,000. He sold the car for Rs.2,20,000. To find the gain percentage, we need to calculate the gain first. The gain is the difference between the selling price and the cost price, which is Rs.2,20,000 - Rs.2,00,000 = Rs.20,000. Now, we can calculate the gain percentage using the formula: (Gain/Cost Price) * 100. Plugging in the values, we get (20,000/2,00,000) * 100 = 10%. Therefore, his gain percentage is 10%.

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The person purchases 4 articles for rupees 5, which means the cost price of each article is 5/4 rupees. They then sell 5 articles for rupees 4, which means the selling price of each article is 4/5 rupees. To calculate the profit or loss percentage, we need to compare the selling price with the cost price.

The cost price of 5 articles is (5/4) * 5 = 25/4 rupees.
The selling price of 5 articles is 4/5 * 5 = 4 rupees.

Profit or loss = Selling price - Cost price = 4 - (25/4) = (16 - 25)/4 = -9/4 rupees.

To calculate the percentage, we divide the profit or loss by the cost price and multiply by 100.

Percentage loss = (9/4)/(25/4) * 100 = 9/25 * 100 = 36%.

Therefore, the total profit or loss is a 36% loss.

If the selling price (SP) of 4 articles is equal to the cost price (CP) of 6 articles, it means that the selling price of each article is 6/4 times the cost price of each article. This implies a profit of 2/4 or 50% on the cost price, as the selling price is 50% higher than the cost price. Therefore, the gain percentage is 50%.

The question states that A is as much younger than B as he is older than C. However, it does not provide any information about the specific ages of A, B, or C. Therefore, the data is inadequate to determine the difference between B and A's age.

The profit percentage can be calculated by finding the difference between the selling price and the cost price, and then dividing it by the cost price. In this case, since 12 articles were sold at the cost price of 15 articles, it means that the selling price is the same as the cost price. Therefore, there is no profit made and the profit percentage is 0%.

If the book was sold for Rs.27.50 at a profit of 10%, it means the cost price of the book was Rs.25.00 (as 10% profit on Rs.25.00 is Rs.2.50). Now, if the book is sold for Rs.25.75, the profit would be Rs.0.75 (as the selling price is Rs.0.75 more than the cost price). To calculate the profit percentage, we divide the profit (Rs.0.75) by the cost price (Rs.25.00) and multiply by 100. This gives us a profit percentage of 3%.

The initial capital of Rs. 2000 increased by 50% every 3 years. After 3 years, the capital would be Rs. 2000 + (50% of 2000) = Rs. 3000. After another 3 years, the capital would be Rs. 3000 + (50% of 3000) = Rs. 4500. This pattern continues for 18 years. Using the formula for compound interest, the final amount can be calculated as A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years. Plugging in the values, we get A = 2000(1 + 0.5/1)^(1*18) = Rs. 22781.25.

If the man sells the article at a profit of 20%, it means he sells it for 120% of the cost price. Now, if he had bought it for 20% less, it means he would have bought it for 80% of the original price. If he sells it at the same price, it means he sells it for 100% of the original price. Therefore, the gain percentage would be the difference between the selling price (100%) and the cost price (80%), which is 20%. And since the cost price is 80%, the gain percentage is 20/80 * 100 = 25%.

Let's assume that the present age of the man and his wife is 4x and 3x respectively. After 4 years, their ages will be 4x+4 and 3x+4. According to the given information, the ratio of their ages after 4 years is 9:7. Therefore, we can set up the equation (4x+4)/(3x+4) = 9/7. Solving this equation, we find x = 4. This means that the present age of the man is 4*4 = 16 years and the present age of his wife is 3*4 = 12 years. Since the ratio of their ages at the time of marriage was 7:5, we can set up the equation 16/x = 7/5, where x represents the number of years ago they were married. Solving this equation, we find x = 4. Therefore, they were married 4 years ago.

The shopkeeper is mixing two varieties of dhall, one costing Rs.20/kg and the other costing Rs.30/kg. The total weight of the mixture is 30 kg + 20 kg = 50 kg. The cost price of the mixture is (30 kg * Rs.20/kg) + (20 kg * Rs.30/kg) = Rs.600 + Rs.600 = Rs.1200. The selling price of the mixture is 50 kg * Rs.27/kg = Rs.1350. The profit made by the shopkeeper is Rs.1350 - Rs.1200 = Rs.150. The profit percentage is (150/1200) * 100 = 12.5%.

The gain percentage can be calculated by finding the difference between the selling price and the cost price, dividing it by the cost price, and then multiplying by 100. In this case, the difference between the selling price (Rs.60) and the cost price (Rs.50) is Rs.10. Dividing Rs.10 by the cost price (Rs.50) gives 0.2. Multiplying 0.2 by 100 gives 20%. Therefore, the gain percentage is 20%.

