A, B and C are partners in a business. A gets \(\displaystyle \frac{2}{5}\) of the profit, and B and C divide the remaining profit equally. If C gets Rs 600 less than A, what is the total profit?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Rs 6,000
Write each share as a fraction of the whole profit; the gap between A’s and C’s fractions is worth the given amount.
Remaining profit \(=1-\frac{2}{5}=\frac{3}{5}\); C gets half of it, \(\frac{3}{10}\)
A’s fraction minus C’s \(=\frac{2}{5}-\frac{3}{10}=\frac{1}{10}\)
\(\frac{1}{10}\) of the profit \(=600\), so profit \(=600\div\frac{1}{10}=6000\)
The total profit is Rs 6,000.
Why the other options are incorrect
Option (1) Rs 3,000 — Incorrect. With a profit of Rs 3,000, A gets Rs 1,200 and C gets Rs 900, a difference of Rs 300, not Rs 600.
Option (2) Rs 1,500 — Incorrect. With a profit of Rs 1,500, A gets Rs 600 and C gets Rs 450, a difference of Rs 150, not Rs 600.
Option (3) Rs 7,500 — Incorrect. With a profit of Rs 7,500, A gets Rs 3,000 and C gets Rs 2,250, a difference of Rs 750, not Rs 600.