Question

The ages of Hari and Harry are in the ratio 5:7.

Four years from now the ratio of their ages will be 3:4.

Find their present ages.

Answer 1

Answer:

Hari is 20 and Harry is 28

Step-by-step explanation:

Call the age of Hari now is a so of Harry now is $\frac{7}{5}$a

4 years later, Their age will be 3:4

⇒(a+4):($\frac{7}{5}$a+4)=3:4

⇒4$\times$(a+4)=3$\times$($\frac{7}{5}$a+4)

⇒4a+16=$\frac{{3}\times{7}}{5}$a+12

⇒4a+16=$\frac{21}{5}$a+12

⇒(4a-16)-(4a+12)=($\frac{21}{5}$a+12)-(4a+12)

⇒4=($\frac{21}{5}$a-$\frac{20}{5}$a)

⇒$\frac{1}{5}$a=4

⇒a=4:$\frac{1}{5}$=4$\times$5=20

⇒$\frac{7}{5}$a=$\frac{7}{5}$$\times$20=28

Answer 2

$\boxed{\pink{\tt Answer}}$

Given:

Ages of Hari and Harry are in the ratio = 5:7

Ratio of ages of Hari and Harry after 4 years = 3:4

To Find:

The present age of Hari.

The present age of Harry.

Solution:

Given that,

Ages of Hari and Harry are in the ratio = 5:7

Ratio of ages of Hari and Harry after 4 years = 3:4

According the question,

$\tt\dfrac{Age \: of \: Hari}{Age \: of \: Harry} =\dfrac{5}{7}$

Let Hari's age be 5x years and Harry's be 7x years.

Then after four years,

Hari's age = $\tt (5x+4)(5x+4)$ years

Harry's age = $\tt (7x+4)(7x+4)$ years

It's given that,

Ratio of ages of Hari and Harry after 4 years = 3:4

Then,

$\tt \dfrac{Hari's \: age \: after \: 4 \: years}{Harry's \: age \: after \: 4 \: years}=\dfrac{3}{4}$

$\tt \longrightarrow \dfrac{5x+4}{7x+4} =\dfrac{3}{4}$

$\tt 4(5x+4)=3(7x+4)$

$\tt 20x+16=21x+12$

$\tt 16-12=21x-20x$

$\tt x=4$

Therefore,

Present age of Hari = $\tt 5x=5 \times 4=20$ years

Present age of Harry = $\tt 7x=7 \times 4=28$ years

Hence the present age of Hari is 20 years and the present age of Harry is 28 years.