Q. 27

# 2 years ago Salim was thrice as old as his daughter and 6 years later he will be 4 years older than twice her age. How old are they now?

Let Salim's present age be x and her daughter's present age be y.

2 years ago

Salim's age = x – 2

Salim's daughter age = y – 2

Salim was thrice as old as his daughter

Salim's age = 3 (y – 2)

x – 2 = 3y – 6

x – 3y = – 4 ……(1)

6 years later

Salim's age = x + 6

Salim's daughter age = y + 6

Salim will be 4 years older than twice her daughter's age

Salim's age = 4 + 2 (y + 6)

x + 6 = 4 + 2y + 12

x – 2y = 10 ……(2)

Eliminate (1) and (2), by subtracting equation (1) from equation (2)

x – 2 y – (x – 3 y) = 10 – (- 4)

- 2 y + 3 y = 10 + 4

y = 14

Put y = 14 in (2)

x – 2 (14) = 6

x = 28 + 6

x = 34

Therefore, Salim's age is 38 years and her daughter's age is 14 years.

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