Question

The respective ratio between the present age of Manisha and Deepali is \(5 : x\). Manisha is 9 years younger than Parineeta. Parineeta's age after 9 years will be 33 years. The difference between Deepali's and Manisha's age is the same as the present age of Parineeta. What will come in place of \(x\)?

• A. 23
• B. 39
• C. 15
• D. None of these

Hint:

First find Parineeta's age, then Manisha's, then use the ratio and the age-difference condition to solve for x.

Answer 1

The Correct Option is D

Let Manisha's present age be $M$, Deepali's present age be $D$, and Parineeta's present age be $P$, with $M : D = 5 : x$.

1. Find Parineeta's present age. Parineeta's age after 9 years is 33, so $P + 9 = 33$, giving $P = 24$.
2. Find Manisha's present age. Manisha is 9 years younger than Parineeta, so $M = P - 9 = 24 - 9 = 15$.
3. Use the ratio to express Deepali's age. Since $M : D = 5 : x$ and $M = 15$, the common multiplier is $15 / 5 = 3$, so $D = 3x$.
4. Apply the age-difference condition. The difference between Deepali's and Manisha's age equals Parineeta's present age: $D - M = P$, that is $3x - 15 = 24$. Solving, $3x = 39$, so $x = 13$.

Since $x = 13$ is not listed among options A, B or C, the correct choice is option D, "none of these".