Question

When an army commander arranged to transport his battalion of soldiers, he considered $30-$ seater, $40-$ seater, and $50$-seater buses. In all three cases, he found that $10$ seats were left vacant. What is the smallest number of soldiers in his battalion?

• A. $600$
• B. $590$
• C. $610$
• D. $580$

Answer 1

Answer: (B)

$590$

To find the smallest number of soldiers in his battalion , We find LCM of these numbers :

$30=2\times 3\times 5$

$40=2\times 2\times 2\times 5$

and $50 = 2 × 5 × 5$

So,

$LCM(30,40and50)=2\times 2\times 2\times 3\times 5\times 5=600$

So,

The smallest number of soldiers in his battalion $=600-10=590$