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Question

# A stationery store sells pack of pens, each pack having 45 pens. He wants to pack 100,978 pens in similiar way. How much pens would be left?

A
43
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B
34
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C
42
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Solution

## The correct option is A 43Concept: A number, divisible by 45, is also divisible by 5 and 9 because 45 is product of two co-prime numbers 5 and 9. Given that the store sells pack of pens, each pack having 45 pens. We need to find the greatest number of pens less than 100,978 that is completely divisible by 45. Its sum of digits is 25 and last digit is 8, hence on adding 2, the number would be divisible by both 5 and 9. But, we can't add more pens hence to make the number divisible by 45, we need to subtract 43 from it. ∵100,978−43=100,935 100,935 pens can be packed in the way the storekeeper wants. 43 pens would be left.

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