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Seven years ago Varun's age was five times the square of Swati

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Seven years ago Varun's age was five times the square of Swati's age. Three years hence, Swati's age will be two-fifth of Varun's age. Find their present ages.

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Seven years ago Varun's age was five times the square of Swati's age. Three years hence, Swati's age will be two-fifth of Varun's age. Find their present ages.

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Text solutionVerified

Seven years ago, let Swati's age be

x

years. Then, seven years ago Varun's age was

5 x^{2}

years.

∴

Swati's present age

= (x + 7)

years
Varun's present age

= (5 x^{2} + 7)

years
Three years hence
Swati's age

= (x + 7 + 3) ye a rs = (x + 10) ye a rs

Varun's age

= (5 x^{2} + 7 + 3) ye a rs = (5 x^{2} + 10) ye a rs

According to the questions,

x + 10 = \frac{2}{5} (5 x^{2} + 10)

\Rightarrow

x + 10 = \frac{2}{5} \times 5 (x^{2} + 2)

\Rightarrow

x +! 0 = 2 x^{2} + 4

\Rightarrow

2 x^{2} - x - 6 = 0

\Rightarrow

2 x^{2} - 4 x + 3 x - 6 = 0

\Rightarrow

2 x (x - 2) + 3 (x - 2) = 0

\Rightarrow

(2 x + 3) (x - 2) = 0

\Rightarrow

x - 2 = 0

2 x + 3 = 0

\Rightarrow

x = 2

[

∵ 2 x + 3 \neq = 0

x > 0

]
Hence, Swati's present age

= (2 + 7) = 9

years
and Varun's present age

= (5 \times 2^{2} + 7) = 27

years.

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Question Text	Seven years ago Varun's age was five times the square of Swati's age. Three years hence, Swati's age will be two-fifth of Varun's age. Find their present ages.
Answer Type	Text solution:1
Upvotes	150

Seven years ago Varun's age was five times the square of Swati's age. Three years hence, Swati's age will be two-fifth of Varun's age. Find their present ages.

Text solutionVerified

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