Question

After five years, A's age will be 10.5 years less than 2.5 times of C's age. Three years ago, the ratio of age of A and C is 3: 1. If B is three times the age of C, then what is the present age of B?

• A. 16 years
• B. 21 years
• C. 20 years
• D. 18 years

Answer 1

The Correct Option is D

The correct option is (C): 9:10.
Let present age of A and C are a years and c years, respectively.
(a + 5) = \(\frac{5(c + 5)}{2}\) - 10.5
=> 2a + 10 = 5c + 25 - 21
=> 2a - 5c = -6 --- (1)
And \(\frac{(a - 3)}{(c - 3)} \)= 3: 1
=> a - 3 = 3c - 9
=> a - 3c = -6 --- (2)
Solving (1) and (2), we get
a = 12 and c = 6
Hence, B = 3 * 6=18 years.