Time And Work - Study Mode

[#216] 25 men can complete a task in 16 days. Four days after they started working, 5 more men, with equal workmanship, joined them. How many days will be needed by all to complete the remaining task?
Correct Answer

(B) 10 days

Explanation

Solution: $$eqalign{
& 25 imes 16 = 25 imes 4 + 30 imes x cr
& left( {{M_1} imes {D_1}}
ight) = left( {{M_1}{D_1} imes {M_2}{D_2}}
ight) cr
& 400 = 100 + 30x cr
& 300 = 30x cr
& x = 10{ ext{ days}} cr} $$

[#217] A and B separately can build a wall in 12 and 16 days, respectively. If they work for each day alternatively, starting with A, in how many days will the wall be built?
Correct Answer

(C) $$13frac{2}{3}{ ext{ days}}$$

Explanation

Solution: 2 days → 4 + 3 = 7 units 12 days → 42 units 13 days → 42 + 4 = 46 units Total time taken = $$13frac{2}{3}{ ext{ days}}$$

[#218] 3 men and 8 women can complete a work in $$frac{{75}}{8}$$ days. While 9 men and 12 women can complete it in $$frac{{25}}{7}$$ days. In how many days will 15 women complete it?
Correct Answer

(C) 20

Explanation

Solution: $$eqalign{
& left( {3m + 8w}
ight) imes frac{{75}}{8} = left( {9m + 12w}
ight) imes frac{{25}}{7} cr
& 63m + 168w = 72m + 96w cr
& 72w = 9m cr
& frac{m}{w} = frac{8}{1} cr
& { ext{Total work}} = left( {3m + 8w}
ight) imes frac{{75}}{8} cr
& = left( {3 imes 8 + 8 imes 1}
ight) imes frac{{75}}{8} cr
& = 4 imes 75 cr
& { ext{Time taken by }}15w = frac{{4 imes 75}}{{15 imes 1}} = 20{ ext{ day}} cr} $$

[#219] If 27 people, working 8 hours a day, can complete a task in 12 days, then in how many days will 18 people finish the task, working 9 hours a day?
Correct Answer

(C) 16 days

Explanation

Solution: 27 × 8 × 12 = 18 × 9 × x x = 16 days

[#220] A can do 40% of a work in 12 days, whereas B can do 60% of the same work in 15 days. Both work together for 10 days. C completes the remaining work alone in 4 days. A, B and C together will complete 28% of the same work in∶
Correct Answer

(D) 2 days