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
A person can complete 20% of work in 8 days and another person y can complete 25% of the same work in 6 days. If they work together, in how many days will 40% of the work be completed?
P works thrice as fast as Q, whereas P and Q together can work four times as fast as R. If P, Q and R together work on a job, in what ratio should they share the earnings?
There are three pillars X, Y and Z of different heights. Three spiders A, B and C start to climb on these pillars simultaneously. In one chance, A climbs on X by 6 cm but slips down 1 cm. B climbs on Y by 7 cm but slips down 3 cm. C climbs on Z by 6.5 cm but slips down 2 cm. If each of them requires 40 chances to reach the top of the pillars, what is the height of the shortest pillar?
There is an order of 19000 quantity of a particular product from a customer. The firm produces 1000 quantity of that product per out of which 5% are unfit for sale. In how many days will the order be completed?
Ram and Shyam work on a job together for four days and complete 60% of it. Ram takes leave then and Shyam works for eight more days to complete the job. How long would Ram take to complete the entire job alone?
