Question

At present, Thenmozhi’s age is 5 years more than that of Murali’s age. Five years ago, the ratio of Thenmozhi’s age to Murali’s age was 3 : 2. Find their present ages.

Answer 1

Let present ages of Thenmozhi and Murali be ‘t’ and ‘m’

Given that at present

Thenmozhi’s age is 5 years more than Murali

∴ t = m + 5  ...(1)

5 years ago, Thenmozhi’s age would be t – 5 and Murali’s age would be m – 5

Ratio of their ages is given as 3 : 2

∴ `("t" - 5)/("m" - 5) = 3/2` ...[∴ By cross multiplication]

2(t – 5) = 3(m – 5)

2 × t – 2 × 5 = 3 × m – 3 × 5

⇒ 2t – 10 = 3m – 15

Substituting for ‘t’ from (1)

2(m + 5) – 10 = 3m – 15

2m + 10 – 10 = 3m – 15

2m = 3m – 15

3m – 2m = 15

m = 15

t = m + 5 = 15 + 5 = 20

∴ Present ages of Thenmozhi and Murali are 20 and 15