Question

There are two positive integers M and N. When M is divided by 289, the remainder is 192. When N is divided by 171 the quotient is same but the remainder is 169. Find the remainder when the sum of M and N is divided by 115.​

Answer 1

Let the quotient obtained in both the cases be n.

Let the quotient obtained in both the cases be n.X = 237 n + 192

Let the quotient obtained in both the cases be n.X = 237 n + 192Y = 117 n + 108

Let the quotient obtained in both the cases be n.X = 237 n + 192Y = 117 n + 108Adding both the equations,

Let the quotient obtained in both the cases be n.X = 237 n + 192Y = 117 n + 108Adding both the equations,X + Y = 354 n + 300

Let the quotient obtained in both the cases be n.X = 237 n + 192Y = 117 n + 108Adding both the equations,X + Y = 354 n + 300= 118 ( 3 n ) + 118 ( 2 ) + 64

Let the quotient obtained in both the cases be n.X = 237 n + 192Y = 117 n + 108Adding both the equations,X + Y = 354 n + 300= 118 ( 3 n ) + 118 ( 2 ) + 64=118 ( 3 n + 2 ) + 64.

Let the quotient obtained in both the cases be n.X = 237 n + 192Y = 117 n + 108Adding both the equations,X + Y = 354 n + 300= 118 ( 3 n ) + 118 ( 2 ) + 64=118 ( 3 n + 2 ) + 64.Therefore, the remainder obtained when sum of X & Y is divided by 118 is 64.

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