Question

If P, Q and R can complete a work in 6 days. P can work twice faster than Q and thrice faster than R, then the number of days R alone can complete the work is :
1. 22 days
2. 33 Days
3. 66 Days
4. 11 Days

Answer 1

Correct Answer - Option 2 : 33 Days

Given:

Efficiency of P and Q = 2 ∶ 1

Efficiency of P and R = 3 ∶ 1

They all can complete work in days = 6        

Calculation:

Efficiency ratio of P : Q : R = 6 : 3 : 2

Q  P  R

1 : 2

     3 : 1

3 : 6 : 2

⇒ Work done by P in a day = 6x

⇒ Work done by Q in a day = 3x

⇒ Work done by R in a day = 2x

Total Work/Total work done by all in a day = Number of days

⇒ Total Work/(6x + 3x + 2x) = 6

⇒ Total Work = 66x

R alone will complete work in days = 66x/2x = 33 days

∴ R alone will complete work in 33 days.