1.

The sum of a two digit number and the number obtained by interchanging its digits is 99. Find the number.

Answer»

Let the digit in unit’s place be ‘x’ and the digit in ten’s place be ‘y’.

Digit in tens placeDigit in units placeNumberSum of the digits
Original
number
yx10y + xy + x
Number obtained by
 interchanging the digits 
xy10x + yx + y

According to the given condition,

 the sum of a two digit number and the number 

obtained by interchanging its digits is 99. 

∴ 10y + x + 10x +y = 99 

∴ 11x + 11y = 99 

Dividing both sides by 11,

 x + y = 9 

if y = 1, then x = 8

If y = 2, then x = 7 

If y = 3, then x = 6 and so on. 

∴ The number can be 18, 27, 36, … etc



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