Question : A, B and C invested their capitals in the ratio 2 : 3 : 5. The ratio of months for which they invested is 4 : 2 : 3, respectively. If the difference between the profit shares of A and B is Rs. 1,86,000, then C's share of profit (in Rs.) is:
Option 1: 19,35,000
Option 2: 10,29,500
Option 3: 15,39,000
Option 4: 13,95,000
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Correct Answer: 13,95,000
Solution : The ratio of capital invested by A, B, and C is 2 : 3 : 5. Let their investments be $2x, 3x$ and $5x$ respectively. The ratio of the time for which they invested is 4 : 2 : 3. Let these times be $4y, 2y$ and $3y$ respectively. The profit is proportional to the product of the capital invested and the time for which it was invested. The ratio of their profits (A : B : C) would be, $(2x×4y : 3x×2y : 5x×3y)=8xy : 6xy : 15xy=8 : 6 : 15$ Let the profits of A, B, and C be $8k, 6k$ and $15k$ respectively. According to the problem, the difference between the profit shares of A and B is Rs. 1,86,000. $⇒8k - 6k = 186000$ $⇒2k = 186000$ $\therefore k = 93000$ Now, C's share of the profit $=15k = 15 × 93000 = 1395000$ Hence, the correct answer is Rs. 13,95,000.
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