Question

The ages of A and B are in the ratio 5 : 3. After 6 years, their ages will be in the ratio 7 : 5. The present age of A is ...
1 point
5 years
10 years
15 years
20 years​

Answer 1

Answer:

Let the sum of the ages of A=5x and B=3x

Then after 6 years, their ages are in ratio 7:5

∴

3x+6

5x+6

=

5

7

∴ 25x+30=21x+42

4x=12

x=3

Present age of A= 5x=15

Present age of B=3x=9

Sum of present age =15+9=24 years

Answer 2

Given :-

☀ Ratio of present ages of A and B = 5 : 3

☀ Ratio after 6 years = 7 : 5

To Find :-

☀ Present age of A

Solution :-

☀ Let their present ages be according to the ratio :

   A = 5x

   B = 3x

☀ After 6 years

   A = 5x + 6

   B = 3x + 6

☀ ATQ :

$\sf \rightarrow \dfrac{5x+6}{3x+6} = \dfrac{7}{5}$

$\sf \rightarrow 5(5x+6) = 3(7x+6)$

$\sf \rightarrow 25x + 30 = 21x + 42$

$\sf \rightarrow 25x-21x = 42-30$

$\sf \rightarrow 4x = 12$

$\sf \rightarrow x = \dfrac{12}{4}$

$\sf \rightarrow x = 3$

☀ Let's find their present ages by substituting the values !

Present age of A  = 5x  = 5 × 3 = 15 years

Present age of B = 3x = 3 × 3 = 9 years

∴ Present age of A is 15 years

_______

All Done ! :D