Question

The ratio of present ages of Deependra and Subendu is 3 : 5 respectively. 5 years ago the ratio of their ages was 10 : 25 respectively. What will be Subendu’s age after 7 years?

Answer 1

Answer:

Step-by-step explanation:

Let dependra age be x

And Subhendu age be y

By first condition

x/y=3/5

5x-3y=0...........1

By second condition

x-5/y-5=10/25

25x-125=10y-50

25x-10y=75

5x-2y=15.............2

By substracting equation 1 from 2

y=15

Subhendu age after 7 years =15+7=22

Answer 2

Answer:

Shubhendu's age after 7 years will be 22 years.

Step-by-step-explanation:

Let the present age of Deependra be x years.

And the present age of Shubhendu be y years.

From the first condition,

$\sf\:\frac{x}{y}\:=\:\frac{3}{5}\\\\\implies\sf\:5x\:=\:3y\\\\\implies\sf\:5x\:-\:3y\:=\:0\:\:\:-\:-\:(\:1\:)$

Now,

Age of Deependra 5 years ago = ( x - 5 ) years.

And age of Shubhendu 5 years ago = ( y - 5 ) years.

From the second condition,

$\sf\:\dfrac{(\:x\:-\:5\:)}{(\:y\:-\:5\:)}\:=\:\cancel{\frac{10}{25}}\\\\\implies\sf\:\dfrac{(\:x\:-\:5\:)}{(\:y\:-\:5\:)}\:=\:\frac{2}{5}\\\\\implies\sf\:5\:(\:x\:-\:5\:)\:=\:2\:(\:y\:-\:5\:)\\\\\implies\sf\:5x\:-\:25\:=\:2y\:-\:10\\\\\implies\sf\:5x\:-\:2y\:=\:-\:10\:+\:25\\\\\implies\sf\:5x\:-\:2y\:=\:15\:\:\:-\:-\:(\:2\:)$

By subtracting equation ( 2 ) from equation ( 1 ), we get,

$\sf\:\cancel{5x}\:-\:3y\:=\:0\:\:-\:-\:(\:1\:)\\\\\sf\:-\underline{\sf\:\cancel{5x}\:-\:2y\:=\:15}\sf\:\:\:-\:-\:(\:2\:)\\\\\implies\sf\:\cancel{-}\:y\:=\:\cancel{-}\:15\\\\\implies\boxed{\red{\sf\:y\:=\:15}}$

Now,

Shubhnedu's present age ( y ) = 15 years.

Now,

Shubhendu's age after 7 years = 15 + 7 = 22 years.

Shubhendu's age after 7 years will be 22 years.