Question

In a certain number is divided by the sum of its two digits, the quotient is 6 and remainder is 3. If the digits are interchanged
and the resultīng number is divided by the sum of the digits, then the quotient is 4 and the remainder is 9. Find the number.
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Answer 1

Answer:

75

Step-by-step explanation:

Let the number be 10x+y and the two digits are x and y

10x+y=6(x+y)+3

4x−5y=3...(i)

As per the second condition,

10y+x=4(x+y)+9

−3x+6y=9...(ii)

Multiplying equation (i) by 3 and (ii) by 4 and adding them, we get

12x−15y=9

−12x+24y=36

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9y=45

y=5

Substitute y=5 in equation (i)

4x−5×5=3

4x=28

x=7

So, the number =10x+y=10×7+5=75        

Answer 2

Here is the solution of this question hope this is helpful to you.