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

Step 1: Set up the present ages using the given ratio.
Let Manisha's present age be \(5a\) and Deepali's present age be \(xa\), since Manisha : Deepali = \(5 : x\).

Step 2: Find Manisha's and Parineeta's present ages.
Manisha is 9 years younger than Parineeta, so Parineeta's present age is \(5a + 9\). Parineeta's age after 9 years is 33, so \(5a + 9 + 9 = 33\), which gives \(5a = 15\), so \(a = 3\). This makes Manisha's present age \(5a = 15\) and Parineeta's present age \(5a + 9 = 24\) (check: \(24 + 9 = 33\), which matches).

Step 3: Apply the condition on Deepali's age.
The difference between Deepali's and Manisha's age equals Parineeta's present age: \(xa - 5a = 5a + 9\). Putting \(a = 3\): \(3x - 15 = 15 + 9 = 24\), so \(3x = 39\) and \(x = 13\).

Final Answer:
Since \(x = 13\) does not match 23, 39 or 15, the correct choice is "none of these". \[ \boxed{x = 13} \]