P can complete a task in 10 days working 6 hours a day. Q can complete the same task in 9 days working 10 hours a day. If both P and Q work together working 6 hours a day, then in how many days can they complete the task?

Correct option is D

Given:

P can complete a task in 10 days working 6 hours a day.

Q can complete the same task in 9 days working 10 hours a day.

Both P and Q work together working 6 hours a day.

Formula used:

Work done in 1 hour = $$\frac{\text{Total work}} {\text{ Number of days × Hours per day}}$$​​

Solution:

Work done by P in 1 hour:

=> $$\frac1 { (10 × 6)} = \frac1 { 60}$$​​

Work done by Q in 1 hour:

=> $$\frac1 { (9 × 10)} = \frac1{ 90}$$​​

Work done by P and Q together in 1 hour:

=> $$\frac1{ 60 }+ \frac1 { 90}$$​​

=> $$\frac{(3 + 2)} { 180}$$​

=> $$\frac5 { 180}$$​​

=> $$\frac 1 { 36}$$​​

Time taken by P and Q together working 6 hours a day:

=> $$\frac 1 {(1 / 36) × 6}$$​​

=> $$\frac1 { (1 / 6)}$$​​

=> 6 days