A two digit number is such that the product of its digit is 14.

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asked Feb 8 in Class X Maths by priya12 (-11,078 points)

A two digit number is such that the product of its digit is 14. When 45 is added to the number, then the digit interchange their places. Find the number.

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answered Feb 8 by aditya23 (-151 points)

Let the ten’s digit be x, then unit’s digits = (14/x)

Then, the number is (10x + 14/x)

When 45 is added to the number, the digits get interchanged.

∴    10x + 14/x + 45 = 10 × 14/x + x

⇒  x2 + 5x – 14 = 0

⇒ (x+ 7)(x – 2) = 0

⇒ x = 2

And  x = - 7 (inadmissible)

Hence, the number is (10x + 14/x)

= (10 × 2 + 14/2)

= 27

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