In a business, A and C invested amounts in the ratio 2 : 1, while the ratio between the amounts invested by A and B was 3 : 2. If the total profit from the business is Rs. 1,57,300, how much amount does B receive as his share of the profit?

Introduction / Context:
This is a partnership question where the ratios between investments are given indirectly. Instead of direct amounts, we know how A relates to B and C. The goal is to determine each partner's relative capital contribution and then use the total profit to compute the exact amount received by B.

Given Data / Assumptions:

• The ratio of investments A : C is 2 : 1.
• The ratio of investments A : B is 3 : 2.
• Total profit from the business is Rs. 1,57,300.
• We need to find B's share of this profit.
• All partners remain in the business for the same period, so only capital ratios matter.

Concept / Approach:
When multiple ratios involving the same person are given, we can combine them to get a single three person ratio. The standard method is to express the common person's investment in a way that matches in both ratios and then deduce the other amounts. Once we know A : B : C, profit is distributed in that same ratio, because time of investment is equal for all partners.

Step-by-Step Solution:
Step 1: Let investments be A, B and C. Step 2: From A : C = 2 : 1, we can write A = 2k and C = k for some k. Step 3: From A : B = 3 : 2, we can write A = 3m and B = 2m for some m. Step 4: Since both expressions represent A, set 2k = 3m. Step 5: Choose convenient values that satisfy this, for example k = 3 and m = 2, giving A = 6. Step 6: Then B = 2m = 4 and C = k = 3. So A : B : C = 6 : 4 : 3. Step 7: Sum of ratio parts = 6 + 4 + 3 = 13. Step 8: B's fractional share of profit = 4 / 13. Step 9: Total profit is Rs. 1,57,300, so B's share = (4 / 13) * 1,57,300. Step 10: Compute this: 1,57,300 / 13 = 12,100 and 12,100 * 4 = 48,400.

Verification / Alternative check:
If B receives Rs. 48,400, then each ratio part is worth 1,57,300 / 13 = Rs. 12,100. A receives 6 parts = 6 * 12,100 = Rs. 72,600. C receives 3 parts = 3 * 12,100 = Rs. 36,300. Adding all three shares gives 72,600 + 48,400 + 36,300 = Rs. 1,57,300, which matches the total profit stated in the question. The ratio between their shares is 72,600 : 48,400 : 36,300 which simplifies to 6 : 4 : 3, consistent with our derived investment ratio.

Why Other Options Are Wrong:
Rs. 54,200, Rs. 64,000 and Rs. 74,000 do not correspond to the correct fraction 4 / 13 of the total profit. Using any of these values breaks the total profit sum or the A : B : C ratio, so they cannot be correct.

Common Pitfalls:
A frequent error is to try to combine the ratios by simple addition or subtraction instead of matching the common term. Another common mistake is to forget to include the third partner when distributing profit, which leads to wrong denominators for the fractions. Always derive a clean three term ratio first and then apply it to the total profit.

Final Answer:
The amount received by B as his share of profit is Rs. 48,400.