if a certain two digit number is divided by the sum of its digits the quotient is 2 and the remainder is 8 if the digits are interchanged and the resulting number is divided by the sum of its digits the quotient is 8 and the remainder is 2 find the number
Answers
Answer:
82
Step-by-step explanation:
x+10y = 8(x+y) + 2
10x+y = 2(x+y) + 8
-7x+2y = 2
8x-y = 8
x = 2 , y = 8
number = 82
The number is 28
Step-by-step explanation:
let the two digit number b 10x+y
and the number obtained by interchanging the digit is 10y + x
as per the condition
10x +y = 2(x+y) +8
8x -y -8=0 ..(1)
similarly
second condition is
10y + x= 8(x+y) + 2
2y - 7x -2 =0 ...(2)
solving equation 1 and 2 with elimination method
we get
y = 8
and x = 2
thus ,
The required number is 10x + y = 10 (2) + 8 = 20 + 8 = 28
hence , The number is 28
#Learn more:
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
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