Time And Work - Study Mode

[#106] There are three boats A, B and C, working together they carry 60 people in each trip. One day an early morning A carried 50 people in few trips alone. When it stopped carrying the passengers B and C started carrying the people together. It took a total of 10 trips to carry 300 people by A, B and C. It is known that each day on an average 300 people cross the river using only one of the 3 boats A, B and C. How many trips it would take to A to carry 150 passengers alone?
Correct Answer

(A) 15

Explanation

Solution: Combined efficiency of all the three boats = 60 passengers /trip Now, consider option (A) 15 trips and 150 passengers means efficiency of A = 10 passengers per trip A's efficiency = 10 passengers per trip Then, (B + C) combined efficiency = 50 passengers per trip Since, combined efficiency is 60 so option (A) is correct

[#107] To do a certain work, the ratio of efficiency of A to that of B is 3 : 7. Working together, they can complete the work in $$10frac{1}{2}$$xa0days. They work together for 8 days. 60% of the remaining work will be completed by A alone in:
Correct Answer

(C) 5 Days

Explanation

Solution: [x08egin{array}{*{20}{c}}
{}&A&{}&B \
{{ ext{Efficiency}} o }&3&:&7
end{array}] $$eqalign{
& { ext{Total work}} = left( {3 + 7}
ight) imes frac{{21}}{2} = 105 cr
& left( {A + B}
ight) imes 8 = left( {3 + 7}
ight) imes 8 = 80 cr
& { ext{Remaining work}} = 105 - 80 = 25 cr
& 60\% { ext{ work done by }}A = frac{{25 imes 60}}{{100 imes 3}} = 5{ ext{ days}} cr} $$

[#108] 3 men and 4 women can do a piece of work in 7 days, whereas 2 men and 1 woman can do it in 14 days. 7 women will complete the same work in:
Correct Answer

(A) 10 days

Explanation

Solution: (3m + 4w) × 7 = (2m + 1w) × 14 3m + 4w = 4m + 2w m = 2w m : w = 2 : 1 Total work = (3 × 2 + 4 × 1) × 7 = 70 unit 7w = 70 unit = $$frac{{70}}{7}$$ = 10 days

[#109] To do a certain work, the ratio of the efficiencies of X and Y is 5 : 4. Working together, they can complete the same work in 10 days. Y alone starts the work and leaves after 5 days. The remaining work will be completed by X alone in:
Correct Answer

(A) 14 days

Explanation

Solution: [x08egin{array}{*{20}{c}}
{}&{ ext{X}}&{}&{ ext{Y}} \
{{ ext{Efficiency}}}&5&:&4
end{array}] Total work = (5 + 4) × 10 = 90 Y × 5 + X × a = 90 4 × 5 + 5 × a = 90 20 + 5a = 90 5a = 70 a = 14

[#110] A contractor decided to complete a work in 80 days and employed 60 men at the beginning and 20 men additionally after 20 days and got the work completed as per schedule. If he had not employed, the additional men, how many extra days would he have needed to complete the work (round off to the nearest integer)?
Correct Answer

(B) 20 days

Explanation

Solution: Total work = 80 × 60 + 60 × 20 = 4800 + 1200 = 6000 60 men × d = 6000 d = 100 days Extra days = 100 - 80 = 20 days