Question

The ages of Hari and Harry are in the ratio of 5:7. Four years from now the ratio of their ages will be 3:4 . Find their present ages.

Answer 1

Let the common ratio of their ages be x
Let the Hari's age be 5x and Harry's age be 7x
Five years later:-
Hari's age=5x+4
Harry's age=7x+4
According to question....
5x+5 = 3
7x+5    4
By cross-multiplication,We get,
4(5x+5)=3(7x+5)
20x+20=21x+15
20-15=21x-20x
5=x
x=5
Present age of Hari=5x=5×5=25 years
Present age of Harry=7x=7×5=35 years

Answer 2

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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.