Question

The present ages of vatsala and sara are 14years and 10years respectively . After how many years will the ratio of their ages become 5:4?​

Answer 1

Answer:6 years

Step-by-step explanation :let the years be 'x'

So

(X+14)/(X+10)=5/4

(X+14)*4=(X+10)*5

4x+56=5x+50

56-50=5x-4x

6=X

So their ages will be in the ratio of 5:4 after 6 years

Answer 2

Present age of Vatsala is 14 years and present age of Sara is 10 years.

We have to find the year after which the ratio of their ages become 5:4.

Let the year after which their ages will be 5:4 is "M" years.

According to question,

$\implies\:\dfrac{M\:+\:14}{M\:+\:10}\:=\:\dfrac{5}{4}$

Cross multiply them

$\implies\:4(M\:+\:14)\:=\:5(M\:+\:10)$

$\implies\:4M\:+\:56\:=\:5M\:+\:50$

$\implies\:5M\:-\:4M\:=\:56\:-\:50$

$\implies\:M\:=\:6$

∴ After 6 years the ratio of Vatsala and Sara age will be 5:4.

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Verification :

From above calculations we have M = 6

Put value of M in this :

$\implies\:\dfrac{M\:+\:14}{M\:+\:10}\:=\:\dfrac{5}{4}$

$\implies\:\dfrac{6\:+\:14}{6\:+\:10}\:=\:\dfrac{5}{4}$

$\implies\:\dfrac{20}{16}\:=\:\dfrac{5}{4}$

$\implies\:\dfrac{5}{4}\:=\:\dfrac{5}{4}$