When X is divided by 237, the remainder is 192. When Y is divided by 117, the quotient is the same but the remainder is 108. The remainder when the sum of X and Y is divided by 118 is ?

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Solution

Let the quotient obtained in both the cases be n.

X = 237 n + 192
Y = 117 n + 108

Adding 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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When X is divided by 237, the remainder is 192. When Y is divided by 117, the quotient is the same but the remainder is 108. The remainder when the sum of X and Y is divided by 118 is ?

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

Let the quotient obtained in both the cases be n.

X = 237 n + 192
Y = 117 n + 108

Adding 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.