P takes twice as long as Q or three times as long as R to complete a task. If they work together, they can complete the task in two days. How long will it take Q to complete the task on his own?

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 24 Jul 2023 Shift 1)

Answer 1

Given:

Time taken by P = Twice the time taken by Q

Time taken by P = Thrice the time taken by R

Formula used:

Efficiency = Total work/Time taken

Calculation:

Let the time taken by P be 6 units

⇒ Time taken by Q = 3 units

⇒ Time taken by R = 2 units

L.C.M of (2, 3 and 6) = 6 units (Total work)

⇒ Efficiency of P = 6/6 = 1 units/day

⇒ Efficiency of Q = 6/3 = 2 units/day

⇒ Efficiency of R = 6/2 = 3 unit/day

Total efficiency = (1 + 2 + 3) = 6 units/day

They complete the task in 2 days,

Hence, total units of work = 6 × 2 = 12 units

Thus, Q takes total time,

⇒ 12/2 = 6 days

It takes 6 days for Q to complete the task on his own.

Shortcut Trick

We know time is inversely proportional to efficiency.

So Ratio of efficiency

⇒ P : Q : R = 1 : 2 : 3

Total work in 2 days = 12

Time take by Q = 12/2 = 6 days