Let the present age of A be x and the present age of B be y. According to the given information, x + y = 54.
Five years ago, A's age was x - 5 and B's age was y - 5. The product of their ages at that time was (x - 5) * (y - 5).
According to the second statement, (x - 5) * (y - 5) = 4(x - 5).
Simplifying this equation, we get xy - 5x - 5y + 25 = 4x - 20.
Rearranging the terms, we get xy - 9x - 5y - 45 = 0.
Using the sum of ages equation, we can substitute y = 54 - x into the rearranged equation.
This gives x(54 - x) - 9x - 5(54 - x) - 45 = 0.
Simplifying this equation, we get x^2 - 14x + 45 = 0.
Factoring this quadratic equation, we get (x - 9)(x - 5) = 0.
Therefore, the possible values for x are 9 and 5.
Since A cannot be 5 years old, the present age of A and B are 9 years and 45 years respectively.

Six years ago, Anita's age was P times Ben's age. Let's assume Ben's age 6 years ago was x. Therefore, Anita's age 6 years ago would be P*x.

Now, if Anita is currently 17 years old, her age 6 years ago would be 17 - 6 = 11. Therefore, we can equate P*x = 11.

To find Ben's current age in terms of P, we need to solve for x. Dividing both sides of the equation by P, we get x = 11/P.

Since we are asked to find Ben's current age, we need to add 6 years to x. Thus, Ben's current age in terms of P is 11/P + 6.

Let's assume the current age of the man is x and the current age of his father is y. According to the given information, x = (2/5)y. After 8 years, the man's age will be x + 8 and the father's age will be y + 8. It is also given that x + 8 = (1/2)(y + 8). By substituting the value of x from the first equation, we get (2/5)y + 8 = (1/2)(y + 8). Solving this equation, we find y = 40. Therefore, the age of the father is 40.

The average age of 80 boys in the class is given as 15. The average age of a group of 15 boys is 16, and the average age of another group of 25 boys is 14. To find the average age of the remaining boys, we need to subtract the sum of the ages of the known groups from the sum of the ages of all 80 boys. The sum of the ages of the first group is 15 * 80 = 1200. The sum of the ages of the second group is 16 * 15 = 240. The sum of the ages of the third group is 14 * 25 = 350. Subtracting the sum of these ages from the sum of all 80 boys gives us 80 * 15 - 1200 - 240 - 350 = 900. Finally, we divide this sum by the number of remaining boys, which is 80 - 15 - 25 = 40, to get the average age of the remaining boys: 900 / 40 = 22.5. However, since this answer is not among the given options, the correct answer is 15.25 years.

Let's assume the daughter's age is represented by D and the mother's age is represented by M. According to the given information, 2D + M = 70 and 2M + D = 95. We can solve these equations simultaneously to find the values of D and M. By substituting the value of D from the first equation into the second equation, we get 2M + (70 - 2M) = 95. Simplifying this equation gives us M = 40. Therefore, the mother's age is 40.

Let's assume the present age of the son is x. Since the ratio of the present ages of the mother and son is 10:1, the present age of the mother would be 10x.

According to the given information, the sum of the ages of the mother and son is equal to the age of the father. So, the present age of the father would be 10x + x = 11x.

Three years later, the father will be six times as old as his son. So, 11x + 3 = 6(x + 3).

Simplifying the equation, we get 11x + 3 = 6x + 18.

Solving for x, we find x = 3.

Substituting the value of x in the equation for the father's present age, we get 11(3) = 33.

Therefore, the age of the father is 33.

Gulzar's grandson Anup is 2 years younger than Mahesh, whose age is 5 years. Therefore, Anup's age is 5 - 2 = 3 years. If 6 years are subtracted from Gulzar's present age and the remainder is divided by 18, we get Anup's age. So, if we add 6 years to Anup's age and multiply it by 18, we should get Gulzar's present age. (3 + 6) * 18 = 9 * 18 = 162. However, the given options do not include 162. The closest option is 60, which is 6 * 18. Therefore, the present age of Gulzar is 60.

Person A's age is twice that of person B's age. Let's assume person B's age is x. Therefore, person A's age would be 2x. The sum of their ages is given as 60, so we can write the equation x + 2x = 60. Simplifying this equation, we find that x = 20. Therefore, person B's age is 20 and person A's age is 40. Five years from now, person B will be 25 and person A will be 45. The sum of their ages 5 years hence is 25 + 45 = 70.

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If the profit percent gained when the object is sold at Rs 464 is equal to the loss percent when it is sold at Rs 436, it means that the object was initially bought at a price that is the average of these two selling prices. Therefore, the cost price of the object is Rs 450.

