Time and Work problems
- 1. Adam and Smith are working on a project. Adam takes 6 hrs to type 36 pages on a computer, while Smith takes 5 hrs to type 40 pages. How much time will they take, working together on two different computers to type a project of 120 pages?
Options- A. 8 hrs 45 min
- B. 8 hrs 42 min
- C. 8 hrs
- D. 8 hrs 34 min Also asked in: GATE, CAT, Bank Exams, Bank PO, Bank Clerk
Correct Answer: 8 hrs 34 min
Explanation:
Number of pages typed by Adam in 1 hour = 36/6 = 6
Number of pages typed by Smith in 1 hour = 40/5 = 8
Number of pages typed by both in 1 hour = (6 + 8) = 14
Time taken by both to type 110 pages = (120 * 1/14) =
= 8 hrs 34 min.
- 2. 6 boys and 8 girls can do job in 10 days , 26 boys & 48 women do work in 2 days. Find time taken by 15 boys and 20 girls to do same work ?
Options- A. 2 days
- B. 3 days
- C. 4 days
- D. 5 days Also asked in: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk, Analyst
Correct Answer: 4 days
Explanation:
One day work of 6 boys and 8 girls is given as 6b + 8g = 1/10 -------->(I)
One day work of 26 boys and 48 women is given as 26b + 48w = 1/2 -------->(II)
Divide both sides by 2 in (I) and then multiply both sides by 5
Now we get, 15b + 20g = 1/4.
Therefore, 15 boys and 20 girls can do the same work in 4 days.
- 3. After working for 8 days, Hari Ram finds that only 1/3 rd of the work has been done. He employs Satya who is 60% as efficient as Hari Ram. How many days more would Satya take to complete the work ?
Options- A. 24 1/2 days
- B. 25 3/2 days
- C. 24 2/3 days
- D. 26 2/3 days Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 26 2/3 days
Explanation:
1/3 ---- 8
1 -------?
Hari can do total work in = 24 days
As satya is 60% efficient as Hari, then
Satya = 1/24 x 60/100 = 1/40
=> Satya can do total work in 40 days
1 ----- 40
2/3 ---- ? => 26 2/3 days.
- 4. Pavan and Sravan are two persons. If Pavan works with his actual efficiency and Sravan twice of his actual efficiency then it takes 25 days to complete the work. But If Pavan works twice of his actual efficiency and Sravan with his normal efficiency then the work is completed in 20 days. How many days would it take if Sravan alone works with his actual efficiency (in Days)?
Options- A. 50
- B. 100
- C. 70
- D. 35 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 100
Explanation:
Let the Efficiency of pavan be E(P)
Let the Efficiency of sravan be E(S)
Here Work W = LCM(25,20) = 100
Now, E(P+2S) = 100/25 = 4 ....(1)
E(2P+S) = 100/20 = 5 ....(2)
Hence, from (1) & (2) we get
E(S) = 1
=> Number of days Savan alone work to complete the work = 100/1 = 100 days.
- 5. Priya can do a work in 16 days. In how many days will the work be completed by Sai, if the efficiency of Sai is 60% more than that of Priya ?
Options- A. 8 days
- B. 12 days
- C. 14 days
- D. 10 days Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 10 days
Explanation:
Ratio of efficiencies of Priya and Sai is
Sai : Priya = 160 : 100 = 8 : 5
Given Priya completes the work in 16 days
Let number of days Sai completes the work be 'd'
=> 5×16 = 8×d
d = 10 days.
Therefore, number of days Sai completes the work is 10 days.
- 6. Kaushalya can do a work in 20 days, while kaikeyi can do the same work in 25 days. They started the work jointly.Few days later Sumitra also joined them and thus all of them completed the whole work in 10 days. All of them were paid total Rs.700. What is the Share of Sumitra?
Options- A. Rs.130
- B. Rs.185
- C. Rs.70
- D. can't be determined Discuss
Correct Answer: Rs.70
Explanation:
Efficiency of kaushalya = 5%
Efficiency of kaikeyi = 4%
Thus, in 10 days working together they will complete only 90% of the work.
[(5+4)*10] =90
Hence, the remaining work will surely done by sumitra, which is 10%.
Thus, sumitra will get 10% of Rs. 700, which is Rs.70
- 7. Three taps P, Q and R can fill a tank in 12 hrs, 15 hrs and 20 hrs respectively. If P is open all the time and Q and R are open for one hour each alternately, starting with Q, then the tank will be full in how many hours ?
Options- A. 9 hrs
- B. 7 hrs
- C. 13 hrs
- D. 11 hrs Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 7 hrs
Explanation:
Given,
P can fill in 12 hrs
Q can fill in 15 hrs
R can fill in 20 hrs
=> Volume of tank = LCM of 12, 15, 20 = 60 lit
=> P alone can fill the tank in 60/12 = 5 hrs
=> Q alone can fill the tank in 60/15 = 4 hrs
=> R alone can fill the tank in 60/20 = 3 hrs
Tank can be filled in the way that
(P+Q) + (P+R) + (P+Q) + (P+R) + ....
=> Tank filled in 2 hrs = (5+4) + (5+3) = 9 + 8 = 17 lit
=> In 6 hrs = 17 x 6/2 = 51 lit
=> In 7th hr = 51 + (5+4) = 51 + 9 = 60 lit
=> So, total tank will be filled in 7 hrs.
- 8. P and Q can do a work in 4 hours and 12 hours respectively. P starts the work at 9am and they work alternately for one hour each. When will the work be completed ?
Options- A. 3 am
- B. 12 pm
- C. 1 pm
- D. 3 pm Also asked in: GATE, CAT, Bank Exams, Bank PO, Bank Clerk
Correct Answer: 3 pm
Explanation:
Work done by P and Q in the first two hours, working alternately
= First hour P + Second hour Q
work is completed in 2 hours
Then, the total time required to complete the work by P and Q working alternately=2 x 3= 6hours
Thus, work will be completed at 3pm.
- 9. K can lay Highway road between two cities in 16 days. L can do the same job in 12 days. With the help of M, they completes the job in 4 days. How much days does it take for M alone to complete the work ?
Options- A. 47/7 days
- B. 59/6 days
- C. 48/5 days
- D. 57/5 days Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 48/5 days
Explanation:
Amount of work K can do in 1 day = 1/16
Amount of work L can do in 1 day = 1/12
Amount of work K, L and M can together do in 1 day = 1/4
Amount of work M can do in 1 day = 1/4 - (1/16 + 1/12) = 3/16 ? 1/12 = 5/48
=> Hence M can do the job on 48/5 days = 9 (3/5) days
- 10. P, Q, and R can do a job in 12 days together. If their efficiency of working be in the ratio 3 : 8 : 5, Find in what time Q can complete the same work alone?
Options- A. 36 days
- B. 30 days
- C. 24 days
- D. 22 days Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO, Database Administrator, IT Trainer
Correct Answer: 36 days
Explanation:
Given the ratio of efficiencies of P, Q & R are 3 : 8 : 5
Let the efficiencies of P, Q & R be 3x, 8x and 5x respectively
They can do work for 12 days.
=> Total work = 12 x 16x = 192x
Now, the required time taken by Q to complete the job alone = days.
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