Question : A, B, and C together invest INR 53,000 in a business. A invests INR 5,000 more than B and B invests INR 6,000 more than C. Out of a total profit of INR 31,800, find the share of A.
Option 1: INR 12,800
Option 2: INR 12,500
Option 3: INR 13,500
Option 4: INR 13,800
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Correct Answer: INR 13,800
Solution :
Given: A, B, and C together invest INR 53,000 in a business.
A invests INR 5,000 more than B and B invests INR 6,000 more than C.
The investment ratio and the profit ratio are directly proportionate in the absence of time.
Let the C's investment be INR $x$.
The investment of B = $x$ + 6000.
The investment of A = $x$ + 6000 + 5000.
According to the question,
$x+x+6000+x+6000+5000=53000$
⇒ $3x+17000=53000$
⇒ $3x=53000–17000$
⇒ $3x=36000$
⇒ $x=$ INR 12,000
The investment of A = 12000 + 6000 + 5000 = INR 23,000.
The investment of B = 12000 + 6000 = INR 18,000.
The investment of C = INR 12,000.
The ratio of the investment of A, B, and C = 23000: 18000: 12000 = 23 : 18 : 12.
The share of A = = $\frac{23}{23+18+12}\times 31800$.
= $\frac{23}{53}\times 31800=23\times 600=$ INR 13,800
Hence, the correct answer is INR 13,800.
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