Question

Sum of the digits of a two-digit number is 11. The given number is less than the number obtained by interchanging the digits by 9.Find the number.

Answer 1

Hey !

Given,

It's a 2 digit No.

Let the Units digit be x

and Tens digit be y

A no. is usually obtained by the sum of product of the digit and it's place value.

=> No. = 10(y) + 1(x)

=> Original No. = 10y +x

Sum of the digits = x+y

x+y = 11(given)

No. obtained by Interchanging digits = 10(x) + 1(y)

= > Reversed No. = 10x+y

As per the data given,

Original No. = Reversed No. - 9

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

=> 9x - 9y = 9

=> x - y = 1 ; which means x > y

x+y = 11. ----[1]

x-y = 1. -------[2]

Do [1] +[2]

=> 2x = 12

=> x = 6

From [2];

=> y = x - 1

=> y = 5

x = 6 ; y = 5

•°• Required Original No. = 10y+x = 10(5)+6 = 56.

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