Question : If 177 is divided into 3 parts in the ratio of $\frac{1}{2}:\frac{2}{3}:\frac{4}{5}$, then the second part is:
Option 1: 75
Option 2: 45
Option 3: 72
Option 4: 60
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Correct Answer: 60
Solution :
Given ratio: $\frac{1}{2}:\frac{2}{3}:\frac{4}{5}$
LCM of 2, 3 and 5 = 30
Multiplying all ratios by 30, we get,
$(\frac{1}{2} × 30) : (\frac{2}{3} × 30) : (\frac{4}{5} × 30)$
$=15 : 20 : 24$
The sum of the terms of the ratio = 15 + 20 + 24 = 59
$\therefore$ The second part $= \frac{20}{59} × 177 = 60$
Hence, the correct answer is 60.
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