Question

The sum of a number of two digit and the number formed by reversing the digit is 110,and the difference of the digits is 6. Find the number​

Answer 1

Step-by-step explanation:

Let the tens place digit of the number be x and unit's place digit be y

Therefore,

Required number = 10x + y

On reversing the digits

New number = 10y + x

Now,

According to the first condition:

10x + y + 10y + x = 110

$\implies \: 11x + 11y = 110 \\ \implies 11(x + y) = 110 \\ \implies x + y = \frac{110}{11} \\ \implies x + y = 10.....(1) \\ according \: to \: the \: second \: condition : \\ x - y = 6.....(2) \\ adding \: equations \: (1) \: and \: (2) \: we \: find : \\ x + y = 10 \\ x - y = 6 \\ - - - - - - \\ 2x = 16 \\ \implies \: x = \frac{16}{2} \\ \implies \: \huge \fbox{x = 8} \\ substituting \: x = 8 \: in \: equation \: (1) \\ 8 + y = 10 \\ \implies \: y = 10 - 8 \\ \implies \: \huge \fbox{y = 2} \\ \therefore \: 10x + y = 10 \times 8 + 2 \\ = 80 + 2 = \huge \fbox{82} \\ thus \: the \: required \: number \: is \: 82.$