Question : Rs. 782 is divided into three parts in the ratio $\frac{1}{2}:\frac{2}{3}:\frac{3}{4}$. The first part is:
Option 1: Rs. 182
Option 2: Rs. 204
Option 3: Rs. 190
Option 4: Rs. 196
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Correct Answer: Rs. 204
Solution :
Given ratio = $\frac{1}{2} : \frac{2}{3} : \frac{3}{4}$
LCM of 2, 3 and 4 = 12
Now, multiplying all ratios by 12, we get,
$(\frac{1}{2} × 12) : (\frac{2}{3} × 12) : (\frac{3}{4} × 12)$
$=6 : 8 : 9$
The sum of the terms of the ratio = 6 + 8 + 9 = 23
$\therefore$ 1st part $=\frac{6}{23} × 782 = 204$
Hence, the correct answer is Rs. 204.
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