Question

Find the solution with statement :



The ages of Vimla and Sarita are in the ratio of 7:5. Four years later their age will be in the ratio of 4:3. Find its ages​

Answer 1

let the Age of vimla 7x. age of Sarita 5x. after 4 Year age of vimla 7x+10.age of Sarita 5x+10.so their present age =7x+10/5x+10=4/3

3(7x+10)=4(5x+10) .21x+ 30=20x+40.21x-20x=40-30.x=10

Answer 2

• Let present age of Vimla be (7M) years and present age of Sarita be (5M) years.

» 4 years later

• Age of Vimla = (7M + 4) years

• Age of Sarita = (5M + 4) years

A.T.Q.

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

Cross-multiply them

→ 3(7M + 4) = 4(5M + 4)

→ 21M + 12 = 20M + 16

→ 21M - 20M = 16 - 12

→ M = 4

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• Present age of Vimla = 7M = 7(4) = 28 years.

• Present age of Sarita = 5M = 5(4) = 20 years.

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✡ VERIFICATION :

From above calculations we have M = 4

Put value of M in this equation :

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

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

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

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

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

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