Let's assume the cost price (CP) of the article is x.
According to the given information, the selling price (SP) at a gain of 8% would be x + 0.08x = 1.08x.
Similarly, the SP at a loss of 8% would be x - 0.08x = 0.92x.
It is given that the SP at a gain of 8% is Rs.12 more than the SP at a loss of 8%.
So, 1.08x - 0.92x = 12.
Simplifying, we get 0.16x = 12.
Dividing both sides by 0.16, we find x = 75. Therefore, the cost price (CP) of the article is Rs.75.

Krish and Vaibhav's ages are currently in the proportion of 3:5. After 9 years, the proportion becomes 3:4. This means that Vaibhav's age increases by a smaller amount compared to Krish's age. Since the ratio of their ages decreases, it implies that Vaibhav is older than Krish. Therefore, the current age of Vaibhav must be greater than 10, 13, and 18. The only option left is 15, which satisfies the given conditions.

The shopkeeper sells the bag at a 25% profit, which means he sells it for 125% of its cost price. Then, he offers a discount of 10%, which means he sells it for 90% of the selling price. To find the profit percentage, we need to calculate the difference between the selling price and the cost price, and then express it as a percentage of the cost price. In this case, the difference is 90% - 100% = -10%. Since the difference is negative, it means there is a loss of 10%. However, the question asks for the profit percentage, so we take the absolute value of the difference, which is 10%. Therefore, the profit percentage is 10%.

Two years ago, Harish was thrice as old as his brother Krish. This means that Harish's age two years ago was three times Krish's age two years ago. Two years later, Harish will be twice as old as Krish. This means that Harish's age in the future will be twice Krish's age in the future. By comparing the two statements, we can conclude that Harish's age is currently double Krish's age. Therefore, if Krish's present age is 6, Harish's present age would be 12, which satisfies both conditions given in the question.

Ravi bought the article at a discount of 10%, which means he paid 90% of the original price. So, the cost price for Ravi was 0.9 * 1500 = Rs. 1350.
Ravi then sold the article to Harsha for Rs. 1566.
His gain is the difference between the selling price and the cost price, which is 1566 - 1350 = Rs. 216.
To find the gain percentage, we divide the gain by the cost price and multiply by 100: (216/1350) * 100 = 16%. Therefore, Ravi's gain percentage is 16%.

The shopkeeper bought 60 apples at the rate of Rs.240 per dozen. To find the cost price of each apple, we need to divide the total cost of 60 apples by the number of apples. Since there are 12 apples in a dozen, the cost of each apple is Rs.240/12 = Rs.20. To gain a 5% profit, the shopkeeper needs to add 5% of the cost price to the cost price. 5% of Rs.20 is Rs.1. Therefore, the selling price of each apple should be Rs.20 + Rs.1 = Rs.21.

Since the cost price (C.P) is 90% of the selling price (S.P), it means that the selling price is 10% more than the cost price. Therefore, the gain percentage would be 10%.

Let the current ages of the two daughters be x and y. According to the question, the father's age is 3(x + y). After 0.5 decades, the father's age will be 3(x + y) + 5, and the total ages of the daughters will be x + y + 5. Since the father's age will be twice the total ages of the daughters, we can set up the equation 3(x + y) + 5 = 2(x + y + 5). Simplifying this equation, we get 3x + 3y + 5 = 2x + 2y + 10. Solving for x and y, we get x = 5 and y = 10. Therefore, the father's current age is 3(x + y) = 3(5 + 10) = 45 years.

In this scenario, the man buys two watches for Rs.1500. He sells one watch at a gain of 20%, which means he sells it for 120% of its original price. He sells the other watch at a loss of 20%, which means he sells it for 80% of its original price.

Let's assume the original price of each watch is x.

Therefore, the selling price of the first watch would be 1.2x and the selling price of the second watch would be 0.8x.

The total selling price of both watches would be 1.2x + 0.8x = 2x.

Since the man bought the watches for Rs.1500, which is equal to 2x, it means he sold them for the same price he bought them. Hence, there is no gain or loss in this transaction.

Let the cost price of a pen be x.
Given that the loss incurred is equal to the cost price of 3 pens, the loss incurred is 3x.
Also, it is given that Ram sold 15 pens for Rs.120.
So, the selling price of 15 pens is Rs.120, which means the selling price of 1 pen is Rs.8 (120/15).
Since selling price = cost price - loss, we can write the equation as 8 = x - 3x.
Simplifying the equation, we get 8 = -2x, which gives x = -4.
Since the cost price of a pen cannot be negative, we can conclude that the cost price of a pen is Rs.10.

Suresh sold the cell phone to Mahesh at Rs. 8400 and made a profit of 12%. This means that the selling price is 112% of the cost price. To find the cost price, we can set up the equation: 112% of the cost price = Rs. 8400. Solving this equation, we can find that the cost price is Rs. 7500.

