given that 45 is the difference between a number and that formed by reversing it's digit. if the sum of digit of the number is 13 then find the number
Answers
Answer:
Original number = 94
Step-by-step explanation:
given that,
45 is the difference between a number and that formed by reversing it's digit.
let the digits of the number be x and y
so,
number will be 10y + x
and reversed digit = 10x + y
given difference = 45
so,
According to the question,
10y + x - (10x + y) = 45
10y + x - 10x - y = 45
9y - 9x = 45
9(y - x) = 45
y - x = 45/9
y - x = 5 ....(1)
also given that,
the sum of digit of the number is 13
so,
y + x = 13 .....(2)
now we have,
y - x = 5. ....(1)
y + x = 13 ....(2)
adding the both equations
y - x + y + x = 5 + 13
2y = 18
y = 18/2
y = 9
from (1)
y - x = 5
9 - x = 5
-x = 5 - 9
-x = -4
x = 4
y = 9
Original number = 10y + x
putting the values,
= 10(9) + 4
= 90 + 4
= 94
so,
Original number = 94
Answer:
Number = 94
Step-by-step explanation:
let the digits of the number be x and y
and number = 10y + x
ATQ,
10y + x - (10x + y) = 45
10y + x - 10x - y = 45
9y - 9x = 45
9(y - x) = 45
y - x = 5 ....(1)
y - x = 5 ....(1)y + x = 13 .....(2)
(1) + (2)
y - x + ( y + x ) = 5 + 13
2y = 18
y = 9
putting the value of y on (1)
y - x = 5
9 - x = 5
-x = 5 - 9
-x = -4
x = 4
Original number = 10y + x
= 10(9) + 4
= 90 + 4
= 94