Question

Sum of the digits of a 2-digit number is 5 and the difference between the
original number and number formed by reversing its digits is 9. Find the
original number.​

Answer 1

Answer:

32

Step-by-step explanation:

Let the ten's digit be ' x ' and one's digit be ' y '

Sum of digits = 5

=> x + y = 5 --- Eq( 1 )

Number formed i.e Original no. = 10x + y

Number formed when digits are reversed = 10y + x

Difference between original no. of number formed when digits are reversed = 9

=> 10x + y - ( 10y + x) = 9

=> 10x + y - 10y - x = 9

=> 9x - 9y = 9

=> 9( x - y) = 9

=> x - y = 1 -- Eq( 2 )

Adding Eq( 1 ) and Eq( 2 )

=> x + y + x - y = 5 + 1

=> 2x = 6

=> x = 3

Substituting x = 3 in Eq( 1 )

=> x + y = 5

=> 3 + y = 5

=> y = 5 - 3 = 2

Original no. = 10x + y = 10( 3 ) + 2 = 30 + 2 = 32.

Therefore the original no. is 32.