Question

The present age of the brother
is 7 years more then his sister.
if 5 years ago the sum of their ages is 15 years then find out their ages.​

Answer 1

Answer:

ANSWER

Ratio of present ages of Ramesh and his elder brother =5:7

Let the present ages of Ramesh and his elder brother be 5x and 7x.

After five years,

Age of Ramesh =5x+5 and Age of elder Brother =7x+5

According to question, then the ratio of their ages =3:4

⇒(5x+5):(7x+5)=3:4

⇒

7x+5

5x+5

=

4

3

⇒4×(5x+5)=3×(7x+5)

⇒20x+20=21x+15

⇒21x−20x=20−15

⇒x=5

Thus, Present age of Ramesh =5x=5×5=25years

Present age of his elder brother =7x=7×5=35years.

Answer 2

To find:-

The present age of Brother and sister.

Assumption:-

Let the present age of sister be (x) years

Present age of Brother = (x + 7) years

Solution:-

5 years ago,

$\sf{Age\: of\: sister = (x - 5) \:years}$

$\sf{Age\: of\: Brother = (x + 7 - 5)\:years}$

ATQ,

$\sf{(x-5) + (x+7-5) = 15}$

= $\sf{(x - 5) + (x + 2) = 15}$

$\sf{\implies x - 5 + x + 2 = 15}$

$\sf{\implies 2x - 3 = 15}$

$\sf{\implies 2x = 15 + 3}$

$\sf{\implies 2x = 18}$

$\sf{\implies x = \dfrac{18}{2}}$

$\sf{\implies x = 9}$

Therefore,

$\sf{Age\:of\:sister = x = 9\:years}$

$\sf{Age\:of\:brother = (x+7) = 9 + 7 = 16\:years}$

Verification:-

5 years ago sum of their ages were 15 years.

5 years ago,

$\sf{Age \:of \:sister = 9 - 5 = 4\:years}$

$\sf{Age\:of\:brother = 16 - 5 = 11\: years }$

Now,

$\sf{Sum \:of \:their \:ages = 11 + 4 = 15\:years \:\:[Hence\:Proved]}$