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Q.

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.


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a

57

b

53

c

52

d

51 

answer is A.

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Detailed Solution

It is given that the sum of two digits number is 12 and after interchanging its digits exceeds the given number by 18.
Let the unit’s digit be y and the ten’s digit be x.
Then, the original number be 10x + y
Sum of the digit = x + y
After reversing the digits:
New number = x + 10y
According to question,
The sum of the digits of a two - digit number is 12.
x + y=12     …. (1)
The number obtained by interchanging its digits exceeds the given number by 18.    10x + y + 18 = x + 10y  
⇒10x-x+y-10y=-18 ⇒10x-x+y-10y=-18 ⇒9x-9y=-18 ⇒x-y=2
⇒x=y-2       …. (2)
Substitute the value of x in equation (1),
x + y = 12   y−2  +y = 12  
y+y=12+2  
2y=14   y= 14 2   y=7  
To determine the value of x, put y = 7 into equation (2) as follows:
x=y-2=7-2=5 Then,
Original number = 10x + y = 10 × 5 + 7= 50 + 7 = 57
⇒the number is 57.
Hence, option (1) is correct.
 
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