Question : A teacher distributes some sweets among his four students in the ratio of $\frac{1}{3}: \frac{1}{5}: \frac{1}{6}: \frac{1}{4}$. What is the minimum number of sweets that the teacher should have so that no sweets need to be broken into parts to be shared?
Option 1: 57
Option 2: 77
Option 3: 76
Option 4: 71
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Correct Answer: 57
Solution :
The ratio of distribution among students = $\frac{1}{3}: \frac{1}{5}: \frac{1}{6}: \frac{1}{4}$
We first convert the fraction ratio into a whole number ratio
$\because$ LCM of denominators 3, 4, 5, 6 is 60, we multiply the ratio by 60.
To convert the fractional ratio into a whole number ratio, multiply each term with LCM of denominators.
On rearranging, the ratio = $(\frac{60}{3}) : (\frac{60}{5}) : (\frac{60}{6}) : (\frac{60}{4})$ = 20 : 12 : 10 : 15
Considering that sweets are distributed in whole numbers, the minimum number of sweets can be when the common ratio is 1.
= The minimum number of sweets = 20 + 12 + 10 + 15 = 57
$\therefore$ The minimum number of sweets the teacher should have, to do this distribution is 57.
Hence, the correct answer is 57.
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