Question

A student was asked to divide a number by 6 and add 12 to the quotient. He however, first added 12 to the number and then divided it by 6, getting 112 as the answer. The correct answer should have been?

Answer 1

Let the number be x.
As per what he did,
(x+12)/6 = 112
x+12 = 672
x = 672-12 = 660.
So, the correct answer = (660/6)+ 12
= 110+12
= 122.

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Answer 2

The correct answer becomes 98.

Solution:  

Let the dividend be X. divisor be 6 after gets divided by 6 the obtained quotient would be z.

By adding 12 to the quotient the resultant would be 12+z. and again by adding 12 to the dividend as 12+x and again divided by 6 results quotient as 112.

As we know that  

Divident=Divisor×Quotient+Reminder.

In case 1:  

$X=6 \times(Z+12) \ldots \ldots \ldots(1)$

In case 2:  

$12+X=6 \times 112=672$

X = 660

By substituting the value of x = 660  in equation (1).

$660=6 \times(Z+12)$

110 = Z+12

Z = 110-12  

  =98.

98 is the correct answer.