Question

the sum of two digit number is 9 if 27 subtracted from the number its digits are interchanged find the number solve in copy pls​

Answer 1

Question:

A number consists of two digits whose sum is 9. If 27 is subtracted from the original number its digits gets interchanged .Find the original number.  

Solution:  

Let the tens digit of the required number be x and the unit (once) digit of the number be y.  

Then;  

The original number = 10x + y  

Also,  

The new number formed after interchanging the digits = 10y + x

Now,  

According to the question;  

The sum of the digits of the required two-digits number is 9.  

ie;  

=> x + y = 9  

=> y = 9 - x -----------(1)

 

Also,  

It is said that ,  

If 27 is subtracted from the original number (required number), then its digits gets interchanged.  

ie;

=> 10x + y - 27 = 10y + x

=> 10x + y - 27 - 10y - x = 0  

=> 9x - 9y - 27 = 0  

=> 9(x - y - 3) = 0  

=> x - y - 3 = 0  

=> x - (9 - x) - 3 = 0 {using eq-(1)}  

=> x - 9 + x - 3 = 0  

=> 2x - 12 = 0  

=> 2x = 12  

=> x = 12/2  

x = 6

Now,  

Putting the x = 6 in eq-(1) , we get;

=> y = 9 - x  

=> y = 9 - 6  

=> y = 3

Thus,  

Tens digit = x = 6  

Unit digit = y = 3  

Hence,  

Required number = 10x + y  

= 10•6 + 3

= 60 + 3  

= 63.

 

Hence,  

The required number is 63.

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Answer 2

What the question basically means is that a 2 digit number has its sum of digits 9 and the difference between it and its reverse is 27.

Since there are only 4 pairs of 2 digit numbers with sum of its digits as 9 and whose reverse is also a 2 digit number, we can list them.

18, 81

27, 72

36, 63

45, 54

We see the difference between 36 and 63 is 27, so those are our two numbers.

The other way to solve it is using simultaneous equations, where two generic equations are formed in x and y where x and y are the two digits.

Here sum is sum of the two digits and difference is the difference between the number and its reverse.

x + y = sum … (1)

10 * x + y = 10 * y + x + difference

9 * x - 9 * y = difference

9 * (x - y) = difference

x - y = difference / 9 … (2)

Putting values we get

x + y = 9 … (1)

x - y = 27 / 9 = 3 … (2)

Solving (1) and (2)

we get x = 6 and y = 3

therefore the required number is 63