Question

A two-digit number is seven times the sum of its digits. If 27 is subtracted from the

number, its digits get interchanged.​.

Answer 1

Given :

A two-digit number is seven times the sum of its digits. If 27 is subtracted from the number, its digits get interchanged

To find :

• Numbers

Solution :

Let the tens digit be x and ones digit be y

• Original number = 10x + y

According to question

• A two-digit number is seven times the sum of its digits.

→ 10x + y = 7(x + y)

→ 10x + y = 7x + 7y

→ 10x - 7x = 7y - y

→ 3x = 6y

→ 3x - 6y = 0

→ 3(x - 2y) = 0

→ x - 2y = 0 ------(i)

Now,

• If 27 is subtracted from the number, its digits get interchanged

• Interchanged number = 10y + x

→ 10x - y - 27 = 10y + x

→ 10x - x - y - 10y = 27

→ 9x - 9y = 27

→ 9(x - y) = 27

→ (x - y) = 27/9

→ x - y = 3 ------------(ii)

Subtract both the equations

→ (x - 2y) - (x - y) = 0 - 3

→ x - 2y - x + y = - 3

→ - y = - 3

→ y = 3

Putting the value of y in equation (ii)

→ x - y = 3

→ x - 3 = 3

→ x = 3 + 3 = 6

•°• Original number = 10x + y = 63

•°• Interchanged number = 10y + x = 36

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Answer 2

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