Question

The ages of Ram and Anu are in the ratio 2 : 3. 15 years hence, the ratio of their ages will be in the ratio 3 : 4. Find the present age of Anu."

Answer 1

SOLUTION

GIVEN

• The ages of Ram and Anu are in the ratio 2 : 3

• 15 years hence, the ratio of their ages will be in the ratio 3 : 4

TO DETERMINE

The present age of Anu.

EVALUATION

Here it is given that the ages of Ram and Anu are in the ratio 2 : 3

Let present age of Ram and Anu are 2x years and 3x years respectively

Now after 15 years

Age of Ram = 2x + 15 years

Age of Anu = 3x + 15 years

Now it is given that 15 years hence, the ratio of their ages will be in the ratio 3 : 4

So by the given condition

$\displaystyle\sf{ \frac{2x + 15}{3x + 15} = \frac{3}{4} }$

$\displaystyle\sf{ \implies \: 9x + 45 = 8x + 60}$

$\displaystyle\sf{ \implies \: x = 15}$

Hence present age of Anu

= 3 × 15 years

= 45 years

FINAL ANSWER

The present age of Anu = 45 years

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