A, B and C invest in a business in the ratio 3 : 4 : 5. The percentages of return on their investments are in the ratio 6 : 5 : 4 respectively. If B's earnings are Rs. 250 more than A's earnings, what is the total amount of earnings of A, B and C together?

Introduction / Context:
This problem involves partners who invest in a business with different capital contributions and different percentage returns. Earnings for each partner depend on both their investment and their individual return percentage. The question asks for the total of all three earnings, given the difference between two of them. It is a good example of combining ratios multiplicatively.

Given Data / Assumptions:

• Investment ratio of A : B : C = 3 : 4 : 5.
• Percentage return ratio of A : B : C = 6 : 5 : 4.
• B's earnings exceed A's earnings by Rs. 250.
• We must find the total earnings of A, B and C combined.

Concept / Approach:
Earnings of each partner are proportional to investment multiplied by percentage return. Thus, earnings are in the ratio (3 * 6) : (4 * 5) : (5 * 4). Once this combined ratio is known, the difference between B and A in this ratio can be matched to Rs. 250 to find the value of one ratio unit. Multiplying each ratio term by this unit gives individual earnings, and their sum gives the total earnings.

Step-by-Step Solution:
Step 1: Earnings are proportional to investment * return percentage.Step 2: Earnings ratio for A : B : C = 3 * 6 : 4 * 5 : 5 * 4 = 18 : 20 : 20.Step 3: Let the common earning unit be k. Then A earns 18k, B earns 20k, and C earns 20k.Step 4: B's earnings exceed A's by 20k - 18k = 2k, and this equals Rs. 250.Step 5: Therefore 2k = 250, so k = 125.Step 6: Earnings of A = 18k = 18 * 125 = Rs. 2250.Step 7: Earnings of B = 20k = 20 * 125 = Rs. 2500.Step 8: Earnings of C = 20k = 20 * 125 = Rs. 2500.Step 9: Total earnings = 2250 + 2500 + 2500 = Rs. 7250.

Verification / Alternative check:
Difference between B and A = 2500 - 2250 = Rs. 250, which matches the given condition.The ratio of A : B : C earnings is 2250 : 2500 : 2500. Dividing by 125 gives 18 : 20 : 20, confirming the combined ratio is correct.

Why Other Options Are Wrong:
Totals such as Rs. 6000 or Rs. 5000 would correspond to different values of k and therefore different earnings differences between A and B. Rs. 6500 also fails to produce a Rs. 250 difference between B and A when split in the ratio 18 : 20 : 20. Only Rs. 7250 ensures both the correct ratio and the Rs. 250 difference.

Common Pitfalls:
Some learners mistakenly add the ratios 3 : 4 : 5 and 6 : 5 : 4 instead of multiplying them term by term. Others equate the investment ratio alone to earnings and ignore the different return percentages. Remembering that earnings depend on both factors and treating them multiplicatively is the key insight.

Final Answer:
The total earnings of A, B and C together amount to Rs. 7250.