Question

An army commander arranged for transporting his battalion of soldiers,he considered 30 seater,40 seater and 50 seater busses.In all 3 cases he found 10 were lwft vacant.what is the smallwst number of soldier's in his batallion

Answer 1

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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 × 3 ×5 

40 = 2 × 2 × 2 × 5
And
50 = 2 × 5 × 5
So,

LCM ( 30 , 40  and 50 ) =  2 × 2 × 2 × 3 × 5 ×5 =  600

So,

The smallest number of soldiers in his battalion =  600 - 10  = 590                                        ( Ans )
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Answer 2

Answer:

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

30 =  2 × 3 ×5 

40 = 2 × 2 × 2 × 5

And

50 = 2 × 5 × 5

So,

LCM ( 30 , 40  and 50 ) =  2 × 2 × 2 × 3 × 5 ×5 =  600

So,

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