Question

seven times a two digit number is equal to four times the number obtained by reversing the order of its digit if the difference between the digit is 3 then find the number​

Answer 1

Given :

Given that, seven times a two digit number is equal to four times the number obtained by reversing of its digits. Also, the difference between the numbers is 3.

To find :

Here, we have to find the number according to the question.

Solution :

Let the digits at one's and tens place be x, y.

So, the number will be :

• 10y + x

Now, the difference between the digits is 3.

So,

• x - y = 3

Interchanging the digits :

• 10x + y

According to the question :

Seven times a two digit number is equal to four times the number obtained by reversing the order of digits :

• 7 (10y + x) = 4 (10x + y)
• 70y + 7x = 40x + 4y
• 70y - 4y + 7x - 40x = 0
• 33x - 66y = 0
• 33 (x - 2y) = 0
• x - 2y = 0

Now, we have two systems of linear equations :

1. x - y = 3
2. x - 2y = 0

Here, we shall multiply the eq.1 with 2 and then subtract it from eq.2 in order to find x :

• (x - 2y) - 2 (x - y) = 0 - (3)(2)
• x - 2y - 2x + 2y = -6
• -x = -6
• x = 6

Substituting x = 6 in eq.1 to get y :

• x - y = 3
• 6 - y = 3
• -y = 3 - 6
• -y = -3
• y = 3

Substituting these values in 10y + x :

• 10(3) + (6)
• 30 + 6
• 36

_________________________

Therefore, the number is 36.

Answer 2

Given:

Given that, seven times a two digit number is equal to four times the number obtained by reversing of its digits. Also, the difference between the numbers is 3.

To find:

Here, we have to find the number according to the question.

Solution:

Let the digits at one's and tens place be x, y.

So, the number will be :

10y + x

Now, the difference between the digits is 3.

So,

x - y = 3

Interchanging the digits :

10x + y

According to the question :

Seven times a two digit number is equal to four times the number obtained by reversing the order of digits :

7 (10y + x) = 4 (10x + y)

70y + 7x = 40x + 4y

70y - 4y + 7x - 40x = 0

33x - 66y = 0

33 (x - 2y) = 0

x - 2y = 0

Now, we have two systems of linear equations :

x - y = 3

x - 2y = 0

Here, we shall multiply the eq.1 with 2 and then subtract it from eq.2 in order to find x :

(x - 2y) - 2 (x - y) = 0 - (3)(2)

x - 2y - 2x + 2y = -6

-x = -6

x = 6

Substituting x = 6 in eq.1 to get y :

x - y = 3

6 - y = 3

-y = 3 - 6

-y = -3

y = 3

Substituting these values in 10y + x :

10(3) + (6)

30 + 6

36

_________________________

Therefore, the number is 36.