Seven times a two digit number is equal to four time the number obtained by reversing the order of its digits . if the difference of the digit is 3 determine the number?

Question

Answer

Let the number be (10x+y)so the number obtained by reversing the digits will be (10y+x)A/c to ques.      7(10x+y)=4(x+10y)》 70x+7y=4x+40y》 66x-33y=0》 2x-y=0》 2x=y -(eq.1)Again,The difference of the digits is 3》 y-x=3》 2x-x=3》 x=3》 y=6 - ( from eq.1).°. that number is 36....Hope this will help...☺

Answer

Let numbers be x at onces place & y at tens place so,
10y+x is the digit.
Reversed digit =10x+y
According to the question ,
∴7(10y+x)=4(10x+y)
⇒x=2y⟶(i)
Now,
Given , x−y=3
from equation (i)2y=x substitute in above equation.
2y−y=3
y=3
So ,
x=2y=2⋅3=6
∴ Required original no: is =10y+x=10⋅3+6=36.

Answer

Problem:
Seven times a two-digit number is equal to four times the number obtained by reversing the order of its digits. If the difference between the two digits is 3, determine the number.

Solution:

Let's break down the problem step by step:

Step 1: Understand the problem
We are given that a two-digit number, let's call it 'xy,' is such that seven times this number is equal to four times the number obtained by reversing the digits. We are also given that the difference between the two digits is 3.

Step 2: Express the problem algebraically
To solve this problem algebraically, we need to express the given information in equations.

Let's represent the two-digit number as 10x + y, where x represents the tens digit, and y represents the units digit.

The number obtained by reversing the digits is 10y + x.

According to the problem, we have the equation:
7(10x + y) = 4(10y + x)

Step 3: Simplify the equation
Now, we can simplify the equation by expanding and combining like terms:

70x + 7y = 40y + 4x

Simplifying further:

70x - 4x = 40y - 7y

66x = 33y

Step 4: Use the given difference between the digits
We are also given that the difference between the two digits is 3. So, we can express this relationship as:

x - y = 3

Step 5: Solve the system of equations
We have two equations:

66x = 33y
x - y = 3

We can solve this system of equations using substitution or elimination.

Step 5.1: Solve by substitution
From the second equation, we can express x in terms of y:

x = y + 3

Substituting this value of x into the first equation:

66(y + 3) = 33y

Simplifying:

66y + 198 = 33y

33y = -198

y = -6

Substituting this value of y back into the second equation:

x - (-6) = 3
x + 6 = 3
x = -3

Step 5.2: Solve by elimination
Multiply the second equation by 33 to make the coefficients of x in both equations equal:

33(x - y) = 33(3)
33x - 33y = 99

66x - 33y = 0

Subtract the second equation from the first:

(66x - 33y) - (66x - 33y) = 99 - 0
0 = 99

This is not possible, so there is no solution using the elimination method.

Step 6: Determine the two-digit number
From our solution in Step 5.1, we found that y = -6 and x = -3. However, since the problem specifies that we are dealing with a two-digit number, we need to consider positive values for x and y.

Let's change the sign of both x and y:

y = 6
x = 3

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