Question

Ronald and Elan are working on an assignment Ronald takes 6 hours to type 32 pages on a computer while Elan takes 5 hours to type 40 pages. How much time will they take working together on two different computers to type an assignment of 110 pages?
a. 7 hours 30 minutes
b. 8 hours
c. 8 hours 15 minutes
d. 8 hours 25 minutes

Answer 1

Hint: Suppose the time taken to type 110 pages as a variable. And now calculate the number of pages typed in this variable time by Elan and Ronald separately using the given information of both of them. Now, equate to 110 by adding them to get the variable.

Complete step-by-step answer:

Let us take time for typing 110 pages of assignment by both Ronald and Elan (working together) together be ‘x’ hours. Now, it is given that Ronald takes 6 hours to type 32 pages on a computer. It means Ronald will take 1 hour to type $\dfrac{32}{6}$ pages on the computer.
So, Ronald will take ‘x’ hours to type $\dfrac{32x}{6}$ pages on the computer.
Similarly, it is also given that Elan will take 5 hours to type 40 pages. So, Elan will take 1 hour to type $\dfrac{40}{5}$ pages. Hence, Elan will take x hours to type $\dfrac{40x}{5}$ pages.
Now, we know that Elan and Ronald are typing 110 pages in x hours. Hence, we can write equation as,
Total pages typed by Elan in x hours + Total pages typed by Ronald in x hours = 110 pages. So, we get
$\begin{align}
  & \dfrac{40x}{5}+\dfrac{32x}{6}=110 \\
 & \dfrac{8x}{1}+\dfrac{16x}{3}=110 \\
\end{align}$
Now, take LCM of 1 and 3 to simplify the equation. So, we get
$\begin{align}
  & \dfrac{24x+16x}{3}=\dfrac{110}{1} \\
 & \dfrac{40x}{3}=\dfrac{110}{1} \\
\end{align}$
Now, on cross multiplying the above equation, we get
$\begin{align}
  & 40x=3\times 110 \\
 & \Rightarrow x=\dfrac{3\times 110}{40}=\dfrac{33}{4} \\
 & x=8\dfrac{1}{4}=\left( 8+\dfrac{1}{4} \right) \\
\end{align}$
Now, we can convert the value of $\dfrac{1}{4}$ hours in minutes by multiplying it by 60, as we know there are 60 minutes in 1 hour. So,
$\begin{align}
  & x=8+\dfrac{1}{4} \\
 & \Rightarrow x=8+\dfrac{1}{4}\times 60 \\
 & x=8+15 \\
\end{align}$
x = 8 hours 15 minutes.
Hence, they will take 8 hours 15 minutes working together to type 110 pages.
So, option (c) is correct.

Note: One may go with another approach that he or she can suppose ‘x’ pages can be typed by Elan and 110 – x pages can be typed by Ronald and hence, calculate time taken for typing x pages by Elan and 110 – x pages by Ronald individually and add them. He or she will not get the time, time will be in terms of ‘x’. So, he or she needs to assume time ‘t’ to type the whole page and hence calculate it with the help of given information. He or she will be able to get a number of pages by Elan and Ronald separately as well. So, this approach is complex as we have to use two variables ‘t’ and ‘x’ to solve it. One may confuse the conversion of $8\dfrac{1}{4}$ hours to 8 hours and 15 minutes. One may multiply the term $8\dfrac{1}{4}=\dfrac{33}{4}$ by 60 to convert it to minutes. Then try to convert it in the form of minutes. So, we get
$\dfrac{33}{4}\times 60=33\times 15=495$ Minutes.
480 minutes +15 minutes = 8 hours and 15 minutes. So, be clear with the conversion part as well to get the accurate option.