The shopkeeper sells one kitten at a loss of 10% and the other at a profit of 10%. This means that for one kitten, the shopkeeper is selling it for 10% less than its cost price, and for the other kitten, the shopkeeper is selling it for 10% more than its cost price. Since the profit percentage and loss percentage are equal, they cancel each other out. Therefore, the net profit or loss in the transaction is 0%, which means there is no gain or loss.

Let the age of A be 3x and the age of B be 4x. It is given that B is 3 years older than A, so 4x = 3x + 3. Solving this equation, we get x = 3. Therefore, the age of A is 3(3) = 9. After 2 years, the age of A will be 9 + 2 = 11.

The man's life can be divided into several stages: childhood, teenage years, adulthood, marriage, and the time after his son's birth. Let's assign variables to represent the length of each stage. Let x be the total length of the man's life.

According to the information given, one sixth of his life was spent in childhood, so x/6 represents the length of his childhood. One twelfth of his life was spent as a teenager, so x/12 represents the length of his teenage years.

One seventh of his life passed between becoming an adult and getting married, so x/7 represents the length of this stage. After five years of marriage, his son was born, so x/7 + 5 represents the time from adulthood to his son's birth.

His son died four years before he did, so x/7 + 5 - 4 represents the time from adulthood to his son's death.

The man lived to be twice as old as his son, so x = 2(x/7 + 5 - 4).

Simplifying the equation, we get x = 2(x/7 + 1).

Multiplying through by 7 to eliminate the fraction, we get 7x = 14(x + 7).

Simplifying further, we get 7x = 14x + 98.

Subtracting 14x from both sides, we get -7x = 98.

Dividing both sides by -7, we get x = -14.

Since a negative age is not possible, we can conclude that the man lived to be 84 years old.

Let's assume the present age of the person is x and the present age of the mother is y. According to the given information, x = (2/5)y. After 8 years, the person's age will be x + 8 and the mother's age will be y + 8. The question states that x + 8 = (1/2)(y + 8). By substituting x = (2/5)y, we can solve the equation to find y = 40. Therefore, the mother is currently 40 years old.

Let's assume Ravi's present age is x. After 15 years, his age will be x + 15. And 5 years back, his age was x - 5. According to the given condition, x + 15 = 5(x - 5). Solving this equation, we get x = 10. Therefore, the present age of Ravi is 10.

The total age of A and B is 12 years more than the total age of B and C. This can be represented as (A + B) = (B + C) + 12. To find the age difference between C and A, we need to subtract the age of C from the age of A. Simplifying the equation, we get A - C = 12. Therefore, C is 12 years younger than A.

One year ago, the ratio of Aman and Ashok's ages was 2:3. This means that Aman's age was 2x and Ashok's age was 3x, where x is a constant. After five years from now, the ratio of their ages becomes 4:5. This means that Aman's age will be 2x+5 and Ashok's age will be 3x+5. Since we know that Aman's age will be 4/5 times Ashok's age, we can set up the equation 2x+5 = (4/5)(3x+5). Solving this equation, we find that x = 5. Therefore, Ashok's age now is 3x = 3(5) = 15 years.

One way to solve this problem is by setting up equations based on the given information. Let's assume the present age of the daughter is x years.

According to the first statement, one year ago, the mother was four times as old as her daughter. This can be written as (x-1)*4 = (present age of the mother - 1).

According to the second statement, six years hence, the age of the mother will exceed twice the age of her daughter by 9 years. This can be written as (present age of the mother + 6) - 9 = 2*(x+6).

Simplifying these equations, we get 4x - 4 = present age of the mother - 1, and present age of the mother - 3 = 2x + 12.

Solving these equations, we find that the present age of the mother is 11x + 44, and the present age of the daughter is 3x + 12.

The ratio of their present ages is (11x + 44) : (3x + 12), which simplifies to 11:3.

Let the cost price of the television be x.
According to the given information, when the television is sold at a loss of 5%, the selling price of the television is 0.95x.
Similarly, when the player is sold at a gain of 10%, the selling price of the player is 1.10x.
Since there is no gain or loss from the transaction, the total selling price is equal to the total cost price: 0.95x + 1.10x = 2.05x.
Now, when the television is sold at a gain of 20%, the selling price of the television is 1.20x.
And when the player is sold at a loss of 10%, the selling price of the player is 0.90x.
According to the given information, the total selling price in this case is 1.20x + 0.90x = 2.10x, which is Rs.3000 more than the total cost price.
So, 2.10x - 2.05x = 3000, which gives x = 20000.
Therefore, the cost price of the television is Rs.20000.

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Rahul sold the article for Rs.100 and incurred a loss of one sixth of its cost. This means that the selling price of the article is equal to five-sixths of its cost. To find the cost of the article, we can set up the equation: 5/6 * cost = Rs.100. Solving for the cost, we get Rs.120.