Question : X can do a work in 3 days, Y can do three times the same work in 8 days, and Z can do five times the same work in 12 days. If they have to work together for 6 hours a day, then how much time will they take to complete the work?
Option 1: 4 hours
Option 2: 5 hours 20 minutes
Option 3: 4 hours 10 minutes
Option 4: 5 hours
Correct Answer: 5 hours 20 minutes
Solution :
X can complete the work in 3 days.
Y can do three times the same work in 8 days.
Z does five times the same work in 12 days.
Working hours per day = 6 hours
Efficiency = $\frac{\text{Total work}}{\text{Total Time}}$
Let the total work be 1 unit.
Time to complete 1 unit by X alone = 3 × 6 = 18 hours
Time to complete the 3 units by Y alone = 8 × 6 = 48 hours
Time to complete the 1 unit by Y alone = $\frac{48}{3}$ = 16 hours
Time to complete the 5 units by Z alone = 12 × 6 = 72 hours
Time to complete the 1 unit by Z alone = $\frac{72}{5}$hours
Efficiency of X = $\frac{1}{18}$ units/hour
Efficiency of Y = $\frac{1}{16}$ units/hour
Efficiency of Z = $ \frac{5}{72}$ units/hour
Combined efficiency of X, Y and Z $=\frac{1}{18} + \frac{1}{16}+ \frac{5}{72}=\frac{(8 + 9 + 10)}{144}=\frac{27}{144}$ units/hour
Time to complete total work by X, Y and Z together
= $\frac{1}{\frac{27}{144}}$= $\frac{144}{27}$ hours = $\frac{144}{27}×60$ = $320$ minutes = 5 hours 20 minutes
Hence, the correct answer is 5 hours 20 minutes.
Related Questions
Know More about
Staff Selection Commission Sub Inspector ...
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Get Updates Brochure
Your Staff Selection Commission Sub Inspector Exam brochure has been successfully mailed to your registered email id “”.
