Answer:

❍ 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 :}}

★AccordingtothegivenQuestion:

⠀

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

⠀

Therefore,

⠀

\begin{gathered}:\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\end{gathered}

:⟹

(7x+5)

(6x+5)

=

8

7

:⟹8(6x+5)=7(7x+5)

:⟹48x+40=49x+35

:⟹48x−49x=35−40

:⟹

−

1x=

−

5

:⟹

x=5

★

⠀

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.}}}∴

Hence, Sachinis36 yearsold.