When a certain 2 digit number is divided by the number obtained by reversing the digits, the quotient is 2 and the remainder is 7. If the number is divided by the sum of its digits the quotient is 7 and the remainder is 6. Find the product of the digits of the original number
Answers
10X+Y=(X+Y)+7 (2)equation
after solving we get X=8,Y=3
so that two digit number will be 83
Answer:
The products of the digits of the original number is (8×3) =24
Step-by-step explanation:
The original number is = 10x + y we take 10x and y because x is of
tens digit and y is of unit digit
The number after reversing = 10y + x
Divided by the number obtained by reversing the digits, the quotient is 2 and the remainder is 7
- 10x + y = (10y + x)2 + 7 (dividend = divisor * quotient + remainder)
- 10x +y = 20y + 2x + 7
- 8x -19y = 7 -------> 1
The number is divided by the sum of its digits the quotient is 7 and the remainder is 6.
- 10x + y = (x+y)7 + 6
- 10x + y = 7x + 7y + 6
- 3x - 6y = 6 ÷ by 3
- x - 2y = 2 --------> 2
From equation 2
x = 2+2y -------> 3
Substitute equation 3 in equation 1
- 8(2+2y) - 19y = 7
- 16 + 16y - 19y = 7
- -3y = -9
- y = 9 ÷ 3 - sign goes off as they cancel each other on the either
sides
- ∴ y = 3
Substitute the value of y in equation 3
- x = 2 + 2(3)
- x = 2+ 6
- ∴ x= 8
The digits
∴The digits are 8 and 3 , 83
The product of the digits of the original number
the product = (8×3) =24
I wish that I have done my best :) (: