A profit of Rs 7,28,000 has to be shared among three partners Amir, Balaraj and Charan in the ratio 7 : 5 : 4. How much money (in rupees) does Charan receive as his share of the profit?

Introduction / Context:
This is a straightforward partnership and ratio distribution problem. When a total profit or amount is shared according to a given ratio, each partner’s share is determined by the proportion of their ratio part to the sum of all parts. Such questions are common in business mathematics and basic quantitative aptitude sections.

Given Data / Assumptions:

• Total profit to be shared = Rs 7,28,000.
• Ratio of shares Amir : Balaraj : Charan = 7 : 5 : 4.
• We need Charan’s share of the profit.

Concept / Approach:
If a total T is divided in the ratio a : b : c, then:

• Total number of ratio parts = a + b + c.
• Each person’s share = (their ratio part / total ratio parts) * T.

Here, Charan’s ratio part is 4 and the total ratio parts are 7 + 5 + 4. We use this to compute Charan’s share directly.

Step-by-Step Solution:
Total profit T = Rs 7,28,000. Ratio of shares: Amir : Balaraj : Charan = 7 : 5 : 4. Total ratio parts = 7 + 5 + 4 = 16. Charan’s ratio part = 4. Charan’s share = (4 / 16) * 7,28,000. 4 / 16 = 1 / 4. Charan’s share = (1 / 4) * 7,28,000. Charan’s share = 7,28,000 / 4 = 1,82,000. Therefore, Charan receives Rs 1,82,000.

Verification / Alternative check:
We can also compute shares of Amir and Balaraj to check:

• One ratio part = total profit / 16 = 7,28,000 / 16 = 45,500.
• Amir’s share = 7 * 45,500 = 3,18,500.
• Balaraj’s share = 5 * 45,500 = 2,27,500.
• Charan’s share = 4 * 45,500 = 1,82,000.
• Total = 3,18,500 + 2,27,500 + 1,82,000 = 7,28,000.

The sum matches the total profit, so the distribution is correct.

Why Other Options Are Wrong:
Values like 2,27,500 or 3,18,500 belong to other partners. Rs 91,000 or 1,75,000 do not maintain the correct ratio when combined with other possible shares. Only Rs 1,82,000 is consistent with Charan’s ratio part of 4 out of 16 and sums correctly with the other partners’ shares to the total profit.

Common Pitfalls:
Some learners divide by 3 instead of the sum of the ratio parts or mistakenly assign the largest share to the smallest ratio. Others may compute parts correctly but miscalculate multiplication with the ratio numbers. Always sum the ratio components first, then calculate the value of one part, and finally multiply by each person’s ratio number to get individual shares.

Final Answer:
Charan receives Rs 1,82,000 as his share of the profit.