When a positive integer X is divided by Y, the quotient is 11 and the remainder is 5. When X is divided by (Y + 3) the quotient is 9 and the remainder is 2. What is the value of X?

Question: When a positive integer X is divided by Y, the quotient is 11 and the remainder is 5. When X is divided by (Y + 3) the quotient is 9 and the remainder is 2. What is the value of X?

Solution:
Given that,
When X is divided by Y. Then we get,
X = 11Y + 5 .......(1)

And,
When X is divided by Y + 3. Then we get,
X = 9(Y + 3) + 2 = 9Y + 27 + 2 = 9Y + 29.......(2)

From (1) and (2), Then we get,
⇒ 11Y + 5 = 9Y + 29
⇒ 11Y - 9Y = 29 - 5
⇒ 2Y = 24
⇒ Y = 24/2
∴ Y = 12

From (1),
X = 11Y + 5 = (11 × 12) + 5 = 132 + 5 = 137

So the value of X is 137.