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.
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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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