Question : A, B, and C subscribe a sum of Rs. 75,500 for a business. A subscribes Rs. 3,500 more than B, and B subscribes Rs. 4,500 more than C. Out of a total profit of Rs. 45,300, how much (in Rs.) does A receive?
Option 1: 17,400
Option 2: 14,700
Option 3: 12,600
Option 4: 15,000
Correct Answer: 17,400
Solution :
Given,
Total investment = Rs. 75,500
Profit = Rs. 45,300
We know,
Profit is divided in the ratio of (investment × time)
Let $x$ be the investment of C.
⇒ C = $x$ ...........(1)
⇒ B = $(x + 4500)$ ..........(2)
And, A = $(x + 4500 + 3500)$ ...........(3)
We know that,
$x + (x + 4500) + (x + 4500 + 3500) = 75500$
⇒ $x + (x + 4500) + (x + 8000) = 75500$
⇒ $3x + 12500 = 75500$
⇒ $3x = 63000$
⇒ $x = 21000$
Put the value of x in equations 1, 2, and 3, we get,
A = 29000
B = 25500
C = 21000
⇒ Ratio of Profit = 29000: 25500: 21000 = 58 : 51 : 42
$\therefore$ A’s share = $\frac{58}{58 + 51 + 42} × 45300=17400$
Hence, the correct answer is 17,400.
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