Question

During a flood relief programme, food
packets were air dropped in lots of equal
size from 3 different aircrafts containing
250, 490 and 850 packets. In each aircraft
same number of damaged packets remained
undropped. If the number of lots has to be
minimum, and the number of damaged
packets is less than the lot size, then how
many lots were dropped in all?
(a) 3 (b) 7 (c) 11
(d) 13​

Answer 1

Given :   food  packets were air dropped in lots of equal  size from 3 different aircrafts containing  250, 490 and 850 packets. In each aircraft

same number of damaged packets remained  undropped

To Find  : how  many lots were dropped in all

Solution:

Let say lot size = L

and Damaged packet = r

250 = aL + r

490 = bL  + r

850 = cL + r

=> 240 = ( b - a) L

    360 = (c - b) L

    600 = ( c - a) L  

120 is the  HCF

120 is the maximum lot size   with damaged product  =   10  

250  =  120 x 2  + 10

490 =   120 x 4 + 10

850 =   120 x 7 + 10

Number of Lots = 2 + 4 + 7 = 13

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