A, B, and C enter into a partnership in which A's capital is used for 5 months, and he claims 1/7 of the profit. B's capital is used for 7 months, and he claims 1/5 of the profit. If C invested ₹4,600 for 9 months, how much total capital was invested by A?

Solution

Solution: C's share of profit \(=1-\frac17-\frac15=\frac{23}{35}\). Therefore, the profit-sharing ratio is \(\frac17:\frac15:\frac{23}{35}=5:7:23\). Profit is proportional to capital × time. C's capital-time \(=4600\times9=41400\), corresponding to 23 parts. One part \(=41400\div23=1800\). A's capital for 5 months corresponds to 5 parts, so A's capital \(=(1800\times5)\div5=1800\). Therefore, A invested ₹1,800. Trick: Convert profit fractions into a common integer ratio, then compare capital × time.