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Question

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

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Solution

## Let the unit's digit in the number be x, then as product of digits is 12, the ten's digit in the number is=12x. Hence, the value of the number is 10×12x+x=120x+x On reversing the digits, unit's digit becomes ten's digit and ten's digit becomes unit's digit and its value will become=10x+12x It is apparent that (10x+12x)≥120x+x by 36 Hence, 10x+12x=120x+x+36 or 9x=120−12x+36 or 9x=108x+36dividing each term by 9 we get x=12x+4 multiply each byx to get x2=12+4xorx2−4x−12=0 i.e. x2−6x+2x−12=0orx(x−6)+2(x−6)=0 i.e. (x+2)(x−6)=0 Hence, x=−2 or x=6 As, we cannot have negative number in units place Hence, 6 is in unit's place and in ten's place we have 126=2 and number is 26

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