Question 23

Logical Reasoning Ratio and Proportion Easy

In a business, \( A \) and \( C \) invested amounts in the ratio \( 2: 1 \) , whereas the ratio between amounts invested by \( A \) and B was \( 3: 2 \) . IfRs. \( 1,57,300 \) was their profit, how much amount did \( B \) receive?

(A) Rs. 24,200
(B) Rs. 72,600
(C) Rs. 36,300
(D) Rs. 48,400
✓ Correct Answer: Option D Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

  1. Combine the Investment Ratios:

    We are given two separate ratios, A:C = 2:1 and A:B = 3:2. To find B's share, we first need to combine them into a single ratio of A:B:C. We do this by finding a common value for the shared term, A.

    • The least common multiple of A's parts (2 and 3) is 6.
    • To make A's part 6 in the first ratio, we multiply by 3: A:C = (2*3):(1*3) = 6:3
    • To make A's part 6 in the second ratio, we multiply by 2: A:B = (3*2):(2*2) = 6:4

    Now we can write the full combined ratio: A:B:C = 6:4:3.

  2. Calculate the Total Ratio Parts:

    We sum the parts of the combined ratio to find the total number of profit shares.

    6 + 4 + 3 = 13 parts
  3. Calculate B's Share of the Profit:

    B's share of the profit is proportional to their ratio part (4) out of the total parts (13). The total profit is ₹1,57,300.

    B's Amount = (4 / 13) * 1,57,300 B's Amount = 4 * 12,100 B's Amount = 48,400

Final Answer: The amount B received is Rs. 48,400.

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