Question

There are 3 different types of rice weighing \(435,\ 493,\) and \(551\) kg respectively. The rice is packed in bags so that no two types are mixed and all bags are of equal size. Find the least number of bags.}

• A. 51
• B. 56
• C. 57
• D. 54

Hint:

“Least number of equal bags’’ \(\Rightarrow\) take the \(\gcd\) as bag size, then sum the quotients.

Answer 1

The Correct Option is A

Step 1: Largest possible bag size
Equal bag size must divide each heap \(\Rightarrow\) use \(\gcd(435,493,551)\).
\(\gcd(435,493)=\gcd(435,58)=\gcd(58,29)=29\). Also \(551=29\times 19\) \(\Rightarrow\) \(\gcd=29\ \text{kg}\).
Step 2: Number of bags
Bags \(=\dfrac{435}{29}+\dfrac{493}{29}+\dfrac{551}{29}=15+17+19=51\).
\[ \boxed{51} \]