Question

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

Answer 1

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

Answer 2

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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