Question

Three people P, Q, R can do a piece of work in 18 days, 24 days, and 30 days respectively. if P works regularly and (Q + R) help him every third day. how long will it take for them to complete the work?
1. 12 days
2. \(12\frac12\) days
3. \(12\frac35\) days
4. 13 days
5. \(13\frac23\) days

Answer 1

Correct Answer - Option 3 : \(12\frac35\) days

GIVEN:

time taken by P to complete the work = 18 days 

time taken by Q to complete the work = 24 days

time taken by R to complete the work = 30 days

P is helped by Q and R every third day

EXPLANATION:

let the total work be 360(L.C.M of 18, 24, 30 )

P's work per day = 20

Q's work per day = 15

R's work per day = 12

work done in three days = 20 × 3 + (15 + 12) = 87

work done in 12 days = 87 × 4 = 348

remaining 12 work will be done by P in \(\frac{12}{20} = \frac35days\)

∴ total time = \(12\frac35days\)