Question

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 1

Answer:

★ Swati's age = 9 Years ★

★ Varun's age = 27 Years ★

Step-by-step explanation:

Given:

• 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.

To Find:

• Present ages of Varun and Swati

Solution: Let seven years ago Swati's age be x years.

∴ Seven years ago Varun's age was 5(x)² = 5x²

★Let's move to the present ages of both -

• Swati's present age = x + 7 years
• Varun's present age = 5x² + 7 years

★And Three years hence their ages will be -

• Swati's age = (x + 7 + 3) years = x + 10 years.

• Varun's age = (5x² + 7 + 3) years = 5x² + 10 years.

A/q

† Three years hence Swati's age will be 2/5th of Varun's age †

$\small\implies{\sf }$ x + 10 = 2/5 (5x² + 10)

$\small\implies{\sf }$ x + 10 = 2 (x² + 2)

$\small\implies{\sf }$ x + 10 = 2x² + 4

$\small\implies{\sf }$ 0 = 2x² – x + 4 – 10

$\small\implies{\sf }$ 0 = 2x² – x – 6

★ By middle term splitting ★

$\small\implies{\sf }$ 0 = 2x² – 4x + 3x – 6

$\small\implies{\sf }$ 0 = 2x (x – 2) + 3 (x – 2)

$\small\implies{\sf }$ 0 = (2x + 3) (x – 2)

$\small\implies{\sf }$ 0 = x – 2

$\small\implies{\sf }$ 2 = x

Hence, Swati's present age is x + 7 = 2 + 7 = 9 years.

∴ Varun's present age is 5x² + 7

→ 5 (2)² + 7

→ 5 x 4 + 7

→ 20 + 7

→ 27 Years.