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Chapter : Set / Time and work Powered by: Destiny Educational Materials[DEM]
1. In an examination, 35% of students passed in Nepali only and 25% passed in mathematics only. If 20% of students were failed in both subject, i. What percent of students passed in both subjects? Ans:20% ii. What percent of students passed in mathematics? Ans:45% iii. Represent above information in a Venn diagram. 2. In the survey of a community of 215 people, it was found that 115 people could speak English language, 119 could speak both languages. i. Represents the above information in a Venn-diagram supposing x as the number of people who can speak both languages. ii. Determine the value of x. Ans:34 iii. Find the number of people who can speak Hindi language only. Ans:85 3. In a survey of a group of people, it was found that 70% of the people liked folk songs, 60% liked modern songs, 4000 people liked both of them and 10% liked none of them then i. Draw a Venn-diagram to illustrate the above information. ii. Find the total number of people in the survey. Ans:10000
4. In a survey of some students, it was found that 60% of the students studied commerce and 40% studied science. If 40 students studied both the subjects and 10% didn’t study any of the subjects, by drawing Venn-diagram, i. Find the total number of students. Ans:400 ii. Find the number of students who studied science only. Ans:120 5. Out of 120 students appeared in an examination the number of students who passed in mathematics only is twice the number of students who passed in science only. If 50 students passed in both subjects and 40 students failed in both subjects then: i. Find the number of students who passed in Mathematics. Ans:70 ii. Find the number of students who passed in science. Ans:60 iii. Show the result in Venn-diagram. 6. In a survey, it was found that the ratio of the people, who liked modern songs and folk songs is 8:9. Out of which, 50 people liked both songs, 40 liked folk songs only and 80 liked none of the songs: i. Represents the above data in a Venn-diagram. ii. Find the number of people who participated in the survey. Ans:200 7. Out of group of 500 Japanese tourists who visited Nepal, 40% have been already to India and 30% to China. 10% of them have been to both the countries. How many have not been to either of the countries. Also illustrate in a Venn-diagram. Ans:200
8. In a certain examination, 58% failed in English, 39% in Account, 25% in statistics, 32% in English and account, 19% in English and statistics, 17% in account and statistics and 13% in all the three subjects. i. Draw the Venn diagram to illustrate above information ii. What percentage didn’t fail in any of the subjects? Ans:33% 9. In a group of students, 15 read English, 12 read Nepali, 10 read Accounts, 6 read English and Nepali only, 4 read Nepali and Account only, 3 read English and Account only and there is no one who reads Nepali only. Draw Venn-diagram for this information and find i. Total number of students in the group. Ans:20 ii. Number of students reading account only. Ans:1 10. Each of a group of 20 students studies at least one of the three subjects Nepali, English and Maths. All of them who study English also study Nepali, 3 study all three subjects, 4 students study Nepali, 8 students study English, 14 students study Nepali. i. Draw Venn-diagram to illustrate above information. ii. How many students study Maths and Nepali but not English? Ans:2 iii. How many students study only Maths? Ans:6 11. Sita can do a work in 6 days and Gita can do it in 10 days. They worked together for 3 days and Sita left the work: i. In how many days can Gita do the remaining work alone? Ans:3 days ii. How many days are needed to complete the whole work? Ans:5 days
12. A and B can finish a piece of work in 40 days. After they worked for 25 days, B left. If A can finish the remaining work in 45 days, how long B alone can finish the whole work? Ans:60 days 13. A and B can finish a piece of work in 12 and 18 days respectively. After some days when both start to work together A leaves and B completes the remaining work in 6 days. How many days has A worked together before he left? Ans:24/5 days
