Age Problems: Ratio And Proportion Quiz!

Explanation
The ratio between the present ages of P and Q is 6:7. If Q is 4 years older than P, it means that Q is currently 4 years more than the age ratio of 7. Therefore, Q's current age would be 7+4=11 and P's current age would be 6+4=10. After 4 years, Q's age would be 11+4=15 and P's age would be 10+4=14. The ratio of their ages after 4 years would be 14:15, which simplifies to 7:8.

Explanation
Five years ago, let the father's age be x and the son's age be y. According to the given information, x + y = 45 and (x-5)(y-5) = 4(x-5). Simplifying the second equation, we get xy - 5x - 5y + 25 = 4x - 20. Rearranging terms, we have xy - 9x - 5y + 45 = 0. Factoring, we get (x-9)(y-5) = 0. Since the sum of their ages is 45, the father's age cannot be 5. Therefore, the father's age is 9 years older than the son's age, which gives us the solution 36, 9.

Explanation
Ten years ago, P was half of Q in age. This means that if Q's age ten years ago was x, then P's age ten years ago was x/2. Let's assume that the present age of P is 3y and the present age of Q is 4y.
According to the given information, 10 years ago, P's age was 3y - 10 and Q's age was 4y - 10.
Since P was half of Q in age, we can set up the equation: (3y - 10) = (1/2)(4y - 10).
Solving this equation, we get y = 10.
Therefore, the present age of P is 3y = 3(10) = 30 and the present age of Q is 4y = 4(10) = 40.
The total of their present ages is 30 + 40 = 70, which is not one of the given answer choices. Therefore, the correct answer cannot be determined based on the given information.

Explanation
Let's assume the present age of Kunal and Sagar as 6x and 5x respectively. Six years ago, their ages would have been 6x-6 and 5x-6. Four years hence, their ages would be 6x+4 and 5x+4. According to the given information, the ratio of their ages four years hence is 11:10. So, we can write the equation (6x+4)/(5x+4) = 11/10. Solving this equation, we get x=4. Substituting this value in the present age of Sagar, we get 5x = 5*4 = 20. Therefore, Sagar's age at present is 20.

Explanation
The father said that he was as old as his son is now at the time of his son's birth. Since the father is currently 38 years old, this means that his son is currently 38 years old as well. Therefore, 5 years back, the son would have been 33 years old.

Explanation
Six years ago, Aasha was P times as old as Ben was. This means that Aasha's age six years ago was P times Ben's age six years ago. Since Aasha is now 17 years old, we can determine Ben's age now by subtracting 6 from Aasha's age and dividing by P. Therefore, Ben's age now in terms of P is 11/P + 6.

Explanation
Ten years ago, the ratio of their ages was 1: 2: 3. Let's assume their ages ten years ago were x, 2x, and 3x respectively.
So, their present ages would be x+10, 2x+10, and 3x+10 respectively.
According to the given information, the total of their present ages is 90 years.
Therefore, (x+10) + (2x+10) + (3x+10) = 90.
By solving this equation, we get x = 10.
So, the age of B at present is 2x+10 = 2*10+10 = 30.

Explanation
The sum of the ages of the 5 children is 50 years. Since the ages are in intervals of 3 years, we can assume that the ages are consecutive numbers. If we let the age of the youngest child be x, then the ages of the other children would be x+3, x+6, x+9, and x+12. Adding these ages together gives us 5x+30=50. Solving for x, we find that x=4. Therefore, the age of the youngest child is 4.

Explanation
Harini's current age is represented by x. Ten years from now, her age will be x + 10. Five years ago, her age was x - 5. According to the given statement, 10(x + 10) + 5(x - 5) = 20x. Simplifying this equation, we get 10x + 100 + 5x - 25 = 20x. Combining like terms, we have 15x + 75 = 20x. Subtracting 15x from both sides, we get 75 = 5x. Dividing both sides by 5, we find that x = 15. Therefore, Harini's current age is 15. Fifteen years from now, her age will be 15 + 15 = 30.

Explanation
Let the present age of the son be x. Then, the father's age is 2.5x (since the son's age is 40% of the father's age) and the mother's age is 2.2x (since the mother's age is 220% of the son's age). The average age of the three members is 38, so (x + 2.5x + 2.2x)/3 = 38. Solving this equation, we get x = 10. Therefore, the present age of the mother is 2.2x = 2.2 * 10 = 22.

