the sum of the digit of a two digit number is 8 if digit are reverse .the new number so formed is increased 18 .the new no. is
Answers
Answer:
Hi there.. Here's the answer for your question..
Step-by-step explanation:
Firstly we have to create a basic idea about the question. A number, suppose 89 can be written in expanded form as ((8x10)+ (9x1)). This idea will help us solve the problem.
Note - (xy)and (yx) represent the number, not the product of x and y.
Let the number be (xy), in expanded form it can be written as (10x + y). It is given that sum of the digits,that is x and y, is 8. Therefore we can state, x+y = 8.
When we reverse (xy) it becomes (yx), in expanded form it can be written as (10y + x). Again it is given that difference between the two numbers is 18. Therefore we can say, (xy) - (yx)= 18.
Now , (xy) - (yx) = 18, which implies ( 10x +y)- (10y+x) = 18.
Simplifying further,
( 10x - x - 10y + y) = 18
9x - 9y =18
9(x-y)= 18 ( Taking common factor 9)
x-y= 18/9 (Transposing 9 to RHS)
x-y=2.
Earlier we stated that, (x +y) = 8. Now we can combine, (x-y)= 2 and ( x+y)= 8.
(x+y)+(x-y) = 8+2
2x = 10
x= 5 ( Transposing 2 to RHS).
Now, x= 5 and (x+y)= 8, we can state y= 3.
So, our number ( xy) is 53, as x= 5 and y=3.
We can check the answer by subtracting 35 from 53, which is 18.
Hope it helps you..
If any doubt ask me..
Thank you...