1) The digits of a two digit number differ by 7.If the digits are interchanged and the resulting number is added to original numbers, we get 121.What is the original number?
2)The digits of a two digit number differ by 3. If the digits are interchanged and the resulting number is added to original numbers, we get 143.What can be the original number
please give answers with full steps and equations
Answers
Step-by-step explanation:
Solution
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Given x and y be the required two digit number.
Let the digit in ten's place be x.
Let the digit in one's place be y.
Therefore the required number is 10x+y. ------ (*)
Given that the digits of a two digit number differ by 7.
x - y = 7 ----- (1)
Given that if the digits are interchanged and the resulting number is added to the original number we get 121.
10x + y + 10y + x = 121
11x + 11y = 121
x + y = 11 -------------- (2).
On solving (1) & (2), we get
x + y = 11
x - y = 7
--------------
2x = 18
x = 9
Substitute x = 9 in (1), we get
x + y = 11
9 + y = 11
y = 11 - 9
y = 2.
Substitute x & y in (*), we get
The original number = 10(9) + 2
= 90 + 2
= 9