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The sum of the digits of a two-digit num...

The sum of the digits of a two-digit number is 12. The number obtained by interchanging its digits exceeds the given number by 18. Find the number.

A

53

B

55

C

57

D

59

Text Solution

Verified by Experts

The correct Answer is:
C
Let the ten's digit of the required number be x and the unit's digit be y. Then,
` " " x+ y = 12 " " `… (i)
Required number = (10x + y )
Number obtained on reversing the digits = ` (10 y + x )`
` therefore (10y + x) - (10x + y ) = 18 rArr 9 y - 9x = 18 rArr y - x = 2`.
On adding (i) and (ii), we get
` " " 2y = 14 rArr y = 7` .
Putting ` y = 7 ` in (i), we get
` " " x + 7 = 12 rArr x = 12 - 7 = 5 `
` therefore x = 5 and y = 7`.
Hence, the required number is 57.
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