Solving Student Work Rate Problems
This problem involves calculating the number of students required based on the amount of work (charts prepared) and the time taken. We can use the principle of combined variation or proportionality.
Calculating Required Students
Let $S$ be the number of students, $C$ be the number of charts, and $T$ be the time in hours. The number of students needed is directly proportional to the number of charts and inversely proportional to the time taken.
This can be expressed as: $ \frac{S \times T}{C} = k $ where $k$ is a constant representing the work rate per student.
Using the initial condition:
- $S_1 = 9$ students
- $C_1 = 117$ charts
- $T_1 = 3$ hours
Using the condition to find:
- $S_2 = ?$ students
- $C_2 = 208$ charts
- $T_2 = 1$ hour
We set up the proportion:
$ \frac{S_1 \times T_1}{C_1} = \frac{S_2 \times T_2}{C_2} $Substitute the known values:
$ \frac{9 \times 3}{117} = \frac{S_2 \times 1}{208} $Simplify the left side:
$ \frac{27}{117} = \frac{S_2}{208} $Reduce the fraction $\frac{27}{117}$ by dividing both numerator and denominator by their greatest common divisor, which is 9:
$ \frac{3}{13} = \frac{S_2}{208} $Now, solve for $S_2$:
$ S_2 = \frac{3 \times 208}{13} $Calculate the value:
$ S_2 = 3 \times 16 $ $ S_2 = 48 $Therefore, 48 students are needed.
Important Questions from Time and work
In a circular race on a track of length 2000 m, X and Y start from the same point at the same time in opposite directions at the speeds of 15 km/h and 33 km/h, respectively. After how much time will they meet next?
Which of the following option figures will complete the pattern in the figure given below?
A has completed two-third of a job in 8 days, and B completes the rest of the job in 20 days. In how many days can they together complete the job?
The smallest 4-digit prime number is:
If Anand can do a piece of work in 9 days and Vinod can complete the same work in 6 days, then in how many days will both of them complete it together?
