Question

There was a coconut farmer, he told his helper to arrange the harvest and count the no. of coconuts.
After a while the helper said
When I arrange it in 2 there is one coconut left.
When I arrange it in 3 there is one coconut left.
When I arrange it in 4 there is one coconut left.
When I arrange it in 5 there is one coconut left.
When I arrange it in 6 there is one coconut left.
When I arrange it in 7 there are no coconut left.

How many coconuts were there?​

Answer 1

Given :  a coconut farmer to arrange coconuts  

To find : Number of coconuts

Solution:

Let say number of coconuts  = C

C = 2a + 1

C = 3b + 1

C = 4c + 1

C = 5d + 1

C = 6e + 1

C = 7n

C - 1 = 2a = 3b = 4c = 5d = 6e

LCM of 2 , 3 , 4 , 5 & 6  =  60

=> C - 1  = 60K

=> C = 60K + 1

60K + 1   = 7n

=> 7*8K + 4K + 1 = 7n

=> 4K + 1 = 7 (n - 8K)

4K + 1 = 7f

=> f = 3   & K = 5

=> 4*5 + 1 = 7 (n - 8*5)

=> 21 = 7(n - 40)

=> 3 = n - 40

=> n = 43

C = 60K + 1    or 7n

C = 60*5 + 1   or 7 * 43

=> C = 301

301 = 2 *150 + 1

301 = 3 * 100 + 1

301 = 4 * 75 + 1

301 = 5 * 60 + 1

301 = 6 * 50 + 1

301 = 7 * 43

301 Coconuts were there

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