Question : Rs. 900 is divided among A, B, and C. The division is such that $\frac{1}{2}$ of A's money =$\frac{1}{3}$ of B's money =$\frac{1}{4}$ of C's money. Find the amounts (in Rs.) received by A, B, and C.
Option 1: 300, 400, and 200
Option 2: 350, 450, and 100
Option 3: 200, 300, and 400
Option 4: 400, 150, and 350
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Correct Answer: 200, 300, and 400
Solution :
Given: Rs. 900 is divided among A, B and C; the division is such that $\frac{1}{2}$ of A's money =$\frac{1}{3}$ of B's money =$\frac{1}{4}$ of C's money.
Let $\frac{1}{2}$ of A's money = $\frac{1}{3}$ of B's money = $\frac{1}{4}$ of C's money = k
Then A's money = 2k, B's money = 3k, and C's money = 4k
⇒ A : B : C = 2k : 3k : 4k = 2 : 3 : 4
Dividing Rs. 900 as per the ratio,
A will get = ($\frac{2}{2+3+4}$) × 900 = $\frac{2}{9}$ × 900 = Rs. 200
B will get = ($\frac{3}{2+3+4}$) × 900 = $\frac{3}{9}$ × 900 = Rs. 300
C will get = ($\frac{4}{2+3+4}$) × 900 = $\frac{4}{9}$ × 900 = Rs. 400
Hence, the correct answer is 200, 300, and 400.
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