the sum of a two digit number and a number formed by interchanging the digits is 187.the new number is 9 less than the original number .find the number.
Answers
Answer:
Is given below.....
Step-by-step explanation:
Let the number be 10x+y, and the number formed by interchanging its digits is 10y+x.
So, 10x+y+10y+x= 187. Therefore 11x+11y+187.
=> x+y=17 (on dividing the whole equation by 11). -> (1).
Now, 10y+x = 10x+y -9.
=> 9y-9x = 9 => y-x+1. -> (2)
On adding both the equations, we get
x+y=17
-x+y=1
2y = 18. Therefore y = 9, and x+9=17. Hence x= 8.
Hope this answer helped you! :)
The original number is 89.
Given:
The sum of a two-digit number and a number formed by interchanging the digits is 187. The new number is 9 less than the original number.
To Find:
The original number.
Solution:
We know that a two-digit number comprises a one's place and a tens place.
Let us assume that in the original number, the one's place is occupied by 'y' and the tense place is occupied by 'x'.
So the original number = 10x + y.
The number obtained on interchanging the digits (the one's and the tens place) thus becomes = 10y + x.
According to the given condition, the sum of a two-digit number and a number formed by interchanging the digits is 187.
⇒ (10x + y) + (10y + x) = 187
⇒ 11x + 11y = 187
⇒ x + y = 17 ..........................(I)
We are also given that the new number is 9 less than the original number.
⇒ (10y + x) - 9 = (10x + y)
⇒ -9x + 9y = 9
⇒ -x + y = 1 ..........................(II)
Adding equations (I) and (II), we have
(x + y) + (-x + y) = 17 + 1
⇒ 2y = 18
⇒ y = 9
On substituting the above value of y in equation (II), we get
-x + 9 = 1
⇒ x = 8.
Hence, the original number = 10x + y = 10(8) + 9 = 89
∴ The original number is 89.
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