This question is taken from linear equations in two variables in which we have to find the number if a number consisting of two digits is seven times the sum of its digits. When 27 is subtracted from the number, the digits are reversed.

RS Aggarwal, Class 10, chapter 3E, question no 12

Let us consider, one’s digit of a two digit number =x and

ten’s digit =y

The number is x+10y

After reversing the digits,

One’s digit =y

and ten’s digit =x

The number is y+10x

As per the statement,

x+10y−27=y+10x

y+10x−x−10y=−27

9x−9y=−27

x−y=−3…..(1)

Again,

7(x+y)=x+10y

7x+7y=x+10y

7x−x=10y−7y

6x=3y

2x=y…..(2)

Using substitution method:

Substituting the value of y in (1)

x−2x=−3

−x=−3

or x=3

From (2): y=2(3)=6

Answer:

Number =x+10y

=3+10(6)

=63