Question

A number consists of two digits. When the number is divided by the sum of its digit, the quotient is 7. If 27 is subtracted from the number,the digit interchange their places, find the number.

Answer 1

SOLUTION:-

Given:

A number consist of two digits. When the number is divided by the sum of its digit, the quotient is 7. If 27 is subtracted from the number, the digit interchang their places.

To find:

The number.

Explanation:

Let the R & M be the units & tenth's places of the given number respectively.

Original number: 10R +M

Reversed number: 10M+ R

According to the question:

$\frac{10M + R}{M + R} = 7 \\ \\ 10M + R = 7(M + R) \\ \\ 10M + R = 7M + 7R\\ \\ 7R- R + 7M - 10M = 0 \\ \\ 6R - 3M = 0 \\ \\ 2R - M = 0 \\ \\ 2R = M................(1)$

&

=) (10M + R) -27 = 10R +M

=) 10M + R -27 = 10R +M

=) 10M- M +R -10R = 27

=) 9M -9R = 27

=) M - R = 3............(2)

Putting the value of M in equation (1), we get;

=) 2R -R =3

=) R = 3

Putting the value of R in equation (1), we get;

=) M= 2R

=) M= 2×3

=) M= 6

• The number is 10M +R

=) 10(6) +3

=) 60 +3

=) 63