Question

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

Answer 1

Let present age of Hari be "5M" years and present age of Harry be "7M" years.

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

After 4 years,

• Age of Hari = (5M + 4) years
• Age of Harry = (7M + 4) years

According to question,

=> $\dfrac{5M\:+\:4}{7M\:+\:4}\:=\:\dfrac{3}{4}$

Cross-multiply them

=> 4(5M + 4) = 3(7M + 4)

=> 20M + 16 = 21M + 12

=> 20M - 21M = 12 - 16

=> 20M - 21M = - 4

=> - M = - 4

=> M = 4

So,

Present age of Hari = 5M

=> 5(4)

=> 20 years

Present age of Harry = 7M

=> 7(4)

=> 28 years

∴ Present age of Hari is 20 years and present age of Harry is 28 years.

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✯ Verification :

From above calculations we have M = 4

Put value of M in this :

$\dfrac{5M\:+\:4}{7M\:+\:4}\:=\:\dfrac{3}{4}$

=> $\dfrac{5(4)\:+\:4}{7(4)\:+\:4}\:=\:\dfrac{3}{4}$

=> $\dfrac{20\:+\:4}{28\:+\:4}\:=\:\dfrac{3}{4}$

=> $\dfrac{24}{32}\:=\:\dfrac{3}{4}$

=> $\dfrac{3}{4}\:=\:\dfrac{3}{4}$

Answer 2

Present age of Hari = 5x

Present ag of Harry = 7x

According to question

5x+4/7x+4 = 3/4

20x + 16 = 21x + 12

x = 4

Answer:-

Age of Hari = 20 years

Age of Harry = 28 years