Question

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.

Answer 1

Therefore..the number is 10x+y
= 10(6)+3
=60+3
=63

Answer 2

Answer:

The two digit number is 63

To find:

Number = ?

Solution:

Assume the number as a and b.

Hence, the two digit number = 10a + b

Number consisting of two digits is seven times the sum of its digits

10a + b = 7(a + b)  

10a + b = 7a + 7b  

10a - 7a = 7b - b

3a  = 6b  

a = 2b    ---------(1)

When 27 is subtracted from the number, the digits are reversed.  

After reversing the digits, the number will be 10b + a.

10a + b - 27 = 10b + a

10a - a - 27 = 10b - b

9a - 27 = 9b

9a - 9b = 27

a - b = 3 ---------(2)

Replacing a = 2b as per (1) in equation (2), we get

a - b = 3  

2b -b = 3

b = 3 i.e. the second digit

Replacing the value of b = 3 in a = 2b

a = 2(3)

a = 6 i.e. the first digit

Hence, the two digit number is 63.