A small number of cards has been lost from a complete pack. If I deal among four people, three cards remain. If I deal among three people, two remain and if I deal among five people, two cards remain. How many cards are there how do you get the answer there are 47 cards
Answers
Given: A small number of cards has been lost from a complete pack.
To find : How many cards are there in Pack
Solution:
Let say n number of cards are lost
cards available = 52 - n
If deal among four people, three cards remain.
=> 4k + 3 = 52 - n
=> n = 52 - 4k - 3
=> n = 52 - 4k - 4 + 1
=> n = 4(12 - k) + 1
n = 1 , 5 , 9 , 13 ,
If I deal among three people, two remain
=> 3k + 2 = 52 - n
=> n = 52 - 3k - 2
=> n = 3(17 - k) - 1
=> n = 2 , 5 , 8 , 11 ,14
d if I deal among five people, two cards remain.
=> 5k + 2 = 52 - n
=> n = 5(10 - k)
=> n = 5 , 10 , 15
Common in all is 5
Hence 5 Cards were removed
remaining cards = 52 - 5 = 47
47 card are there in pack
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