Time and Work
- A report of 100 pages is to be typed by three typists. Typist A can type 100 pages in 10 hours. Typist B can type the same pages in 20 hours and typist C in 25 hours. Allthe three typist started typing at 09.00 a.m. At 01.00 p.m. typist A stopped typing. The other two typist finished the job, approximately at what time the report was typed ?
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∵ No. of pages typed by the typist A in 4 hours = 100 x 4/10 = 40
∴ No. of remaining pages = 100 - 40 = 60
Let B and C worked for H hours
∵ (100 x H)/20 + (100 x H)/25 = 60
⇒ 5H + 4H = 60Correct Option: D
∵ No. of pages typed by the typist A in 4 hours = 100 x 4/10 = 40
∴ No. of remaining pages = 100 - 40 = 60
Let B and C worked for H hours
∵ (100 x H)/20 + (100 x H)/25 = 60
⇒ 5H + 4H = 60
∴ H = 60/9 = 20/3 hours = 6 hours 40 min
∴ The time at which the report was typed 03.40 p.m.
- 16 men and 12 women together complete a work in 20 days. If 18 women complete the same work in 40 days. Then how many days will be taken by 12 men and 27 women together to complete the same work ?
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∵ In 20 days the work is completed by = 16 men + 12 women
∴ In 1 day the work is completed by = 20 x (16 men + 12 women )
= 320 men + 240 women
In 40 days the work is complete by 18 women
∴ 1 day the work is complete by = 18 x 40 = 720 women
∵ 720 women = 320 men + 240 women
⇒ (720 - 240)women = 320 men
⇒ 480 women = 320 menCorrect Option: D
∵ In 20 days the work is completed by = 16 men + 12 women
∴ In 1 day the work is completed by = 20 x (16 men + 12 women )
= 320 men + 240 women
In 40 days the work is complete by 18 women
∴ 1 day the work is complete by = 18 x 40 = 720 women
∵ 720 women = 320 men + 240 women
⇒ (720 - 240)women = 320 men
⇒ 480 women = 320 men
∴ 1 men = 480/320 = 3/2 women
∴ 12 men + 27 women = 12 x (3/2) + 27 = 45 women
∵ 18 women complete work in 40 days
∴ 45 women complete 1 work = 40 x 18/45 = 16 days
- Two workers A and B working together completed a job in 5 days. If A worked twice as efficiently as he actually did and B worked 1 / 3 as efficiently as he actually did the work, then they would have completed the work in 3 days. Find the time for A to complete the job alone ?
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Efficiency is proportional to work done per day. Work done per day N number of days
= Amount of work done. Considering efficience of A and B initially as 1.
Let A alone can do the work in M days and B alone can do the same work in N days.
Then, 5/M + 5/N = Total work done = 1
Since efficiency of A and B are 2 and 1/3 respectively
⇒ 6/M + 1/N = 1 ....(i)
and 1/M + 1/N = 5 .....(ii)Correct Option: B
Efficiency is proportional to work done per day. Work done per day N number of days
= Amount of work done. Considering efficience of A and B initially as 1.
Let A alone can do the work in M days and B alone can do the same work in N days.
Then, 5/M + 5/N = Total work done = 1
Since efficiency of A and B are 2 and 1/3 respectively
⇒ 6/M + 1/N = 1 ....(i)
and 1/M + 1/N = 5 .....(ii)
Now, subtracting equation (ii) from equation (i), we have M = 25/4 = 61/4 days.
- A and B can together finish a work in 30 days. They worked for it for 20 days and then B left. the remaining work was done by A alone in 20 more days. A alone can finish the work in ?
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(A + B)'s 20 day's work = (20 x 1/30) = 2/3
Remaining work = (1 - 2/3) = 1/3
1/3 work is done by A in 20 daysCorrect Option: D
(A + B)'s 20 day's work = (20 x 1/30) = 2/3
Remaining work = (1 - 2/3) = 1/3
1/3 work is done by A in 20 days
Whole work can be done by A in (3 x 20) days = 60 days.
- Ramesh can finish a job in 20 days. He worked for 10 days alone and completed the remaining job working with Dinesh, in 2 days. How many days would both Dinesh and Ramesh together can complete the whole work ?
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Ramesh alone finish 1/2of the work in 10 days.
Remaining 1/2 of the job was finished by Ramesh and Dinesh together in 2 days.Correct Option: A
Ramesh alone finish 1/2of the work in 10 days.
Remaining 1/2 of the job was finished by Ramesh and Dinesh together in 2 days.
Therefore, they both together can finish the complete job in 4 days.
