Discussion
A sum of ₹ \(x\) is divided between A, B and C such that the ratio of shares of A and C is 3 : 7 and the ratio of shares of C and B is 4 : 5. If the difference between the shares of A and C is ₹ 1920, then what is the value of \(x\) ?
Answer: C
The value of x is 9000. The ratio of A to C is 3 : 7 and of C to B is 4 : 5. Making C the same in both, A : C = 12 : 28 and C : B = 28 : 35, so A : C : B = 12 : 28 : 35 with 75 parts in all.
\[ 28 - 12 = 16 \text{ parts} = 1920 \]
\[ 1 \text{ part} = 120 \]
\[ x = 75 \times 120 = 9000 \]
The options 8400, 8640 and 9120 do not equal 75 parts of 120, so the third option is correct. As a check, one part is 120, so A has 1440, C has 3360 and B has 4200. These add up to 9000, and A and C differ by 1920 as the question says.
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