Time And Work - Study Mode
[#211] Kiran, Vishal and Dinesh work in a juice factory. Kiran takes 2 hours to extract as much juice as Vishal can in 3 hours. Dinesh takes 5 hours to extract as much juice that Kiran extracts in 4 hours. A tank can be filled with juice in 48 hours, if all of them work together. How long will it take to fill the tank, if Dinesh alone is trying to fill the tank?
Correct Answer
(B) 148 hrs
Explanation
Solution: $$eqalign{
& 3 imes V = 2 imes K cr
& frac{V}{K} = frac{2}{3} = frac{{10}}{{15}} cr
& 4 imes K = D imes 5 cr
& frac{K}{D} = frac{5}{4} = frac{{15}}{{12}} cr
& { ext{Total work}} = 48 imes left( {10 + 15 + 12}
ight) cr
& { ext{Time of Dinesh}} = left( {frac{{48 imes 37}}{{12}}}
ight) = 148{ ext{ hr}} cr} $$
[#212] A and B can do a work in 12 days and 18 days, respectively. They worked for 4 days after which B was replaced by C and the remaining work was completed by A and C in the next 4 days. In how many days will C alone complete 50% of the same work?
Correct Answer
(B) 18
Explanation
Solution: 4 day work = 5 × 4 = 20 Remaining work = 36 - 20 = 16 (A + C) complete in 4 days A + C $$ o frac{{16}}{4} = 4$$ 3 + C = 4 C = 1 50% of work = $$frac{{36}}{2}$$ = 18 C do = $$frac{{18}}{1}$$ = 18 days
[#213] A can complete a certain work in 35 days and B can complete the same work in 15 days. They worked together for 7 days, then B left the work. In how many days will A alone complete 60% of the remaining work?
Correct Answer
(A) 7
Explanation
Solution: 7 days work of (A and B) = 7 × 10 = 70 Remaining work = 105 - 70 = 35 60% of remaining work done by A = $$frac{{35 imes frac{3}{5}}}{3}$$ xa0= 7 days
[#214] Shyam can complete a task in 12 days by working 10 hours a day. How many hours a day should he work to complete the task in 8 days?
Correct Answer
(D) 15
Explanation
Solution: 10 × 12 = 8 × x 15 = x x = 15 days
[#215] 30 men working 8 hours per day can dig a pond in 16 days. By working how many hours per day can 32 men dig the same pond, in 20 days?
Correct Answer
(A) 6 hours/day
Explanation
Solution: Understanding the Problem: Imagine digging a pond. It takes a certain amount of effort. That effort is made up of the number of workers, the number of hours they work each day, and the number of days they work. What we know: 30 men working 8 hours a day take 16 days to dig the pond. What we want to find: How many hours a day will 32 men need to work to dig the *same* pond in 20 days? Think of it like this: The total work is the same (digging the same pond). Total work is calculated as: (Number of men) x (Hours per day) x (Number of days). Let's calculate the total work: Total work = 30 men x 8 hours/day x 16 days = 3840 man-hours Now, let's use the total work to find the hours needed for 32 men working for 20 days: 3840 man-hours = 32 men x (Hours per day) x 20 days Solve for "Hours per day": (Hours per day) = 3840 man-hours / (32 men x 20 days) (Hours per day) = 3840 / 640 = 6 hours/day Therefore, the answer is: A: 6 hours/day Alternative Solution 8 × 30 × 16 = 32 × 20 × $$x$$ $$x$$ = 6 hours per day