Shipping
Number Theory
Level
2
A merchant can place 8 large boxes or 10 small boxes into a carton for shipping. In one shipment, he sent a total of 96 boxes. If there are more large boxes than small boxes and the merchant must ship at least one small box, then how many cartons did he ship?
The answer is 11.
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Since we have 96 boxes and no. of big boxes >no. of small boxes ------(1)
Also there are some big boxes and small boxes. -------(2)
So no. of big boxes=multiple of 8
no. of small boxes=multiple of 10 (always result last digit as 0)
As per above facts, to have total 96 boxes we must have a multiple of 8 that have last digit as 6 which are 16 and 56 and 96.
If big boxes cartons are 2 (16 boxes) then small are of 8 (80 small boxes) --(3)
If big boxes cartons are 7 (56 boxes) then small are of 4 (40 small boxes) --(4)
If big boxes cartons are 12 (96 boxes) then small are of 0 (0 small boxes)---(5)
only (4) satisfy (1) and (2).
Hence total no. of cartons=7(big)+4(small)=11