Question

# If the unit of the weight is $\dfrac{15}{4}kg$ , what number will $\dfrac{3}{2}$ quintal represent:(a) 25(b) 6(c) $\dfrac{1}{9}$ (d) None

Hint:It is given that the unit of weight is $\dfrac{15}{4}kg$ or 3.75 kg and we are asked to find the answer of $\dfrac{3}{2}$ quintal in this 3.75 kg unit. We know that 1 quintal is equal to 100 kg and as the unit of weight given in the question is 3.75 kg so multiply 100 by 3.75 to get the answer.

The unit of weight given in the above problem is:
$\dfrac{15}{4}kg$
Simplifying the above fraction in terms of decimal we get,
3.75kg
From the above, we have the unit of weight in terms of decimal as 3.75 kg.
We are asked to find that what is the number $\dfrac{3}{2}$ quintal will represent in terms of the unit of weight given in the question.
So, first of all we should do the basic conversion of quintal to kg which is:
$1\text{ quintal}=100kg$
Now, we want the units in 3.75 kg so multiply the right hand side of the above equation by 3.75 kg.
\begin{align} & 1\text{ quintal}=100\left( 3.75 \right)kg \\ & \Rightarrow 1\text{ quintal}=375kg \\ \end{align}
We need to find for $\dfrac{3}{2}$ quintal so multiplying $\dfrac{3}{2}$ on both the sides we get,
\begin{align} & \dfrac{3}{2}\text{quintal}=375\left( \dfrac{3}{2} \right)kg \\ & \Rightarrow \dfrac{3}{2}\text{quintal}=562.5kg \\ \end{align}
From the above solution, we have converted $\dfrac{3}{2}$ quintal in terms of the unit of weight given in the question and the result is 562.5 kg.
Hence, the correct option is (d).

Note: In the question given above don’t confuse that we have to convert $\dfrac{3}{2}$ quintal into kgs. Yes, we have to convert $\dfrac{3}{2}$ quintal in kgs but in the unit of weight which is $\dfrac{15}{4}kg$ . Generally, students just convert $\dfrac{3}{2}$ quintals using the below formula in kgs and then stop.
\begin{align} & 1\text{ quintal}=100kg \\ & \dfrac{3}{2}\text{ quintal}=100\left( \dfrac{3}{2} \right)kg \\ & \Rightarrow \dfrac{3}{2}\text{ quintal}=150kg \\ \end{align}
The problem with the above derivation is that here, you did not convert quintal in the units of $\dfrac{15}{4}kg$ .
So, beware of making this mistake.