A sum of Rs 47,600 is divided among A, B, C and D such that the ratio of the shares of A and B is 8 : 9, that of B and C is 3 : 4, and that of C and D is 4 : 13. What is the difference between the shares of A and C?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs 2800
To join the ratios, the common person must get the same number in both ratios: make B the same in the first two, then C the same in the last two.
B is 9 in the first ratio and 3 in the second, so B : C \(=3:4=9:12\)
A : B : C \(=8:9:12\)
C is 12 here and 4 in C : D, so C : D \(=4:13=12:39\)
A : B : C : D \(=8:9:12:39\); total parts \(=68\)
One part \(\displaystyle =\frac{47600}{68}=\) Rs 700
A \(=8\times700=\) Rs 5600 and C \(=12\times700=\) Rs 8400
Difference \(=8400-5600=\) Rs 2800
The shares of A and C differ by Rs 2800.