Question
- A and B put in Rs 300 and Rs 400 respectively into a business. A reinvests into the business his share of the first year’s profit of Rs 210 whereas B does not. In what ratio should they divide the second year’s profit?
Answer: Option C
To determine the ratio in which A and B should divide the second year's profit, we need to calculate their respective investments in the business after the reinvestment of A's share of the first year's profit.
Here are the steps to determine the correct ratio:
Summary:
A invested Rs 300, B invested Rs 400, Total investment = Rs 700First year's profit was Rs 210, A's share of the profit was Rs 90A reinvested his share of the first year's profit, A's investment after reinvestment = Rs 390, B's investment remained Rs 400Total investment after reinvestment = Rs 790Second year's profit was Rs X, A's share = 39/79 * X, B's share = 40/79 * XCorrect ratio = 39:40 (Option C)
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To determine the ratio in which A and B should divide the second year's profit, we need to calculate their respective investments in the business after the reinvestment of A's share of the first year's profit.
Here are the steps to determine the correct ratio:
- A and B's initial investments:
- A invested Rs 300
- B invested Rs 400
- Total investment = Rs 300 + Rs 400 = Rs 700
- The first year's profit:
- The first year's profit was Rs 210
- A's share of the profit = (Rs 300 / Rs 700) * Rs 210 = Rs 90
- A's reinvestment:
- A reinvested his share of the first year's profit, i.e., Rs 90
- A's total investment after reinvestment = Rs 300 + Rs 90 = Rs 390
- B's total investment:
- B did not reinvest his share of the first year's profit
- B's total investment remains Rs 400
- Total investment after reinvestment:
- Total investment after reinvestment = A's investment + B's investment
- Second year's profit:
- Let's assume the second year's profit was Rs X
- A's share of the second year's profit = (A's investment / Total investment) * X
- B's share of the second year's profit = (B's investment / Total investment) * X
Summary:
A invested Rs 300, B invested Rs 400, Total investment = Rs 700First year's profit was Rs 210, A's share of the profit was Rs 90A reinvested his share of the first year's profit, A's investment after reinvestment = Rs 390, B's investment remained Rs 400Total investment after reinvestment = Rs 790Second year's profit was Rs X, A's share = 39/79 * X, B's share = 40/79 * XCorrect ratio = 39:40 (Option C)
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A's profit=3/7*210=90
Second year capital ratio=390:400
39:40
3: 4
A = 3/7*210 = 90
390: 400
39:40
So, ratio of their investment
= A : B = 300 : 400 = 3 : 4.
At the end of the 1 year, they get profit of Rs 210, then
A’s share = (3/7)× 210 = 90.
Thus, after one year A’s share = Rs 90.
For second year,
A’s investment = (300+90) = Rs 390 and
B’s investment = Rs. 400.
∴ Ratio of their investment
= 390 : 400
= 39 : 40.
Hence option A is correct answer.
So, ratio of their investment
= A : B = 300 : 400 = 3 : 4.
At the end of the 1 year, they get profit of Rs 210, then
A’s share = × 210 = 90.
Thus, after one year A’s share = Rs 90.
For second year,
A’s investment = (300+90) = Rs 390 and
B’s investment = Rs. 400.
∴ Ratio of their investment
= 390 : 400
= 39 : 40.
Hence option A is correct answer.
3. : 4
Total first yr profit =210/7=30
A first year profit= 30*3=90
A second year 300+90=390
A:B second year 390:400=39:40