Question

In a two digit number the sum of digits is 14 and if 29
is subtracted from the number, the two digits will be
equal. Find the Number.
​

Answer 1

Step-by-step explanation:

Let the number be x and y

Also

10x + y - 29 = 10d + d —- Where d is some digit

10x + 14 - x - 29 = 11d

9x - 15 = 11d

9x = 11d + 15

Since LHS is a multiple of 9, RHS also should be. 15 leaves a remainder of 6 when dividing with 9. So 11d should leave a remainder of 3, the only such possibility is when d is 6.

So d = 6, x = 9, y = 5

Answer is 95

Please note we can also arrive at the solution by using trial and error using all permutations combinations of digits whose sum is 14. In this case (9,5),(8,6),(7,7)

Answer 2

Required number = 95

Step-by-step explanation:

Since the sum of the digits is 14, let us take the two digits to be x and (14 - x), where x is in units place and (14 - x) in tens.

Then the number is

(14 - x) × 10 + x × 1

= 140 - 10x + x

= 140 - 9x

When 29 is subtracted, the resulting number is

(140 - 9x) - 29

= 140 - 9x - 29

= 111 - 9x

= (11 - x) × 10 + (1 + x) × 1

According to the question, when 29 is subtracted, we will have

11 - x = 1 + x

⇒ 2x = 10

⇒ x = 5

So, the resulting number (after 29 is subtracted)

111 - 9 × 5

= 111 - 45

= 66

Thus the required number is

66 + 29

= 95

#SPJ3