1.

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

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 :}}

⠀

  • 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.}}}


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