Explanation
The given information states that 5 times A's share is equal to 12 times B's share, which is also equal to 6 times C's share. To find the ratio between their shares, we can compare the multiples of their shares. We can see that 5 times A's share is equal to 12 times B's share, and 12 times B's share is equal to 6 times C's share. Therefore, we can conclude that the ratio between the shares of A, B, C is 12:5:10.

Explanation
In the given question, the coins are in the proportion of 5:6:2. Let's assume the common ratio to be x. So, the number of 50 paise coins would be 5x, the number of 25 paise coins would be 6x, and the number of 1 rupee coins would be 2x.

Now, we are given that the total value of all the coins is Rs. 42.

The value of 50 paise coins = 0.50 * 5x = 2.50x
The value of 25 paise coins = 0.25 * 6x = 1.50x
The value of 1 rupee coins = 1.00 * 2x = 2.00x

Adding up the values, we get:
2.50x + 1.50x + 2.00x = 42
6x = 42
x = 7

So, the number of 25 paise coins would be 6x = 6 * 7 = 42.

Therefore, the correct answer is 42.

Explanation
Let's assume that the number of pigeons in the zoo is P and the number of hares is H. Since each animal has one head, the total number of heads is P + H = 200. Pigeons have 2 legs and hares have 4 legs, so the total number of legs is 2P + 4H = 580. By solving these two equations simultaneously, we can find that P = 110 and H = 90. Therefore, the number of hares in the zoo is 90.

Explanation
To make the ratio of milk and water 1:2, the total ratio should be 1+2=3. Currently, the ratio is 2:1, so the total ratio is 2+1=3. This means that the current mixture already has the desired total ratio. Therefore, no water needs to be added to achieve the desired ratio. Hence, the answer is 60, which represents the total amount of the mixture.

Explanation
Let's assume that person A's income is 3x and person B's income is 4x. According to the given information, their expenditures are in the ratio 2:4. This means person A's expenditure is 2y and person B's expenditure is 4y. It is stated that both persons save Rs. 100 per month. So, we can set up the equation 3x - 2y = 100. Since we need to find person A's income, we can solve this equation to find the value of x, which is 50. Therefore, person A's income is 3x = 3 * 50 = 150.

Explanation
The given amount of Rs. 1560 is divided among A, B, and C in the ratio 1/2 : 1/3 : 1/4. To find the share of C, we need to calculate 1/4 of the total amount. This can be done by multiplying 1560 by 1/4, which equals 390. Therefore, the share of C is Rs. 390. However, none of the given answer options match this calculation. Therefore, the correct answer is not available.

Explanation
The ratio of tin in alloy A is 2:5 and the ratio of tin in alloy B is 1:5. To find the amount of tin in the new alloy, we need to calculate the weighted average of the two ratios based on the amount of each alloy used.

For alloy A, the proportion of tin is 2/5 * 60 kg = 24 kg.
For alloy B, the proportion of tin is 1/5 * 100 kg = 20 kg.

Therefore, the total amount of tin in the new alloy is 24 kg + 20 kg = 44 kg.

Explanation
Let's assume the current ages of the man and his wife are 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. So, we can set up the equation (4x + 4)/(3x + 4) = 9/7. Solving this equation, we get x = 4. Therefore, the current ages of the man and his wife are 16 and 12 respectively. At the time of their marriage, the ratio of their ages was 5:3. So, the number of years ago they got married would be 16 - 12 = 4 years ago.

Explanation
Let's assume that the present age of P is 2x and the present age of Q is 3x. According to the given information, Q's present age minus P's age after 3 years is equal to 5. So, 3x - (2x + 3) = 5. Solving this equation, we get x = 8. Therefore, P's present age is 2x = 2(8) = 16 and Q's present age is 3x = 3(8) = 24. The sum of P's and Q's present ages is 16 + 24 = 40.

Explanation
If Aakash's age after 5 years is 8, it means that his current age is 3. Therefore, the remainder obtained when Jagan's age is divided by 18 is 3. Since Jagan's age is 6 years more than Aakash's age, the remainder obtained when Jagan's age is divided by 18 is also 6. This means that Jagan's age is 6 years more than a multiple of 18. The only option that satisfies this condition is 60, as 60 - 6 = 54, which is a multiple of 18. Therefore, the present age of Jagan is 60.