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Question

# A two-digit number is 3 more than six times the sum of its digits. If 18 is added to the number obtained by interchanged by interchanging the digits, we get the original number. Find the number.

A
25
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B
45
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C
75
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D
None of these
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Solution

## The correct option is C 75 Let the tens and the units digits in the number be x and y, respectively.So, the number may be written as 10x+y.According to the given condition.10x+y=6(x+y)+3⇒4x−5y=3 .....(i)If we interchange the digits of Original number then we get new number. i.e 10y+xAccording to the given condition10y+x+18=10x+y⇒9x−9y=18⇒x−y=2 .....(ii)Now multiplying equation (ii) by 4. we get,4x−4y=8 ....(iii)On subtracting (iii) from (i). we get,4x−5y−(4x−4y)=3−8∴y=5On substituting y=5 in (ii). we get,x−5=2⇒x=7∴ number is 10x+y=10(7)+5=75

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