Aman buys 52 coconuts, but some are lost on his way home. if he evenly divides the amount of coconuts he has left among four people, 3 coconuts are left. if he divides the coconuts among three people, 2 remain. and if he divides the coconuts among five people, he's left with 2 coconuts. how many coconuts did he lose on his way home?

5 coconuts

Step-by-step explanation:

If there were no loss , and 52 coconuts were distributed among 4 people, the number of coconuts each one would have obtained would be 13. Now as few coconuts are spoiled, the each one of those 4 people can get

1) 12 coconuts , and as per condition given there will be 3 more coconuts left. Hence total number of coconuts would be 12*4+3=48+3=51

Hence 1 coconuts would have been spoiled. Now let us see if this satisfies the second condition too.

If 51 coconuts are distributed equally among 3 people , each one gets 17 coconuts and none is left. But the condition says that 2 coconuts are left. Hence

Our assumption of loss of coconut was wrong.

2) 11 coconuts, as per condition given there will be 3 more coconuts left. Hence total number of coconuts would be 11*4+3=44+3=47

Hence 52-47=5 coconuts would have been spoiled. Now let us see if this satisfies the second condition too.

If 47 coconuts are distributed equally among 3 people , each one gets 15 coconuts and 2 coconuts are left. Hence it satisfies the second condition also. Let us see, if it satisfies third condition too.

If 47 coconuts are distributed among 5 people , each one gets, 9 cocnuts and coconuts left will be 2. Hence it satisfies the third condition also.

Hence , there were 5 coconuts spoiled.

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