14. A and B can do a piece of work in 30 and 45 days respectively. They worked it together for some days then B leaves. If B leaves 5 days before the completion of the work, how many days did they work together? Ans:15 days 15. Hari can do 2/5 of work in 9 days. He calls Shankar to finish the remaining work. They work together and finish it in 6 days. How many days will be taken by Shankar to finish whole work alone? Ans:18 days 16. 20 men can do a piece of work in 30 days. After working for how many days, should 5 men leave the work so that the entire work will be completed in 35 days? Ans:15 days 17. 20 men can do a piece of work in 24 days. After working for 6 days, an additional number of men is taken to finish the work in 21 days from the beginning. Find the number of additional men. Ans: 4 men 18. Men undertook a contract to finish a piece of work in 32 days and he immediately employed 28 laborers to do the work. After
24 days only two third of the work was finished. How many laborers should added to finish the work in time? Ans:14 workers 19. A contractor undertook to finish a piece of work in 100 days. He appointed some workers in the beginning but half of the work in 60 days. How many workers are appointed first so that the work will be finished on the specified on time if 10 extra workers are added? Ans: 20 workers 20. A, B and C can finish a piece of work in 30, 40 and 60 days respectively. 10 days after they started to work together b leaves. 4 days after B left, A leaves and C completes the remaining work. Find how many days can C had worked altogether. Ans:17 days
complete the work if all of them work together. How long would B take to do all the work by himself? Ans;66 days 25. A takes twice as much time as B and thrice as much time as C to finish a piece of work. If they work together they can finish the whole work in 5 days. Find the time each will take to finish the work separately. Ans:30, 15, 10 days 26. A and B together can do a piece of work in 12 days while B and C together can do it in 16 days. After A has been working at it for 5 days, and B for 7 days, C finishes it in 13 days. In how many days can C do the whole work alone? Ans:24 days
21. A, B and C can do a piece of work in 30, 40 and 60 days respectively. All of them started to work together but B left after working for 8 days. In how many days A and C can complete the remaining work? ANs: 8 days
27. 40 men can do a piece of work in 24 days. After working for a few days 8 men are added and the whole work was completed in 3 days earlier. After how many days were those 8 men added? Ans:6 days 28. A man and a boy can do a piece of work in 72 days. If the man works alone for last 20 days, it is finished in 80 days. In what time can the man do the whole work by himself? Ans:288 days
22. A, B and C can do a work in 30, 50 and 75 days respectively. All of the three started the work together but A left the work after 12 days and B left it 10 days, before the completion. Find in how many days the work would have been finished. Ans:24 days
29. Three taps can fill a cistern in 36 minutes, 30 minutes and 20 minutes respectively. The cistern being empty all the three taps are kept open and after 6 minutes the first tap is closed. In how many more minutes will the cistern be full? Ans:4 min
23. There are three water taps in a water tank. Tap A can fill the tank in 8 minutes, B can fill in 12 minutes and C can empty that tank in 16 minutes. If all the three taps are opened together, how long will it take to fill the empty tank? Ans 47/7 min 24. A can do as much work in 2 days as B can do in 3 days, and B can do as much work in 4 days as C in 5 days. It takes 20 days to
30. To complete a piece of work, A would take twice a long as B and C together and B three times as long as C and A together. A, B and C together can do it in 12 days. In what time each do it? Ans:36, 48, 144/5 days
31. X, Y and Z can do a piece of work in 10, 20 and 30 days respectively. They all worked for 4 days. After 4 days X leaves. Y and Z go on together for some days and Z leaves 5 days before completion the work. In how many days would whole work be completed? Ans:91/15 days 32. A did 3/5 of a work in 6 hrs, B did 3/4 of what remained in 2 hrs and C finished it in half an hour. How long would they have been doing the work if they had worked together? Ans:14/13 hrs 33. A tap can fill 25% of a tank in 3 hours and another tap can empty whole tank in 15 hours. If both the taps are opened at the same time and the capacity of a tank is 1000 liter, in what time 100 liter water will be collected in the tank? Ans:6 hrs 34. A can do a piece of work in 20 days, B can do it in 30 days and C in 40 days. Three of them started the work together. A left the work after 5 days and C left it in 10 days before its completion. Find in how many days the work might have been finished? Ans:120/7 days 35. Two taps P and Q can fill a tank in 2 hours and 4 hours respectively. They opened at once. After sometime P was shut up and the tank was filled in 2 hours more. How long after the pipes had been opened was the tap P shut up? Ans:40min