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Question

A number consists of two digits whose sum is $$13$$. If $$27$$ is subtracted from the number , the digits are reversed. Find the number.


Solution

$$ Let$$ that no. be $$10x+y$$
$$Given,$$ $$x+y=13$$..........1
According to question,$$10x+y-27=10y+x$$
$$9x-9y=27$$
$$x-y=3$$ .........2
Now substitute  the value of  $$x$$ from 2 to 1
$$y+3+y=13$$
$$2y=10$$
$$y=5$$
Now put the value of y in 2
$$x-5=3$$
$$x=8$$
so, that no. is $$10(8)+5$$ $$=$$ $$85$$

Mathematics

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