Question

The digit sum of a two digit number is 9. If you divide the number by three and multiply the result by eight, the result is the reverse of the number. What is the number?

Answer 1

Solution:

According to the question

The digit sum of a two digit number is 9

Let the number be xy

x+y=9 (given)...(1)

Then it is given that if you divide the number by three and multiply the result by eight, the result is the reverse of the number.

Let the two digit no. be 10x + y

So,(10x+y)*8/3=10y+x

=> (80x + 8y)/3 = 10y + x

=> 80x + 8y = 30y + 3x

=> 80x -3x = 30y - 8y

=> 77 x = 22y

=> x/y = 2/7

x:y = 2:7

According to equation (1) x + y = 9,2+7 = 9

Hence value of x = 2 ,y = 7

Required two digit no. is 10x + 7 = 10×2 +7 = 27.