Q. 33.9( 9 Votes )

# The sum of the digits of a 2-digit number is 6. The number obtained by interchanging its digits is 18 more than the original number. Find the original number.

Answer :

Let the two numbers of the two-digit number be 'a' and 'b'.

a + b = 6 ... (1)

The number can be written as ( 10a + b ).

After interchanging the digits, the number becomes ( 10b + a ).

( 10a + b ) + 18 = ( 10b + a ) 9a − 9b = −18

a − b = −2 ... (2)

Adding equations (1) and (2):

2a = 4

∴ a = 2

Using a = 2 in equation (1),

b = 6 – a = 6 – 2 = 4

Therefore, the original number is 24.

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