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Question

A two digit number is such that the product of its digits is 12.When 36 is added to this number, the digits are interchanged.Find the number

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Solution

Let the units digit of the two-digit number be x

Since the product of its digits is 12, its ten's digit is 12x

the number is 10(12x)+x

On interchanging the digits, the number is 10x+12x

Given:120x+x+36=10x+12x

12012x+x10x+36=0

108x9x+36=0

12xx+4=0

x24x12=0

x26x+2x12=0

x(x6)+2(x6)=0

x=6 or x=2 but x being a digit of a number cannot be negative.

x=6

Units's digit=6 and ten's digit=126=2

Hence the required number is 26

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