A profit of Rs 12,400 has to be divided among three partners A, B and C in the ratio 5 : 7 : 8. How much money, in rupees, does partner B receive?

Introduction / Context:
This is a direct application of ratios in distributing a given total amount among three partners. The total profit and the ratio of shares are known, and we are asked to find the numerical share of one particular partner, B. Such problems are common in partnership and ratio topics in aptitude exams.

Given Data / Assumptions:

• Total profit to be distributed = Rs 12,400.
• Ratio of shares of A : B : C = 5 : 7 : 8.
• We assume the entire profit is distributed with no remainder.
• We need the exact amount received by B.

Concept / Approach:
If three quantities are in ratio a : b : c and their sum is S, then each quantity is given by (a / (a + b + c)) * S, (b / (a + b + c)) * S and (c / (a + b + c)) * S respectively. Here, a = 5, b = 7 and c = 8. We first find the sum of the ratio numbers, then compute B share as (7 / total parts) multiplied by 12400.

Step-by-Step Solution:
Ratio of shares A : B : C = 5 : 7 : 8. Total number of ratio parts = 5 + 7 + 8 = 20. Total profit = Rs 12,400. Share of B = (7 / 20) * 12,400. Compute (1 / 20) of 12,400: this is 12,400 / 20 = 620. So B share = 7 * 620 = 4340. Therefore, B receives Rs 4340.

Verification / Alternative check:
We can also compute the shares of A and C to verify the entire distribution. A share = (5 / 20) * 12,400 = 5 * 620 = 3100. C share = (8 / 20) * 12,400 = 8 * 620 = 4960. The sum of all three shares is 3100 + 4340 + 4960 = 12,400, which matches the total profit given, thus confirming that B share is correctly calculated as Rs 4340.

Why Other Options Are Wrong:
3440, 3340, 4430 and 3740 do not match (7 / 20) of 12,400. If any of these values were used instead of 4340, the total of the three shares would not equal Rs 12,400 when keeping the same ratio 5 : 7 : 8.

Common Pitfalls:
A frequent mistake is to divide 12,400 directly by 7 or to forget to sum the ratio numbers first. Another error is to miscalculate (7 / 20) of 12,400 due to arithmetic slips. Carefully adding the ratio parts and working step by step through the fraction helps avoid such errors.

Final Answer:
Partner B receives Rs 4340.