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25 students can do a job in 12 days, but on the starting day, five of them informed me that they are not coming. By what fraction will the number of days required for doing the whole work get increased?
\[\begin{align}
  & A.\dfrac{3}{5} \\
 & B.\dfrac{3}{7} \\
 & C.\dfrac{3}{4} \\
 & D.\dfrac{1}{4} \\
\end{align}\]

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Last updated date: 13th Jun 2024
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Answer
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Hint: In this question, we are given a number of days in which 25 students can do a job. We have to find the fraction by which the number of days increased for doing work if 5 students left. For this, we will first use inverse proportion to find the number of days represented by 20 students to do the same work. After that, we will find an increased number of days and thus find the required fraction given by $\dfrac{\text{Increased number of days}}{\text{Number of days in which 25 students do work}}$.

Complete step by step answer:
Here, we are given that 25 students can do a job in 12 days. Since, 5 students left on the first day, so remaining students are 20. Hence, we need to find the number of days required to complete the work by 20 students. Let us suppose it to be x.
Now, we know, less the number of people, more time it will take to complete a job. So, 20 students will take more time. Hence, we will use the inverse proportion here.
Table for inverse proportion look like:
Number of students2520
Number of days12x


Using inverse proportion, we get:
\[\Rightarrow 25\times 12=20\times x\]
Dividing both sides by 20, we get:
\[\begin{align}
  & \Rightarrow x=\dfrac{25\times 12}{20} \\
 & \Rightarrow x=\dfrac{300}{20} \\
 & \Rightarrow x=15 \\
\end{align}\]
Hence, it will require 15 days to complete a job by 20 students. Increased number of days are 15-12 = 3 days. Our required fraction is $\dfrac{\text{Increased number of days}}{\text{Number of days in which 25 students do work}}=\dfrac{3}{12}=\dfrac{1}{4}$.
Hence $\dfrac{1}{4}$ is our required answer.

So, the correct answer is “Option D”.

Note: Students should understand the problem carefully to check if the problem is of direct proportion or inverse proportion. While calculating the fraction make sure to divide increased days by days required for 25 students. For simplification, students can also first find the number of days required by one student by multiplying 12 by 25 and then find the number of days required by 20 students by dividing 20 by $12\times 25$.