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Q5) 18 men promised to do a job in a few days. 2 of them were absent and it took 1 more day than the
planned number of days. Find the planned number of days? 1) 16 2) 12 3) 10 4) 8 Solution: Where y be the planned number of days. So, 18 men can do the job in y days. 16 men did this job in (y + 1) days. So, 18y = 16(y + 1) On solving, y = 8 Hence, option 4. Q6) 20 people can dig a trench 75 m long, 50 m wide and 15 m deep in 15 days working 10 hours a day. Find the number of people required to dig a trench 60 m long, 45 m wide and 21 m deep in 12 days working 9 hours a day? 1) 15 2) 18 3) 28 4) 25 Solution: In this question we are given 3 parameters, men, days and hours. So, Work = k(Men)(Days)(Hours) Work1 (Volume of Trench) = 75×50×15 Work2 (Volume of Trench) = 60×45×21 20×15×10/75×50×15 = y×12×9/60×45×21 On solving, y = 28 Hence, option 3. Download: Chain Rule/Unitary Method PDFQ7) 4 boys or 3 men can do a piece of work in 26 days. How long will 5 boys and 6 men take to do a piece of work twice as great? 1) 8 days 2) 12 days 3) 16 days 4) None of these Solution: 4b = 3m 5b + 6m = 5b + 8b = 13b 4×26/W = 13×y/2W On solving, y = 16 days Hence, option 3. Q8) A contractor employs 50 men to build a house in 80 days. After 40 days he found that only 40% of the house is built. How many additional men should be employed to complete the work on time? 1) 25 2) 20 3) 30 4) 27 Solution: Let W be the total work Work done by 50 men in 40 days = 0.4 W Let y be the additional number of men required Work done by 50 + y men in next 40 days = 0.6 W 50×40/0.4W = (50 + y)×40/0.6W On solving, y = 25 Hence, option 1. Q9) A garrison of 400 men had a provision for 18 weeks. If at the end of 5 weeks they are reinforced by 120 men. How long will the provision last? 1) 12 weeks 2) 13 weeks 3) 10 weeks 4) 15 weeks Solution: Let us suppose that the provision will last for y days 400×13 = 520×y y = 10 Hence, option 3. Q10) A lady can make a pot in 3/4 of an hour. If she works for 7.75 hours, then how pots will she make? 1) 11 2) 10.66 3) 10.5 4) 10.33 Solution: 3y/4 = 31/4; y = 10.66 Hence, option 2. Q11) A certain number of craftsmen can do a piece of work in 15 hours. In how many hours will an equal number of craftsmen of another group can do a piece of work thrice as great given that 5 craftsmen of the first group do as much work in an hour as 2 craftsmen of the second group do in 1.5 hours? 1) 45 hours 2) 36 hours 3) 27 hours 4) None of these Solution: In this question efficiency of craftsmen in both the groups is different. So have to consider the parameter of efficiency also. Let c be the number of craftsmen in each group, e and E be the efficiency of craftsmen in the two groups, h be the hours required by craftsmen of group 2. c×15×e/W = c×h×E/3W e/E = h/45 As, 5 craftsmen of the first group do as much work in an hour as 2 craftsmen of the second group do in 1.5 hours. 5×1×e/work = 2×1.5×E/work e/E = 3/5 h/45 = 3/5 i.e. h = 27 hours |