Question

A two dogit number is such that the product of its digits is 12.if 36 is added to the number, its digit are reversed.what is that number?

Answer 1

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Number is 26

Explanation:

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 is greater than 120x+x by 36

Hence 10x+12x=120x+x+36

or 9x=120−12x+36

or 9x=108x+36 and dividing each term by 9 we get

x=12x+4 and now multiply each by x to get

x2=12+4x or x2−4x−12=0

i.e. x2−6x+2x−12=0

or x(x−6)+2(x−6)=0

i.e. (x+2)(x−6)=0

Hence, x=−2 or x=6

But 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

Regards ♡♡《 Nitish kr 》♡♡