Cross-Multiplication Method of Finding Solution of a Pair of Linear Equations
The sum of a ...
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, 4x−5y+14=0
⇒x+y−10=0 and, 4x−5y+14=0
By using cross-multiplication, we have
x14−50=y−40−14=1−5−4
⇒x−36=y−54=1−9
⇒x=−36−9 and y=−54−9
⇒x=4 and y=6.
Putting the values of x and y in equation (i), we get