Question

A number consists of two digits whose sum is 15. If the number formed by reversing
the digits is less than the original number by 27​

Answer 1

Answer:

ANSWER

Let the tens digit be and the units digit be y. Then the number is 10x+y.

Sum of the digits is x+y=11.

The number formed by reversing the digits is 10y+x.

Given data, (10x+y)−9=10y+x

⇒10x+y−10y−x=9

9x−9y=9

Dividing by 9 on both sides, x−y=1 ........ (2)

Equation (2) becomes x=1+y .......... (3)

Substituting x in (1) we get, 1+y+y=11

⇒2y+1=11

2y=11−1=10

∴y=

2

10

=5

Substituting y=5 in (3) we get, x=1+5=6

∴ The number is 10x+y=10(6)+5=65