Question

One year ago, the ratio of Gaurav's and Sachin's age was 6:7 respectively. Four years
hence, this ratio would become 7:8. How old is Sachin?

Answer 1

❍ Let Gaurav's and Sachin's ages one year ago be 6x and 7x respectively.

Then,

— Four years hence their ages;

• Gaurav's age = (6x + 1) + 4 = (6x + 5) years
• Sachin's age = (7x + 1) + 4 = (7x + 5) years

$\underline{\bigstar\:\boldsymbol{According\; to \;the\; given\; Question :}}$

⠀

• According to given condition, Four years hence the ratio of their ages (Gaurav's age & Sachin's age) would become 7: 8.

⠀

Therefore,

⠀

$:\implies\sf \dfrac{(6x + 5)}{(7x + 5)} = \dfrac{7}{8} \\\\\\:\implies\sf 8(6x + 5) = 7(7x + 5) \\\\\\:\implies\sf 48x + 40 = 49x + 35\\\\\\:\implies\sf 48x - 49x = 35 - 40 \\\\\\:\implies\sf \cancel{\;-}\:1x = \cancel{\;-}\;5\\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 5}}}}}\;\bigstar$

⠀

Hence,

⠀

• Gaurav's present age = (6x + 1) = 6(5) + 1 = (30 + 1) = 31 years.

• Sachin's present age = (7x + 1) = 7(5) + 1 = (35 + 1) = 36 years.

⠀

$\therefore{\underline{\textsf{Hence, \; Sachin\;is\;\textbf{36 years}\;old.}}}$

Answer 2

Given :-

Ratio of Gaurav and Sachin age = 6:7

After 4 years ratio becomes 7:8

To Find :-

Age of Sachin

Solution :-

Let their present ages be 6x and 7x

After 4 years

6x + 4/7x + 4 = 7/8

7(7x + 4) = 8(6x + 4)

(7 $\times$ 7x) + (7  $\times$ 4) = (8  $\times$ 6x) + (8  $\times$ 4)

49x + 28 = 48x + 32

49x - 48x = 32 - 28

x = 4

Present age of Sachin's

$\sf 7 \times 4$

$\sf 28 \; years$