P alone can complete the work in 20 days, Q alone can complete the work in 30 days while R alone can complete the work in 10 days. They start working in turns as P works on first day, Q on second day and R on third day, so on till sixth day. On seventh day, all three worked together to complete remaining work. Find the approx. time in which whole work is completed.?

9.45 days
8.60 days
7.75 days
8.85 days

LohaHridoy

5 views

2025-01-04 04:42

1 Answers

AhmedNazir

Option 1 : 9.45 days

Calculation:

P's 1 day's work = 1/20

Q's 1 day's work = 1/30

R's 1 day's work = 1/10

(P + Q + R)'s 1 days work = 1/20 + 1/30 + 1/10 = 11/60

(P + Q + R)'s 6 days work = 2 × 11/60 = 11/30

Remaining work after 6 days = 1 - 11/30 = 19/30

Remaining work completed in = 19/30 × 60/11 = 38/11 days

∴ Required time to complete work = 38/11 + 6 = 104/11 ≈ 9.45 days

Alternate Method

Percentage of unit work done in 1 day by P = 100/20 = 5 units per day

Similarly,

Q = 100/30 = 10/3 = units per day

R = 100/10 = 10 units per day

(P + Q + R) work units per day = 5 + 10/3 + 10 = 55/3 units per day

(P + Q + R) 6 days working units = 2 × 55/3 = 110/3 units per day

Remaining work after 6 days - 100 - 110/3 = 190/3

Remaining work completed in = 190/3 × 3/55 = 190/55

∴ Required time to complete work = 190/55 + 6 = 104/11 ≈ 9.45 days

5 views Answered 2022-09-04 04:29

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