Profit share proportional to capitals (same duration): Rajan and Sajan invest ₹ 14,200 and ₹ 15,600, respectively, for the whole year. If the total profit is ₹ 74,500, find Rajan’s share.

Introduction / Context:
With equal investment periods, the profit share is simply proportional to the invested capitals. Compute Rajan’s fraction as his capital divided by the total capital, then multiply by the total profit to get his share.

Given Data / Assumptions:

• Rajan = ₹ 14,200; Sajan = ₹ 15,600.
• Total profit = ₹ 74,500.
• Duration is the same for both.

Concept / Approach:
Rajan’s fraction = 14,200 / (14,200 + 15,600) = 14,200 / 29,800 = 71 / 149. Multiply this by the total profit to get the exact amount.

Step-by-Step Solution:

Verification / Alternative check:
Sajan’s share = 74,500 − 35,500 = ₹ 39,000. The ratio 35,500 : 39,000 reduces to 71 : 78 = 14,200 : 15,600, confirming correctness.

Why Other Options Are Wrong:
₹ 39,600 and ₹ 39,000 refer to Sajan’s side or rounding errors; ₹ 35,000 and ₹ 36,000 do not match the precise fraction 71/149 applied to ₹ 74,500.

Common Pitfalls:
Approximating the fraction instead of using the exact division; losing precision leads to incorrect rupee amounts.

Final Answer:
₹ 35500