Question

Certain number when successively divided by 3, 4 and 5 leaves remainders 1, 2 and 3 respectively. When the same number be divided by 4, what is the remainder ?

Answer 1

Answer:

3

Step-by-step explanation:

for successive division we slove

3,4,5 leaves remainder 1,2,3

so first add divisor 5+ remainder 3 = 8

8*4 divisor =32

next 32+2remainder = 34

34*3divisor =102

102+1remainder =103

so certain number is 103 when divide by 4 it leaves remainder 3

Answer 2

Given :  Certain number when successively divided by 3, 4 and 5 leaves remainders 1, 2 and 3 respectively.  

To Find : When the same number be divided by 4, what is the remainder ?

Solution:

N = 3A + 1

A = 4B + 2

B = 5C + 3

=> A = 4(5C + 3) + 2

=> A = 20C + 12 + 2

=> A = 20C + 14

N = 3A + 1

=> N = 3(20C + 14) + 1

=> N = 60C + 42 + 1

=> N = 60C + 43

=> N = 60C + 40 + 3

=> N = 4(15C + 10) + 3

=> N = 4K + 3

Remainder = 3 when divided by 4

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