a ten digit number is 3 more than 4 times the sum of its digits if 18 is added to that number the digits are reversed. find the number
Answers
Answer:
Let the two digits of two digit number be y at 10s place and x at 1s place. Accordingly the number will be 10y + x
A two digit number is 3 more than 4 times the sum of its digits.
The sum of digits is x + y
(10y + x) = 4 ( y + x) + 3
10y + x = 4y + 4x + 3
10y - 4y + x - 4x = 3
6y - 3x = 3. .
2y - x = 1
2y = 1 + x .Eq..1
If 18 is added to the number, its digits are reversed. What is the number
(10y + x) + 18 = (10x + y)
10y + x + 18 = 10x + y
10y - y + x - 10x = - 18
9y - 9x = - 18
9 (y - x) = - 18
y - x = - 2
y = x - 2…Eq..2
Now derived value of y is substituted in Eq..1
2y = 1 + x
2(x - 2) = 1 + x
2x - 4 = 1 + x
2x - x = 1 + 4
x = 5
The 1s digit is 5
Substituting the value of x in Eq..2 to drive the value of y
y = x - 2
y = 5 - 2
y = 3
The digit at 10s place is 3, and at Is place is 5 therefore the number is 35.
Answer the number is 35