Question

Eight years hence from now, ratio of ages of ‘A’ and ‘B’ will be 10 : 9, respectively. Present age of ‘B’ is 60% more than age of ‘C’ 8 years ago from now. If ratio of present ages of ‘A’ and ‘C’ is 3:2, respectively then find the present age of ‘C’.

• A. 48 years
• B. 64 years
• C. 72 years
• D. 60 years

Answer 1

The Correct Option is A

Let, ages of ‘A’ and ‘B’, eight years hence from now will be ‘10x’ years and ‘9x’ years, respectively.
Let, present age of ‘C’ is ‘y’ years.
So, (9x – 8) = 1.60 × (y – 8)
Or, 9x – 8 = 1.6y – 12.8
Or, 1.6y – 9x = 4.8
And, \(\frac{(10x – 8)}{y} = \frac{3}{2}\)
Or, 20x – 16 = 3y
Or, 20x – 16 = \(\frac{3(4.8 + 9x)}{1.6}\)
Or, 32x – 25.6 = 14.4 + 27x
Or, 5x = 40
Or, x = 8
Present age of ‘C’ = \(\frac{(20 × 8 – 16)}{3}\) = 48 years
So, the correct option is (A) : 48 years.