Question
βPβ, βQβ, and βRβ can
complete a task in 10 days, 15 days, and 20 days, respectively. βPβ starts the task alone and is joined by βQβ on the second day. On the third day, βQβ is replaced by βRβ, and again on the fourth day, βPβ works alone. The process repeats in the same manner. Find the total time taken to complete the task. (Round off to two decimal places)Solution
ATQ,
Let the total work be the LCM of [10, 15, 20] = 60 units. Efficiency of βPβ = 60/10 = 6 units/day. Efficiency of βQβ = 60/15 = 4 units/day. Efficiency of βRβ = 60/20 = 3 units/day. Work done on the first day = 6 Γ 1 = 6 units. Work done on the second day = (6 + 4) Γ 1 = 10 units. Work done on the third day = (6 + 3) Γ 1 = 9 units. Total work done in the first three days = 6 + 10 + 9 = 25 units. Remaining work = 60 β 25 = 35 units. Time taken to complete the remaining work = (6/6) + (10/10) + (9/9) + (10/17) β 3 + (10/17) β 3.59 days. Total time = 3 + 3.59 = 6.59 days.
3 men, 4 women and 5 boys can do a piece of work in 15 days, 20 days and 25 days respectively. For first 3 days 3 men and 2 women work together and for ...
B is 20% more efficient than A. If B was 60% more efficient than A, then, B could complete the work in 18 days lesser than days taken by A. What fractio...
X men can complete the piece of work in 50 days and (X + 51) men can complete the same work in 30 days less than that of days taken by X men. Find the v...
βnβ men working 12 hours a day can complete a work in 15 days while (3n β 8) men working 12 hours a day can complete the same work in 9 days. In h...
- 8 men working for 5 hours a day can complete a work in 28 days. If 16 women are employed to work, then find how many hours a day they have to work to compl...
A and B together can complete a piece of work in 48 days while B and C together can complete the same work in 58 days. All of three together can complet...
A alone can complete a work in 16 days and B alone in 12 days. Starting with A, they work on alternate days. In how many days, total work will be comple...
The amount of work completed by 24 men in 5 hours is equivalent to the work done by 21 women in 8 hours. A team of 33 men, working 6 hours daily, can fi...
4 girls working together for 1 day complete the same amount of work as 6 men working together for 1 day. The efficiency of 1 man ...
P and Q together can finish a task in 72 days while Q and R can do it in 48 days. If P worked for 18 days, Q worked for 30 days, and then R finished the...