Problems on time and work part 9

Q. 16. 39 men can repair a road in 12 days working 5 hours a day. In how many days will 30 men working 6 hours peer day complete the work?(a) 10 (b) 13 (c) 14 (d) 15 (e) None of theseAns: (b) 13Explanation:1 work done = 39 12 539 12 5 = 30 6 ?days? days = 39 12 5/ 30 6 = 13 days. Ans.Q. 17. A certain number of men can do a work in 40days. If there were 8 men more, it could be finished in 10 days less. How many men were there initially?(a) 30 (b) 24 (c) 16 (d) 20 (e) None of theseAns: (b) 24Explanation:Let x be the initial number of menThen, 1 work done = x 40Then, x 40 = (x + 8 ) (40 10) 40x = 30x + 24010x = 240Therefore, x = 240/10 = 24 men. Ans.Q. 18. If 4 men or 6 boys can finish a work in 20 days. How long will 6 men and 11 boys take to finish the same work?(a) 10 days (b) 6 days (c) 4 days (d) 3 days (e) None of theseAns: (b) 6 daysExplanation:4 men = 6 boysThen, 1 boy = 4/6 men = 2/3 men11 boys = 2/3 11 men = 22/3 menThen, 6 men + 11 boys = 6 + 22/3 men = 40/3 men1 work done = 4 men 20daysThat is, 4 20 = 40/3 ? days? days = 4 20 3/40 = 6 days. Ans.Q. 19. A works twice as fast as B. if B can complete a work in 12 days independently. The number of days in which A and B can together finish the work?(a) 18 days (b) 8 days (c) 6 days (d) 4 days (e) None of theseAns: (d) 4 daysExplanation:If B takes 12 days to finish the work, then A takes 6 days to finish the same work.If A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days.Therefore, the Number of days taken by A and B together to finish the same work = 6 12/18 = 4 days. Ans.Q. 20. A and B can do a piece of work in 4 days. If A can do it alone in 12 days, B will finish the work in(a) 4 days (b) 6 days (c) 8 days (d) 10 days (e) None of theseAns: (b) 6 daysExplanation:If A and B together can do a piece of work in x days and A alone can do the same work in y days, then B alone can do the same work in x y/ y x days.Therefore, the number of days B will take to finish the work = 4 12/ 12 4 = 48/8 = 6 days. Ans.