Question

The sum of the digits of a two-digit number is 5. If 9 is added to the number, its digits get reversed. Find the original number.
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Answer 1

Correct option is B)

Let ten's place digit =x and unit place digit =y

Number=10x+y

x+y=5 ...(i)

10x+y−9=10y+x

9x−9y=9x−y=1 ...(ii)

from (i) and (ii) we get,

x=3,y=2

∴Number=10×3+2=32.

Answer 2

Step-by-step explanation:

Solution :

Let,

• Units digit = x
• Tens digit = 5 - x

★ Original No. :

= 10 (5 - x) + x

= 50 - 10x + x

= 50 - 9x

If 9 is added to the number

Its digits get reversed

After interchanging the digits, the new number :

= 10 (x) + (5 - x)

= 10x + 5 - x

= 9x + 5

★ According to the Question :

(50 - 9x) + 9 = 9x + 5

59 - 9x = 9x + 5

59 - 5 = 9x + 9x

54 = 18x

x = 54/18

x = 3

Units digit = 3

• Tens digit = 5 - x

5 - 3 = 2

Tens digit = 2

Original number = 23

• 50 - 9x

• 50 - 9(3) = 50 - 27

• 23

Therefore, the original number is 23.