5 Views

Question : Vijay and Sahil together complete a piece of work in 40 days, Sahil and Ranjit can complete the same work in 48 days and Ranjit and Vijay can complete the same in 60 days. In how many days can all three complete the same work while working together?

Option 1: 16 days

Option 2: 24 days

Option 3: 32 days

Option 4: 38 days


Team Careers360 12th Jan, 2024
Answer (1)
Team Careers360 13th Jan, 2024

Correct Answer: 32 days


Solution : Given: Vijay(V) and Sahil(S) complete a work in 40 days.
Sahil(S) and Ranjit(R) can complete the same work in 48 days.
Ranjit(R) and Vijay(V) can complete the same work in 60 days.
Total work is LCM of (40, 48, 60) = 240 units
Efficiency of Vijay and Sahil is $\frac{240}{40} = 6$
Efficiency of Sahil and Ranjit is $\frac{240}{48} = 5$
Efficiency of Ranjit and Vijay is $\frac{240}{60} = 4$
So, the efficiency of Vijay(V) and Sahil(S), Sahil(S) and Ranjit(R) and Ranjit(R) and Vijay(V) is (6 + 5 + 4) = 15.
Now, 2(V + S + R) = 15.
The efficiency of (V + S + R) is $\frac{15}{2}$.
So, the time taken by (V + S + R) is $\frac{\text{Total work}}{\text{Efficiency}}$.
$ \frac{240}{\frac{15}{2}} = 32$ days
Hence, the correct answer is 32 days.

Know More About

Related Questions

TOEFL ® Registrations 2024
Apply
Accepted by more than 11,000 universities in over 150 countries worldwide
Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books