Question

If the number obtained by interchanging the digits of two digit numbers is 18 more than the original number and the sum of the digits is 8 then, what is the original number.

Answer 1

Hint: To solve this question, first we will let the number at tens place be x and number at one’s place be y. Then using the conditions given in question, we will make the system of linear equations. After that, we will add both the equation and obtain the value of x, and then, we will put value x back in any of the equation and obtain the value of y. Then, we will form the two digit number by putting the value of x and y in equation 10x + y.

Complete step-by-step answer:
Let, the ten’s digit be x and the one’s digit be y.
Then, the number will be equal to 10x + y.
Now, in question it is given that, the sum of the digits is 8
Then, we can say that x + y = 8 ……( i )
Again, it is given that if the number obtained by interchanging the digits of two digit number is 18 more than the original number,
10x + y = 18 + ( 10y + x )
On simplifying, we get
10x + y - ( 10y + x ) = 18
10x + y - 10y - x = 18
9x – 9y = 18
On solving, we get
x – y = 2 ……( ii )
now adding equation ( i ) and equation ( ii ), we get
x + y + ( x – y ) = 8 + 2
on simplifying, we get
2x = 10
On solving, we get
x = 5
Putting x = 5 in equation ( ii ), we get
5 – y = 2
On simplifying, we get
y = 5 – 2,
y = 3
So, the original number will be 10x + y
On putting values of x = 5 and y = 3 in 10x + y, we get
= 10(5) + 3
On solving, we get
= 50 + 3
= 53
Hence, the required number is 53.

Note: To solve the system of linear equations of two variables, there are many ways to solve for the value of variables. One of the ways is substituting the value of any of the one variables from one equation to the another equation. Try not to make any calculation errors while solving and try not to forget multiplying 10 for ten’s place.