Question

The current ages of Rohit and Laxmi are in the ratio 5;3.Five years from now, their ages will be in the ratio 10;7. Then, Laxmi's current age is:

15 years

9 years

3 years

5 years

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Answer 1

Given :

Ages' ratio of Rohit and Laxmi : 5:3

Ratio of ages, five years later : 10:7

To find :

The present age of Laxmi.

Solution :

Let the age of Rohit be 5x.

Let the age of Laxmi be 3x.

According to the question,

$\sf \dashrightarrow (5x : 3x) + 5 = 10:7$

$\sf \dashrightarrow \dfrac{5x + 5}{3x + 5} = \dfrac{10}{7}$

$\sf \dashrightarrow 7(5x + 5) = 10(3x + 5)$

$\sf \dashrightarrow 35x + 35 = 30x + 50$

$\sf \dashrightarrow 35x - 30x = 50 - 35$

$\sf \dashrightarrow 5x = 15$

$\sf \dashrightarrow x = \dfrac{15}{5}$

$\sf \dashrightarrow x = 3$

Now, as we have found with the value of x, we should now find the ages of Laxmi and Rohit.

Age of Laxmi :

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

$\sf \dashrightarrow 15 \: years$

Age of Rohit :

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

$\sf \dashrightarrow 9 \: years$

Hence, the present age of Laxmi is 15 years.

Hence, the present age of Laxmi is 15 years.Thus, Option (1) is correct.

Answer 2

Answer:

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