Time and work
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The document contains examples and questions related to time and work problems. It discusses concepts like work done by individuals in a given time period, ratios of work done, and examples of calculating time taken to complete a piece of work when multiple people work together or independently. Sample problems are provided along with explanations of the solutions and calculations involved.
Time and work
- 2. Work from Days If A can do a piece of work in n days, then A's 1 day's work = 1 . n • Days from Work: • If A's 1 day's work = 1 , then A can finish the n work in n days.
- 3. Ratio • If A is thrice as good a workman as B, then: Ratio of work done by A and B = 3 : 1. Ratio of times taken by A and B to finish a work = 1 : 3.
- 4. Question • Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same job. How long should it take both A and B, working together but independently, to do the same job? • A. 4 2/9 days • B. 4 4/9 days • C. 4 5/9 days • D. 4 7/9 days
- 5. • Answer: Option B • Explanation: • A’s 1 hour’s work = 1/8 • B’s 1 hour’s work = 1/10 • (A+B)’s 1 hour’s work = (1/8+1/10) = 9/40 • Both A and B will finish the work in 40/9= 4 4/9 days
- 6. Question • Rohan can do a piece of work in 36 days but with the help of Mohan he can complete the work in 24 days. Find the no of days in which Mohan alone can complete the work? • A 80 days • B 84 days • C 72 days • D 74 days
- 7. C 72 days • Total work done by Rohan and Mohan=L.C.M of 36 & 24= 72 days • Work rate of Rohan= 72/36=2 • Combine work rate(R+M)=72/24=3 • Work rate of Mohan=3-2=1 • No.of days required by Mohan=72/1 =72 days
- 8. Question • A and B together can complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work? • A. 6 days • B. 4 days • C. 8 days • D. 9 days
- 9. • Answer: Option A • Explanation: • (A+B)’s 1 day’s work = ¼ • A’s 1 day’s work = 1/12 • B’s 1 day’s work = ¼ - 1/12 = 1/6 • B alone can complete the work in 6 days.
- 10. Question • A and B can do a work in 25 days and 20 days. Both together work for 5 days and then A leaves off. How many days B take to finish the remaining work? • A 16 days • B 11 days • C 12 days • D 14 days
- 11. B 11 days • A can finish work in 25 days & B can finish the work in 20 days • Total work done=100(L.C.M of 25&20) • A’s Contribution=100/25=4 • B’s Contribution =100/20=5 • First we need to calculate 5 days work=9x5=45 • Remaining work=100-45=55 • B require No.of days=55/5=11 days
- 12. Question • A is twice as good a workman as B and together they finish a piece of work in 18 days. In how many days will A alone finish the work? • A. 27 days • B. 24 days • C. 28 days • D. 29 days
- 13. • Answer: Option A • Explanation: • (A’s 1 day’s work) : (B’s 1 day’s work) = 2 : 1 • (A+B)’s 1 day’s work = 1/18 • Divide 1/18 in the ratio 2 : 1 • A’s 1 days work = 1/18 x 2/3 = 1/27 • So, A alone can finish the work in 27 days.
- 14. Question • A can finish a work in 24 days. B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. The remaining work was done by A in • A 9 days • B 10 days • C 11 days • D 12 days
- 15. B 10 days • Total work done= L.C.M of 24,9,8=72 • Work rate of A =72/24=8 • Work rate of B= 72/9=8 • Work rate of C=72/12=6 • In 3 days B & C can complete work=14x3=42 part • Remaining work= 72-42=30(A’s Work) • No of days required by A= 30/3= 10 days
- 16. Question • A and B working separately can do a piece of work in 9 and 12 days respectively. If they work for a day alternately, A beginning, in how many days, the work will be completed? • A. 10 ¼ days • B. 10 ½ days • C. 8 ¼ days • D. 8 ½ days
- 17. • Answer: Option A • Explanation: • (A+B)’s 2 day’s work = 1/9+1/12 = 7/36 • Work done in 5 pairs of days = 5x7/36=35/36 • Remaining work = 1 – 35/36 = 1/36 • On 11th day, it is A’s turn. • 1/9 work done by him in 1 day. • 1/36 work done by him in (9x1/36) = ¼ days. • Total time taken = 10 + ¼ = 10 ¼ days.
- 18. Question • A and B can do a piece of work in 20 days and 12 days resp. A alone started the work and then after 4 days B joined him till the completion of work. How long did the work last? • A 10 days • B 12 days • C 13 days • D 11 days
- 19. A 10 days • Total Work Done by A & B =L.C.M OF 20&12 =60 • Work done by A=60/20=3 part • Work done by B =60/12=5 part • In 4 days work done= 4x3=12 • Remaining work=60-12=48 • Combine work rate=A+B=3+5=8 • No.of days both A&B work=48/8=6 • Total no.of days work last=6+4=10 days
- 20. Question • 45 men can complete a work in 16 days. Six days after they started working, 30 more men joined them. How many days will they now take to complete the remaining work? • A. 6 days • B. 4 days • C. 8 days • D. 9 days
- 21. • Answer: Option A • Explanation: • 45 men can complete the work in 16 days. • (45x16) men can complete the work in 1 day. • 1 man’s 1 day’s work = 1/720 • 45 men’s 6 day’s work = 45/720 x 6 = 3/8 • Remaining work = 1 – 3/8 = 5/8 • 75 men’s 1 day’s work = 75/720 = 5/48. • Now, 5/48 work is done by them in 1 day. • So, 5/8 work is done by them in 48/5 x 5/8 = 6 days
- 22. QUESTION • IF 5 MEN OR 19 WOMEN CAN DO A PIECE OF WORK IN 19 DAYS. IN HOW MANY DAYS CAN 3 MEN AND 6 WOMEN WILL DO THE SAME WORK? • A 10 • B 15 • C 18 • D 20
- 23. B-15 DAYS • 5M/9W Can do work in 19 days.3M & 6W =d2(find) • 5MX 19=(3M+6W)d2 • 1W=5/9M, 6W=5/9X6=10/3M • 5MX19=(3M+6W)d2 • 5MX19=(3M+10/3M)d2 • 5X19=(3+10/3)d2 • d2= 15 days
- 24. Question • Sachin can do a piece of work in 10 days while Rahul can do it in 15 days. They work together for 5 days and the rest work is done by Virat in 2 days. If they get Rs 4500 for the whole work what is the share of Virat? • A 700 Rs • B 780 Rs • C 800 Rs • D 750 Rs
- 25. D 750 Rs • Sachin Work= 10 , Rahul Work=15 • Total work done by both= 30 • Work rate of Sachin= 30/10=3 • Work rate of Rahul=30/15=2 • One day Sachin & Rahul can complete 3+2=5 piece of work • In 5 days work complete=5(sachin & rahul work)x 5(no.of days)=25 • S & R: V=25:5=5:1 • Virat Share=4500/6x 1=750 Rs
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