Question

In a division sum, the remainder is 0. A student mistook the divisor by 12 instead of 21 and obtained 35 as quotient. What is the correct quotient?
A. 0
B. 12
C. 13
D. 20

Answer 1

Hint: Questions like this can easily solved by assuming the mistook and correct values by some variable and then we can apply the concept of dividend rule i.e. $Dividend = divisor \times quotient + remainder$ and compare the equations then find the correct value of the correct quotient.

Complete step-by-step answer:
According to question the correct divisor = d = 21, the mistook divisor = d’ = 12 and the obtained = 35
We have to find the correct quotient let ‘q’ be the correct quotient
Let ‘D’ be the dividend and let ‘R’ be the remainder
By the formula of $Dividend = divisor \times quotient + remainder$
For the correct value putting the correct value in the formula \[D = 21 \times q + R\] ----(equation 1)
Now for the mistook value putting the values in formula \[D = 12 \times 35 + R\] ------(equation 2)
Since the Dividend is the same for the correct and mistook values
Therefore by comparing equation 1 and equation 2
We get \[12 \times 35 + R = 21 \times q + R\]
$ \Rightarrow $$q = \dfrac{{12 \times 35}}{{21}} = 20$
Hence, the correct quotient is 20.

Notes: In this question terms like dividend, divisor, quotient, remainder have a relation with each other. The number which we divide is called the dividend, the number by which we divide is called the divisor, the result obtained is called the quotient and the number left over is called the remainder.