Question

Tick the correct statement.
A. Long distances are measured in kilometres.
B. $\dfrac{4}{35}ml+\dfrac{8}{135}ml=\dfrac{12}{500}ml$
C. We divide by 1000 to convert grams into kilograms.
D. Kilometres means 1000 litres.

Answer 1

Hint: Check all the options one-by-one. For option A, find if there are other units for measuring long distances. For option B, add the given volumes in the L.H.S by taking the L.C.M of the denominators and compare it with the R.H.S. For option C, use the conversion formula : 1 kg = 1000 gm. For option D, check whether kilometre and litre are the units of the same physical quantity or not.

Complete step-by-step answer:
Here, we have been provided with four statements and we have to choose the correct one. Since, all the statements are independent of each other so we have to check all of them one-by-one.
1. In option A, the statement is : Long distances are measured in kilometres.
We know that there are other units such as miles, nautical miles etc, which are greater than kilometres and are used to measure long distances. In the case of very long distances, we use light years. So, we can conclude that the statement in this option will not be true in all the cases.
2. In option B, we have to check the equality : $\dfrac{4}{35}ml+\dfrac{8}{135}ml=\dfrac{12}{500}ml$.
Here, let us consider the L.H.S part.
$\Rightarrow L.H.S=\dfrac{4}{35}+\dfrac{8}{135}$
Taking $\dfrac{4}{5}$ common, we get,
$\begin{align}
  & \Rightarrow L.H.S=\dfrac{4}{5}\times \left[ \dfrac{1}{7}+\dfrac{2}{27} \right] \\
 & \Rightarrow L.H.S=\dfrac{4}{5}\times \left[ \dfrac{27+14}{7\times 27} \right] \\
 & \Rightarrow L.H.S=\dfrac{4\times 41}{5\times 7\times 27} \\
 & \Rightarrow L.H.S=\dfrac{164}{945}ml \\
\end{align}$
Now, $R.H.S=\dfrac{12}{500}ml$. Therefore, clearly, we can see that $L.H.S\ne R.H.S$, so option B is incorrect.
3. In option C, the statement is : We divide by 1000 to convert grams into kilograms.
We know that : 1 kg = 1000 gm, so dividing both sides with 1000, we get,
$\begin{align}
  & \Rightarrow \dfrac{1}{1000}kg=1gm \\
 & \Rightarrow 1gm=\dfrac{1}{1000}kg \\
\end{align}$
Clearly, we can see that statement in option C is correct.
4. In option D, the statement is : Kilometres means 1000 litres.
Here, we know that kilometres is the unit of distance and litre is the unit of volume, so they cannot be compared. Hence, option D is incorrect.

So, the correct answer is “Option C”.

Note: One must note that here four different options were provided and they were independent of each other. That is why we needed to check all the options one-by-one and eliminate the wrong statements. To solve the above question, we must know about units of different physical quantities like distance, volume, mass etc.