Question

In a division sum, the divisor is 12 times the quotient and 5 times the reminder. If the remainder is 48, then what is the dividend?
a) 240
b) 576
c) 4800
d) 4848

Answer 1

Hint: To find the dividend we have to use the division formula. However, as only the value of remainder is given, we should first find the quotient and divisor from the remainder and then use them in the division formula.

Complete step-by-step answer:
In this question, we have to use the division formula which states that
\[Dividend=\text{ }Divisor\times Quotient+\text{ }Remainder\] …………(1.1)
However, in this question, only the value of the remainder is given. So, we have to find the values of quotient and divisor first.
The given relation is \[Divisor=\text{ }5\times Remainder\]. So, the divisor will be given by
\[Divisor=\text{ }5\times 48=240\]
And the relation between divisor and quotient is given by
\[Divisor=\text{ }12\times Quotient\]
$\Rightarrow $240=12$\times $Quotient
$\Rightarrow $Quotient=$\dfrac{240}{12}=20$
Thus, using the values of divisor, quotient and remainder in the division formula (equation (1.1)), we obtain
\[Dividend\text{ }=\text{ }240\times 20\text{ }+\text{ }48\text{ }=\text{ }4800\text{ }+\text{ }48\text{ }=\text{ }4848\]
Thus the correct answer to the question will be option (d) which has the value 4848.

Note: In the division formula, four variables (dividend, divisor, quotient and remainder) are present, thus if we have the value of any one of the variables, and any two other independent relations, we can find the values of all the four variables. Thus, we should try to derive the values of the variables by elimination from the given equations and then use the division formula.