Question

5. A number has two digits whose sum is 14. If 36 is added to the number, its digits are
interchanged. The number is.
answer in one variable​

Answer 1

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Number is 59

Step-by-step explanation:

Let the unit's digit be x

• as sum of digits is 14
• ten's digit is 14 − x

then the number is 10×(14−x)+x

⠀

i.e.

140−10x+x

or

140−9x

⠀

Reversing the digits number, unit digit becomes

14−x

and tens digit becomes x

• hence number is

10x+14-x=9x+14

As adding 36 to 140 - 9x makes it 9x + 14

we have

140−9x+36=9x+14

or

176−14=9x+9x

or

18x=162

or

x=9

and hence, unit''s digit is 9

and tens digit is 5

and number is 59