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Question

The sum of a two digit number and the number formed by interchanging its digits is 110. If 10 is subtracted from the first number, the new number is 4 more than 5 times the sum of the digits in the first number. Find the first number.

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Solution

Let the digits at units and tens place in the given number be x and y respectively. Then,
Number =10y+x (i)

Number formed by interchanging the digits =10x+y

According to the given conditions, we have
(10y+x)+(10x+y)=110
and, (10y+x)10=5(x+y)+4

11x+11y=110
and, 4x5y+14=0

x+y10=0
and, 4x5y+14=0

By using cross-multiplication, we have

x1450=y4014=154

x36=y54=19

x=369 and y=549

x=4 and y=6.

Putting the values of x and y in equation (i), we get

Number =10×6+4=64.

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