Question

There are three persons 'A', 'B' and 'C' such that 8 times the present age of 'A' is equal to 9 times the present age of 'B' while 5 times the present age of 'B' is equal to 6 times the present age of 'C'. If the present ages of all three are integers and the age of 'D' after 15 years will be equal to the sum of the minimum possible present ages of 'A', 'B' and 'C', together, then find the present age of 'D'?

Q: Answer-There are three persons 'A', 'B' and 'C' such that 8 times the present age of 'A' is equal to 9 time...

Let the present ages of A, B and C be x years, y years and z years respectively According to the question, 8x 9y Or, xy 98 2724 Also, 5y 6z Or, yz 65 2420 Let x and y be 27a and 24a, respectively Therefore, z 24a X 2024 20a Therefore, xyz 272420 Therefore, age of D 15 years hence from now 27 24 20 71 years Therefore, required age 71 - 15 56 years Hence, the correct answer is B.