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Q.

In a two-digit number, the sum of the digits is 9. If the digits are reversed, the number is increased by 9. Find the number.

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a

34

b

54

c

45

d

72 

answer is C.

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Detailed Solution

It is given that the number 9 represents the sum of digits of a two number.
The number obtained by interchanging the digits is greater than the given number by 9.
Let the unit’s digit be y and the ten’s digit be x.
Therefore, the required number will be 10x+y and the number obtained on reversing its digits will be 10y+x.
According to the first statement,
x+y=9...(1)  
According to the second statement,
⇒ 10y+x−(10x+y)=9 ⇒ 9y−9x=9 ⇒ y−x=1...........(2)  
Adding equations 1 and 2,
⇒x+y+y−x=9+1 ⇒2y=10 ⇒y=5  
Using this value of y to calculate x,
⇒x+5=9 ⇒x=4  
Therefore, the number is 45.
Hence, option 3 is correct.
 
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In a two-digit number, the sum of the digits is 9. If the digits are reversed, the number is increased by 9. Find the number.