Question

Sushma is now 15 years older than Vijay but in three more years she will be 8 times as old as Vijay was three years ago how old are they now

Answer 1

Let the age of Vijay be x years.

Then the age of Sushma is 15 years older than Vijay = (x+15) years.

Given that in 3 years she will be 8 times as old as Vijay was 3 years ago.

(x + 15) + 3 = 8(x - 3)

x + 15 + 3 = 8x - 24

x + 18 = 8x - 24

7x = 42

x = 42/7

x = 6.

If Vijay's present age is 6 years, Then the age of Sushma = (x+15) = 21 years.

The age of Vijay = 6 years.

The age of Sushma = 21 years

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Answer 2

• Let the present age of Sushma be x.
• Let the present age of Vijay be y.

By data,

Sushma is now 15 years older than Vijay

x = y + 15

Let the above equation be equation 1.

Let's assume,

• The age of Sushma after three years be x + 3.
• The age of Vijay before three years be y - 3.

Again by data,

In three more years Sushma will be 8 times as old as Vijay was three years ago.

$x + 3 = 8 \times (y - 3) \\ \\ x + 3 = 8y - 24 \\ \\ x + 3 + 24 = 8y \\ \\ 27 = 8y - x$

Let the above equation be equation 2.

Let's substitute equation 1 in equation 2.

$27 = 8y - x \\ \\ 27 = 8y - (y + 15) \\ \\ 27 = 8y - y - 15 \\ \\ 27 = 7y - 15 \\ \\ 27 + 15 = 7y \\ \\ 42 = 7y \\ \\ y = \dfrac{42}{7} \\ \\ y = 6$

The present age of Vijay is 6.

Substitute y = 6 in any one of the equations.

Let's substitute the value of y in equation 1.

$x = y + 15 \\ \\ x = 6 + 15 \\ \\ x = 21$

The present age of Sushma is 21.

ANSWERS:

• Sushma is 21 years old now.
• Vijay is 6 years old now.