Question

7 times a two-digit number is equal to 4 times the number formed by changing the digits, if the difference between the unit and the tens digits is 3, then tell the number.​

Answer 1

Given:

1. 7 times a 2 digit number is equal to 4 times the number formed by changing the digits.
2. The difference between the units and the tens digit is 3.

Find:

The 2 digit number.

Solution:

Let us denote the units digit by a variable x and the tens digit by a variable y.

Then, the difference between the digits is:

x - y = 3. → Equation 1.

The actual number in it's expanded form is:

10y + x.

The number formed when the tens and units place are interchanged[in expanded form]:

10x + y.

It is given that:

7[10y + x] = 4[10x + y].

70y + 7x = 40x + 4y.

70y - 4y = 40x - 7x.

66y = 33x.

33x - 66y = 0.

Dividing all the terms by 33:

x - 2y = 0. → Equation 2.

From Equation 2, we can say that:

x = 2y.

Substituting the value of x obtained in Equation 2 in Equation 1:

x - y = 3.

(2y) - y = 3.

2y - y = 3.

y = 3.

Substituting the value of y in Equation 2:

x - 2y = 0.

x - 2(3) = 0.

x - 6 = 0.

x = 6.

Therefore:

1. The units digit is 6 and the tens digit is 3.
2. The number formed is 36.
3. The number formed by reversing the digits is 63.

Note: I have used Substitution Method to solve the problem, but we can also solve it using Elimination Method and Cross-Multiplication Method.

Answer 2

Step-by-step explanation:

let the tenth digit and unit' digit be

x and y respectively

According to question

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

70x+7y=40y+4x

66x=33y

y=66x/33

y=2x...................... (1)

and

ATQ

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

substitute y value in equation (2)

2x-x=3

x=3

substitute x value in (1)

y=2x

y=2*3

y=6

therefore the number is

36.