Question

The sum of the digits of a two digit number is 14. If the number formed by reversing the digits is
less than the original number by 18. Find the original number.
​

Answer 1

EXPLANATION.

Let the digital at tens place be = x

Let the digit at unit place be = y

original number = 10x + y

reversing number = 10y + x

The sum of the digit of a two digit

number is = 14.

=> x + y = 14 ......(1)

If the number formed by reversing the

digit is less than the original number

by 18.

=> 10y + x = 10x + y - 18

=> 9y - 9x = -18

=> y - x = -2 ......(2)

From equation (1) and (2) we get,

=> 2y = 12

=> y = 6

put the value of y = 6 in equation (1)

we get,

=> x + 6 = 14

=> x = 8

Therefore,

original number = 10x + y = 10(8) + 6 = 86.

Answer 2

Given :-

• The sum of the digits of a two digit number is 14.

• The number formed by reversing the digits is less than the original number by 18.

To Find :-

• Original Number.

Solution :-

☯️ Let,

Digit at Ten's Place = x.

Digit at One's Place = y.

Original Number :- 10x + y.

And, Reversed Number = 10y + x.

According To The Question,

x + y = 14. (Equation 1).

And,

➨ 10y + x = 10x + y – 18.

➨ y – x = -2. (Equation 2).

➨ 2y = 12.

➨ y = 6.

Now, Value Of x :-

➨ x + 6 = 14.

➨ x = 8.

Original Number :- 86.