Question

The ratio of the ages of Richa and Shelly is 5 : 8. The ratio of their ages 10 years hence would be 7:10. What is the present age of Shelly?

Answer 1

Let the present age of Richa and Shelly be 5x and 8x

10 years hence there would be

Richa agewould be = 5x+10 years

and Shelly agewould be = 8x+10 years

ATP

(5x+10) ÷ (8x+10) =7:10

(5x+10) ÷ (8x+10) =7÷10

10×(5x+10) =7× (8x+10)

50x+100=56x+70

100-70=56x-50x

30=6x

30÷6=x

5=x

Richa age present would be = ( 5x) =5×5=25 years ANS

and Shelly agewould be = (8x) =8×5 =40 yearsANS

Answer 2

Let ,

The present age of Richa and Shelly be :- 5a and 8a

Ration of their age is 10 years . Hence,

Age of Richa be = 5a + 10 years. (1)

Age of Shelly be = 8a + 10 years. (2)

According to equation (1) and (2)

$\frac{(5a + 10)}{(8a + 10)} = 7:10$

$\frac{(5a + 10)}{(8a + 10)} = \frac{7}{10}$

10(5a+10) = 7(8a+10)

50a+100 = 56a+70

100-70. = 56a-50a

30. =6a

$\frac{30}{6} = a$

5. = a

Richa present age. = 5a

= 5×5

= 25

Shelly present age = 8a

=8×5

=40

#SPJ2