Three persons A,B and C divide certain amount of money such that A's share is…

Concept

When a word problem describes a total being divided into successive shares expressed as fractions or remainders of what is left, translate each share into an algebraic expression in terms of the unknown total. Since all the shares must add up to the total, summing them gives one linear equation in the total, which can then be solved directly.

Application

Let the total amount be P.

1. A's share is Rs 8 less than half the total: A = P/2 - 8.

2. What remains after A takes her share: P - (P/2 - 8) = P/2 + 8.

3. B's share is Rs 6 more than half of what is left: B = (P/2 + 8)/2 + 6 = P/4 + 4 + 6 = P/4 + 10.

4. C takes the rest, which is given as Rs 22, so the three shares together must add up to the total: (P/2 - 8) + (P/4 + 10) + 22 = P.

5. Combine like terms: P/2 + P/4 + 24 = P, i.e. 3P/4 + 24 = P.

6. So P - 3P/4 = 24, which gives P/4 = 24, hence P = 96.

Cross-check

With P = 96: A = 96/2 - 8 = 40. Amount left after A = 96 - 40 = 56. B = 56/2 + 6 = 34. C = 96 - 40 - 34 = 22, which matches the Rs 22 given in the question, confirming the total.