Explanation:

Suppose N=5x+1

A took (x+1) biscuit.


Now 4x is of the form 5y+1 then x must be in the form 5z+4

⇒4(5z+4)=5y+1

⇒y=4z+3 and x=5z+4

The ratio of number of biscuits that A and B took is



[(5z+4)+1]:[(4z+3)+1]=5:4



So, we can say that any two successive persons A, B, C and D take coins in the ratio of 5:4

Let the number of biscuits that A, B, C and D took be a, b, c and d respectively.




a:b=b:c=c:d=5:4

a:b:c:d=125:100:80:64

⇒a=125k

⇒x=125k−1 and N=5x+1=625k−4



As, N>1000, the least value of N is when k=2

⇒N= 1246