the digit of a two digit number differ by3.If the digits are interchanged and the resulting number is added to the original number,we get 121.Find the original number
Answers
Given,
The digits of a two digit number differ by 3.
Let the two digits be x and y.
According to the problem,
x - y = 3 ------(1)
Then the number = 10x + y
When the digits are reversed then the number= 10y + x
The sum of the the number and reversed number = 121
10x + y + 10y + x = 121
11x + 11y = 121
11(x + y) = 121
x + y = 121/11
x + y = 11 -----(2)
Add the both eq (1) & (2)
x - y + x + y = 11 + 3
2x = 14
x = 14/2
x = 7
Substitute x in eq - 1
(7) - y = 3
7 - 3 = y
y = 4
Then the number = 10x + y = 10(7) + 4 = 74
Therefore, the number = 74
Answer:
Step-by-step explanation:
let the unit digit be x and tenth digit be 10(x-3) or 10x - 30 so the no. is 10x-30+x
after interchanging digits will be = unit place be (x-3) and tenth place be 10(x) or 10x ,so the no. will be 10x + x -3
then the equation will be,
original no. + resulting no. = 121
(10x -30 + x) + (10x + x - 3) = 121
11x - 30 + 11x - 3 = 121
22x - 33 = 121
22x = 154
x = 154/22 = 7
the digits of the original no. is = tenth place = 10(x-3) = 10(7-3) = 40
= unit place = x = 7
the no is 40+7 = 47