Present ages of Vatsala and Sara are 14 years and 10 years respectively. After how many years the ratio of their ages will become 5 : 4?

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Solution

Let after x years, the ratio of their ages will become 5 : 4.

Age of Vatsala after x years = (14 + x) years

Age of Sara after x years = (10 + x) years

$∴ \frac{14 + x}{10 + x} = \frac{5}{4} \Rightarrow 56 + 4 x = 50 + 5 x \Rightarrow 5 x - 4 x = 56 - 50 \Rightarrow x = 6$
Thus, the ratio of their ages will become 5 : 4 after 6 years.

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Present ages of Vatsala and Sara are 14 years and 10 years respectively. After how many years the ratio of their ages will become 5 : 4?

Let after x years, the ratio of their ages will become 5 : 4. Age of Vatsala after x years = (14 + x) years Age of Sara after x years = (10 + x) years ∴14+x10+x=54⇒56+4x=50+5x⇒5x-4x=56-50⇒x=6 Thus, the ratio of their ages will become 5 : 4 after 6 years.