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

Answer :

Given  : An army commander arranged to transport his battalion of soldiers he considered 30 seater,40 seater, 50 seaters buses.In all three cases he found that 10 seats were left vacant.

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 $\times$ 5 $\times$ 5
So,

LCM ( 30 , 40  and 50 ) =  2 $\times$ 2 $\times$ 2 $\times$ 3 $\times$ 5 $\times$ 5 =  600

So,

The smallest number of soldiers in his battalion =  600 - 10  = 590                                        ( Ams )