Question

Seven times a two-digit number is equal to four times the number obtained by reversing the digits. If the difference between the digits is 3. Find the number.

Answer 1

Given : Seven times a two-digit number is equal to four times the number obtained by reversing the digits. If the difference between the digits is 3.  

Solution:

Let the digit in the unit's place be x and the digit at the tens place be y.

Number = 10y + x

The number obtained by reversing the order of the digits is = 10x + y

 

ATQ :

Condition : 1

x - y = ±3 ………….(1)

 

Condition : 2

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

70y + 7x = 40x + 4y

40x + 4y – 70y-7x = 0

33x – 66y = 0

33(x - 2y) = 0

x - 2y = 0  ………….(2)

Thus , we obtain two following systems of linear equations :  

(i) x - y = 3 ………….(3)

x - 2y = 0 ………….(4)

 

(ii) x –  y = - 3………….(5)

x - 2y = 0 ………….(6)

 

(i) First, we solve eq. (3) & (4) by subtracting :

x - y = 3

x - 2y = 0  

(-)  (+)   (-)

------------------

y  = 3  

On putting y = 3 in eq (3)  we obtain :  

x - y = 3

x - 3 = 3

x = 3 + 3

x = 6

Number = 10y + x = 10 × 3 + 6 =  30 + 6 = 36

Hence, the number is 36.

(ii) Now, we solve eq. (5) & (6) by subtracting :

x - y = - 3

x - 2y = 0  

(-)  (+)   (-)

------------------

y  = - 3  

On putting y = - 3 in eq (5)  we obtain :  

x - y = - 3

x- (- 3) = - 3

x + 3 = - 3

x = - 3 - 3

x = - 6

In the second systems of linear equations the values of x and y are negative. But  digits are can’t be negative. So we cant take the value of x and y.

Hence, the number is 36.

Hope this answer will help you…

 

Some more questions from this chapter :  

The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

https://brainly.in/question/17204442

 

The difference between two numbers is 26 and one number is three times the other.Find them.

https://brainly.in/question/17204165

Answer 2

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AnSwer :

= > 36

ExplaNation :

Let the unit digit be 'p' and tenth unit be 'q'.

So, the number = 10q + p

It is given that :

★ The number is seven times equal to the reversing order of its digit.

Here,

= > 7 ( 10 q + p ) = 4 ( 10 p + q )

= > 70 q + 7 p = 40 p + 4 q

= > 66 q = 33 p

= > p = 2 q .......(a)

★ It is also given that number difference is 3.

That is, p - q = 3 .......(b)

Now,

★ From (a) and (b) we get ,

= > 2 q - q = 3

= > q = 3

★ Putting (q = 3) in (a) we get :

= > p = 2 q [q = 3]

= > p = 6

★ So, the number :

= > 30 + 6

= > 36

Hence the proof.

$\bold{\huge{\fbox{\color{Purple}{Thanks}}}}$