Question

the age of hari and harry are in the ratio 5:7 four years from now the ratio of hari ages will be 3:4 find their present ages.​

Answer 1

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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,

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

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

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

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

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

$\sf x=4$

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.

Answer 2

✦ Question

The present age ratio of between Hari and Harry is 5 : 7. After 4 years the ratio of their ages will be 3 : 4. Find their present ages.

✦ Given

• The present age ratio of between Hari and Harry is 5 : 7.
• After 4 years the ratio of their ages will be 3 : 4.

✦ To Find

What's their present ages ?

✦ Solution

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

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

Consider Hari present age = 5x years

Harry present age = 7x years

Four years later, Hari age = ( 5x + 4 ) years

Harry age = ( 7x + 4 ) years

As per the Question ,

$\frac{5x + 4}{7x + 4} = \frac{3}{4}$

By cross multiplication, we have

4 ( 5x + 4 ) = 3 ( 7x + 4 )

= 20x + 16 = 21x + 12

= 16 - 12 = 21x - 20x

4 = x

Hence ,

Hari's present age = 5x years = ( 5 × 4 ) years = 20 years.

Harry's present age = 7x years = ( 7 × 4 ) years = 28 years.