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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
A two digit number is such that the product of its digits is 12. If 36 is added to the number, the digits
interchange their places. What is the number?
Solution
Let the two-digit number be 10x + y,
where x = tens digit, y = units digit.
Step 1: Product condition
x × y = 12 … (1)
Step 2: Interchange condition
If digits interchange, new number = 10y + x
Given: (10x + y) + 36 = (10y + x)
⇒ 9x – 9y = –36
⇒ x – y = –4 … (2)
Step 3: Solve equations
From (2): x = y – 4
Put in (1): (y – 4) × y = 12
⇒ y² – 4y – 12 = 0
⇒ (y – 6)(y + 2) = 0
⇒ y = 6 (since digit can’t be –2)
Then x = y – 4 = 2
Number = 10x + y = 10×2 + 6 = 26
✅ Final Answer: The number is 26.
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