Question : Rs. 13000 is divided among X, Y, and Z such that 2 times X's share is equal to 3 times Y's share which is equal to 4 times Z's share. What is the share of Y?
Option 1: Rs. 3200
Option 2: Rs. 4800
Option 3: Rs. 5600
Option 4: Rs. 4000
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Correct Answer: Rs. 4000
Solution :
Let $2X = 3Y = 4Z = k$
$X =\frac{k}{2}, Y = \frac{k}{3}, Z = \frac{k}{4}$
The sum of shares of all of them together = 13000
⇒ $\frac{k}{2} + \frac{k}{3} + \frac{k}{4} = 13000$
⇒ $\frac{6k+4k+3k}{12}=13000$
⇒ $\frac{13k}{12}=13000$
⇒ $k = 12000$
$\therefore$ Share of $Y = \frac{1}{3}\times 12000=4000$
Hence, the correct answer is Rs. 4000.
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