Question

26. The difference between the ages of two cousins is 10 years. 15 years ago, if the elder one was
twice as old as the younger one, find their present ages. ..... pls tell me the answer of this question ​

Answer 1

$\sf\red{\underline{\underline{Answer:}}}$

$\sf{The \ present \ ages \ of \ the \ cousins}$

$\sf{is \ 35 \ years \ and \ 25 \ years \ respectively.}$

$\sf\orange{Given:}$

$\sf{\implies{The \ difference \ between \ the \ ages}}$

$\sf{of \ cousins \ is \ 10 \ years.}$

$\sf{\implies{15 \ years \ ago, \ if \ the \ elder \ one}}$

$\sf{was \ twice \ as \ old \ as \ younger \ one.}$

$\sf\pink{To \ find:}$

$\sf{The \ present \ ages \ of \ the \ cousins.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{Let \ the \ age \ of \ the \ elder \ cousin \ be \ x \ years}$

$\sf{and \ age \ of \ the \ younger \ cousin \ be \ y \ years.}$

$\sf{According \ to \ the \ fist \ condition.}$

$\sf{x-y=10...(1)}$

$\sf{According \ to \ the \ second \ condition.}$

$\sf{x-15=2(y-15)}$

$\sf{x-15=2y-30}$

$\sf{x-2y=-15...(2)}$

$\sf{Subtract \ equation (2) \ from \ equation (1)}$

$\sf{x-y=10}$

$\sf{-}$

$\sf{x-2y=-15}$

____________________

$\boxed{\sf{y=25}}$

$\sf{Substitute \ y=25 \ in \ equation (1)}$

$\sf{x-25=10}$

$\sf{x=10+25}$

$\boxed{\sf{x=35}}$

$\sf\purple{\tt{\therefore{The \ present \ ages \ of \ the \ cousins}}}$

$\sf\purple{\tt{is \ 35 \ years \ and \ 25 \ years \ respectively.}}$

Answer 2

Given :

• The difference between the ages of two cousins is 10 years.

• 15 years ago, if the elder one was twice as old as the younger one.

To find :

• Their present ages =?

Step-by-step explanation :

Let the present age of first cousin be x

Then, the present age of second cousin be = x + 10.

15 years ago first cousin age = x - 15.

15 years ago second cousin age = (x + 10 - 15)

According to the question :

➮ 2(x - 15) = (x + 10 - 15)

➮ 2x - 30 = x - 5

➮ 2x - x = - 5 + 30

➮ x = 25.

Therefore, We got the value of, x = 25.

Hence,

The present age of first cousin, x = 25 years.

Now, the present age of second cousin, x + 10 = 25 + 10 = 35 year's