A school is running a tree plantation drive to bring awareness among students about the environment. If 3 teachers can complete the work of tree plantation in 4 days and 4 students take 6 days to do the same work, then how many days will 3 teachers and 2 students take to complete the work of tree plantation?
- A3
- B8
- C4
- D6
Solution & Step-by-step Explanation
Let the efficiency of a teacher be T and a student be S.
According to the problem, the total work is the same:
Total Work=3T×4=4S×6
12T=24S⟹1T=2S
Let the total work in terms of student-days be:
Total Work=24S
Now, we need to find the time taken by 3 teachers and 2 students:
Combined Efficiency=3T+2S
Since 1T=2S:
Combined Efficiency=3(2S)+2S=6S+2S=8S
Number of days required:
Days=
Combined Efficiency
Total Work
=
8S
24S
=3 days
According to the problem, the total work is the same:
Total Work=3T×4=4S×6
12T=24S⟹1T=2S
Let the total work in terms of student-days be:
Total Work=24S
Now, we need to find the time taken by 3 teachers and 2 students:
Combined Efficiency=3T+2S
Since 1T=2S:
Combined Efficiency=3(2S)+2S=6S+2S=8S
Number of days required:
Days=
Combined Efficiency
Total Work
=
8S
24S
=3 days