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Question

When a natural number X is divided by 5 ,the remainder is 2. When a natural number Y is divided by 5,the remainder is 4, the remainder is Z when X+Y is divided by 5.The value of 2z/3-5/3


Solution

Let q1  be the quotient when X is divided by 5

therefore X = 5q1  +  2

let q2 be the quotient when Y is divided by 5

therefore, Y = 5q2  + 4

X + Y = 5q1 + 5q2 +6

on dividing X+Y by 5 i.e. (5q1+5q2+6)/5  we get  (q1 + q2 + 1)  as quotient and  1 as reminder 

hence z=1
Therefore,  2z/3 - 5/3  =  2*1/3 - 5/3  = 2/3 -5/3 = -3/3 = -1 Ans.

 

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