Question

The sum of the digits of a two-digit number is 8. If the digits are interchanged, new number is 10 more than double the original number. Find the original number.

Answer 1

Let the ten’s digit be a and the unit’s digit be b,

Then the original number = 10a + b and,

The reversed number = 10b + a,

According to the given conditions,

(i) Sum of digits:

a + b = 8     ...(1)

(ii) Reversed number:

(New number is 10 more than double the original)

10b + a = 2(10a + b) + 10

10b + a = 20a + 2b + 10

10b − 2b = 20a − a + 10

8b = 19a + 10     ...(2)

Now, substituting b = 8 − a from equation (1) into equation (2):

8(8 − a) = 19a + 10

64 − 8a = 19a + 10

64 − 10 = 19a + 8a

54 = 27a

a = `54/27`

∴ a = 2

Then, b = 8 − a = 6

So the original number = 10a + b

=10(2) + 6

= 20 + 6

= 26

Hence, the original number is 26.