If P, Q and R can complete a work in 6 days. P can work twice faster t

1.	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 days2. 33 Days3. 66 Days4. 11 Days
Answer» 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.

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 days2. 33 Days3. 66 Days4. 11 Days

Answer» 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.

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