Question

the present ages of kaira and mihir are in the ratio 3:5. white years from now, their ages will be in the ratio 2:3. find their ages five years ago.​

Answer 1

Correct Question

The present ages of Kaira and Mihir are in the ratio of 3:5. Five years from now, their ages will be in the ratio 2:3. Find their ages five years ago.

Answer

As we know that, there are two persons in which we are given with the ratio of the ages of those both. We are also given with the ratio of those both five years later.

Let the age of Kaira be 3x years.

Let the age of Mihir be 5x years.

According to the question,

$\sf \dashrightarrow 3x + 5 : 5x + 5 = 2 : 3$

$\sf \dashrightarrow \dfrac{3x + 5}{5x + 5} = \dfrac{2}{3}$

$\sf \dashrightarrow 3 (3x + 5) = 2 (5x + 5)$

$\sf \dashrightarrow 9x + 15 = 10x + 10$

$\sf \dashrightarrow 9x - 10x = 10 - 15$

$\sf \dashrightarrow -1x = -5$

$\sf \dashrightarrow x = \dfrac{-5}{-1}$

$\sf \dashrightarrow x = 5$

Now, we can find the present ages of Kaira and Mihir

Present age of Kaira :

$\sf \dashrightarrow 3x = 3(5)$

$\sf \dashrightarrow 15 \: years$

Present age of Mihir :

$\sf \dashrightarrow 5x = 5(5)$

$\sf \dashrightarrow 25 \: years$

Now, we can find the answers of this question i.e, ages of both five years ago.

Kaira's age (Five years ago) :

$\sf \dashrightarrow 15 - 5$

$\sf \dashrightarrow 10 \: years$

Mihir's age (Five years ago) :

$\sf \dashrightarrow 25 - 5$

$\sf \dashrightarrow 20 \: years$

Hence, the ages of Kaira and Mihir, five years ago are 10 and 20 years respectively.