Discussion
A sum of ₹ 1,710 is divided in A, B and C such that 4 times of A, 6 times of B and 9 times of C are equal. What is the difference between A and C ?
Answer: B
The difference between A and C is ₹ 450.
Let 4A = 6B = 9C = k. Then A = k/4, B = k/6 and C = k/9, so A : B : C = 9 : 6 : 4 (multiplying through by 36).
\[ \begin{aligned} 9 + 6 + 4 &= 19\ \text{parts} = 1710 \\ 1\ \text{part} &= 90 \\ A &= 810,\ C = 360 \\ A - C &= 450 \end{aligned} \]
₹ 360 is C's share itself, not the difference. The usual trap is writing the ratio as 4 : 6 : 9 instead of its reciprocal; that gives A = 360 and C = 810, with the same difference, so check the shares make 4A = 6B = 9C (4 × 810 = 3240 = 9 × 360).
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