The sum of a two digit number and the number obtained by interchanging its digits is 99. Find the number
The sum of a two digit number and the number obtained by interchanging its digits is 99. Find the number.
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Let the digit in unit’s place be ‘x’ and the digit in ten’s place be ‘y’.
| Digit in tens place | Digit in units place | Number | Sum of the digits | |
| Original
number |
y | x | 10y + x | y + x |
| Number obtained by
interchanging the digits |
x | y | 10x + y | x + 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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