Ratio of A’s age 8 years after to present age of B is 3: 5 and B’s present age is 25% of C’s age after 15 years

Q. Ratio of A’s age 8 years after to present age of B is 3: 5 and B’s present age is 25% of C’s age after 15 years. After 4 years A’s age is 12.5% of D’s age after 4 years. If the sum of the ages of A, B, C and D after 1 year is 101, then what is the present age of B?

A. 18 years

B. 15 years

C. 12 years

D. 14 Years

Ans: 15 years

Sol:

(A +8)/B = 3/5
B =25/100* (C +15)
(D+4)*12.5/100= (A +4)
5 A +40 = 3B
B =(5A +40)/3
B = 25/100 * (C +15)
(5A + 40)/3 = 1/4* (C+15)
20A +160 = 3C+45
(20A +115) = 3C
C = (20A + 115)/3
(D+4) 12.5/100 = (A +4) (D +4)1/8 = (A +4)
D +4 = 8A +32
D = 8A + 28
Total age of all four together after one year
(A +1)+ (C +1)+ (B +1)+ (D +1) = 101
A + B + C + D = 97

A +(20A +115)/3+(5A +40)/3+ (8A +28) = 97
52A = 291-239
A = 1
B = (5A + 40)/3
Present age of B = (5(1) + 40)/3
=15 years.