Question

13) The ages of Sachin and Vinod are in the ratio 2:5. Eight years from now 1
the ratio of their ages will be 2:3. Find the present age of Sachin? *
8 years
O 2 years
4 years
O 10 years​

Answer 1

Solution :

$\underline{\bf{Given\::}}}}$

The ages of Sachin & Vinod are in the ratio 2:5. 8 years from now the ratio of their ages will be 2:3.

$\underline{\bf{To\:find\::}}}}$

The present age of Sachin.

$\underline{\bf{Explanation\::}}}}$

Let the present age of Sachin's be 2r years.

Let the present age of Vinod's be 5r years.

A/q

$\underbrace{\sf{8\:years\:later\::}}}$

The age of Sachin's will (2r + 8) years.

The age of Vinod's will (5r + 8) years.

Now;

$\longrightarrow\sf{\dfrac{2r+8}{5r+8} =\dfrac{2}{3}} \\\\\\\longrightarrow\sf{3(2r+8)=2(5r+8)\:\:\underbrace{\sf{Cross-multiplication}}}\\\\\longrightarrow\sf{6r+24=10r+16}\\\\\longrightarrow\sf{6r-10r=16-24}\\\\\longrightarrow\sf{-4r=-8}\\\\\longrightarrow\sf{r=\cancel{-8/-4}}\\\\\longrightarrow\bf{r=2\:years}$

Thus;

$\boxed{\sf{The\:present\:age\:of\:Sachin's\:will\:be\:2r=2(2)\:years=\boxed{\bf{4\:years}}}}}$