Question

If it takes 5 machines 5 minutes to make 5 fidget spinners. How long would it take 100 machines to make 100 fidget spinners?

Answer 1

Hint: We will apply a unitary method to solve this question. By the unitary method we mean the method in which we consider the value of any object in large amounts. After that we solve it to find the individual value. For example, in this question, it takes 5 minutes by 5 machines to make 5 fidget spinners. This is clearly the work done by the 5 machines to make 5 fidget spinners. So, we can find about the work done by 1 machine with the division by 5 in 5 fidget spinners. This results in 1 machine taking 5 minutes only.

Complete step-by-step answer:

According to the question we have 5 machines and they together make 5 fidget spinners in 5 minutes. By using a unitary method here we find that if 5 machines take 5 minutes to make 5 fidget spinners therefore, 1 machine takes 5 minutes to make $\dfrac{5}{5}$ fidget spinners. Thus, 1 machine takes 5 minutes to make 1 fidget spinner.
Now, we are here to find the time taken by the 100 machines to make 100 fidget spinners. As we have known that 1 machine takes 5 minutes to make 1 fidget spinner thus 100 machines will make 100 fidget spinners in 5 minutes only.
Hence, 100 machines will take 5 minutes to make 100 fidget spinners.

Note: We will consider here the time taken by 100 machines to make 100 fidget spinners as x minutes. We can also solve by $\dfrac{MDT}{W}$ formula in which M are the number of machines which will work, D are days, T is time and W is work done. Therefore we will have $D=\dfrac{W}{MT}$. As here we have ${{M}_{1}}=5,{{T}_{1}}=5,{{W}_{1}}=5$ and ${{M}_{2}}=100,{{T}_{2}}=x,{{W}_{2}}=100$ so, by taking D as common between them we get,
   $\begin{align}
  & D=D \\
 & \dfrac{{{W}_{1}}}{{{M}_{1}}{{T}_{1}}}=\dfrac{{{W}_{2}}}{{{M}_{2}}{{T}_{2}}} \\
 & \Rightarrow \dfrac{5}{5\times 5}=\dfrac{100}{100\times x} \\
 & \Rightarrow 5=x \\
\end{align}$
Hence, 100 machines will take 5 minutes to make 100 fidget spinners.