A, B and C start a business together. A invests Rs 6,500 for 6 months, B invests Rs 8,400 for 5 months and C invests Rs 10,000 for 3 months. A is the working partner and receives 5% of the profit for this. The profit earned is Rs 7,400. Find B’s share in the profit (in Rs).
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 2660
The working partner’s 5% is taken out first; the rest of the profit is shared in the ratio of capital × months.
A’s 5% \(=\frac{5}{100}\times7400=\) Rs 370
Profit left to share \(=7400-370=\) Rs 7,030
A: \(6500\times6=39000\); B: \(8400\times5=42000\); C: \(10000\times3=30000\)
A : B : C \(=39:42:30\), total \(111\) parts
B’s share \(\displaystyle =\frac{42}{111}\times7030=42\times\frac{190}{3}=\) Rs 2,660
B’s share is Rs 2,660.
Why the other options are incorrect
Option (1) 1900 — Incorrect. This is C’s share: \(\frac{30}{111}\times7030=1900\).
Option (3) 2800 — Incorrect. This is B’s share of the whole Rs 7,400, without first taking out A’s 5%.
Option (4) 2840 — Incorrect. It does not come from the ratio 39 : 42 : 30 applied to the Rs 7,030 that is shared.