A number consisting of two digits is seven times the sum of its digits

1.	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. Find the number.
Answer» 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

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. Find the number.

Answer»

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