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Question

The digit in the tens place of a two-digit number is four times the digit in the units place. When the digits are reversed, the number obtained is 27 less than the original numbers. Find the original number.

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Solution

Let the digit's in tens place be x

and digit in units place be y

Hence the original number will be xy=10×x+y

Given that x=4y

Then the reversed number will be yx=10×y+x
Given:

10y+x=10x+y−27
9x=9y+27
x=y+3
4y=y+3 [ ∵ x=4y ]
3y=3
y=1

and x=4(1)=4

∴ The original number =10x+y = 10(4)+1 = 40+1 = 41


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