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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Question : A, B, and C invest to start a restaurant. The total investment is Rs. 3 lakhs. B invested Rs. 50,000 more than A and C invested Rs. 25,000 less than B. If the profit at the end of the year was Rs.14,400, then what is C's share of the profit (in Rs.)?
Option 1: 3600
Option 2: 4800
Option 3: 6000
Option 4: 7200
Question : A started a business with a capital of Rs. 54,000 and admitted B and C after 4 months and 6 months, respectively. At the end of the year, the profit was divided among the three in the ratio 1 : 4 : 5. What is the sum (in Rs.) of the capital invested by B and C?
Option 1: 8,64,000
Option 2: 8,40,060
Option 3: 8,46,000
Option 4: 8,60,400
Question : If Rs.126.50 is divided among A, B and C in the ratio of 2 : 5 : 4 the share of B exceeds that of A by:
Option 1: Rs. 36.50
Option 2: Rs. 35.50
Option 3: Rs. 34.50
Option 4: Rs. 33.50
Question : A, B, and C made certain investments and the ratio of their time periods is 3 : 2 : 7 respectively. The ratio of the profits of A, B, and C is 4 : 3 : 14 respectively. What is the ratio of the investments of A, B, and C?
Option 1: 1 : 3 : 4
Option 2: 7 : 9 : 11
Option 3: 8 : 9 : 12
Option 4: 2 : 3 : 11
Question : A and B started a business partnership by investing in a ratio of 3 : 8. C joined them after 4 months with an amount equal to $\frac{3}{4}$th of B. What was their profit (in Rs.) at the end of the year if C got Rs. 24,000 as his share?
Option 1: 1,20,000
Option 2: 1,50,000
Option 3: 90,000
Option 4: 1,80,000
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