Chain Rule: Formulas, Shortcuts and Solved Examples — MCQs with Answers (Set 2)

20 men take 18 days, so the whole job equals 20 x 18 = 360 man-days of work. 20 women also finish it in 18 days, so 1 woman does 20/20 of a man’s daily work. So 19 women are worth 19 x 20/20 = 19 men. Together with 17 men, the team equals 17 + 19 = 36 men. Days needed = 360 / (36) = 10. Check: (36) x 10 = 360, which equals the same 360 man-days.

8 men take 23 days, so the whole job equals 8 x 23 = 184 man-days of work. 16 women also finish it in 23 days, so 1 woman does 8/16 of a man’s daily work. So 10 women are worth 10 x 8/16 = 5 men. Together with 3 men, the team equals 3 + 5 = 8 men. Days needed = 184 / (8) = 23. Check: (8) x 23 = 184, which equals the same 184 man-days.

6 men take 24 days, so the whole job equals 6 x 24 = 144 man-days of work. 30 women also finish it in 24 days, so 1 woman does 6/30 of a man’s daily work. So 1 women are worth 1 x 6/30 = 1/5 men. Together with 1 men, the team equals 1 + 1/5 = 6/5 men. Days needed = 144 / (6/5) = 120. Check: (6/5) x 120 = 144, which equals the same 144 man-days.

10 men take 12 days, so the whole job equals 10 x 12 = 120 man-days of work. 15 women also finish it in 12 days, so 1 woman does 10/15 of a man’s daily work. So 8 women are worth 8 x 10/15 = 16/3 men. Together with 8 men, the team equals 8 + 16/3 = 40/3 men. Days needed = 120 / (40/3) = 9. Check: (40/3) x 9 = 120, which equals the same 120 man-days.

12 men take 20 days, so the whole job equals 12 x 20 = 240 man-days of work. 20 women also finish it in 20 days, so 1 woman does 12/20 of a man’s daily work. So 1 women are worth 1 x 12/20 = 3/5 men. Together with 9 men, the team equals 9 + 3/5 = 48/5 men. Days needed = 240 / (48/5) = 25. Check: (48/5) x 25 = 240, which equals the same 240 man-days.

18 men take 17 days, so the whole job equals 18 x 17 = 306 man-days of work. 6 women also finish it in 17 days, so 1 woman does 18/6 of a man’s daily work. So 4 women are worth 4 x 18/6 = 12 men. Together with 5 men, the team equals 5 + 12 = 17 men. Days needed = 306 / (17) = 18. Check: (17) x 18 = 306, which equals the same 306 man-days.

18 men take 14 days, so the whole job equals 18 x 14 = 252 man-days of work. 12 women also finish it in 14 days, so 1 woman does 18/12 of a man’s daily work. So 6 women are worth 6 x 18/12 = 9 men. Together with 3 men, the team equals 3 + 9 = 12 men. Days needed = 252 / (12) = 21. Check: (12) x 21 = 252, which equals the same 252 man-days.

12 men take 18 days, so the whole job equals 12 x 18 = 216 man-days of work. 21 women also finish it in 18 days, so 1 woman does 12/21 of a man’s daily work. So 4 women are worth 4 x 12/21 = 16/7 men. Together with 8 men, the team equals 8 + 16/7 = 72/7 men. Days needed = 216 / (72/7) = 21. Check: (72/7) x 21 = 216, which equals the same 216 man-days.

Assume every man works at the same rate each hour. 14 men working 5 hours a day for 8 days do 14 x 5 x 8 = 560 man-hours of work in total. More men or more hours per day both need fewer days, so days is inversely proportional to each of them. With 7 men working 4 hours a day, days needed = 560 / (7 x 4) = 20. Check: 7 x 4 x 20 = 560, which equals the same 560 man-hours.

Assume every man works at the same rate each hour. 17 men working 8 hours a day for 20 days do 17 x 8 x 20 = 2720 man-hours of work in total. More men or more hours per day both need fewer days, so days is inversely proportional to each of them. With 16 men working 5 hours a day, days needed = 2720 / (16 x 5) = 34. Check: 16 x 5 x 34 = 2720, which equals the same 2720 man-hours.

Assume every man works at the same rate each hour. 13 men working 11 hours a day for 12 days do 13 x 11 x 12 = 1716 man-hours of work in total. More men or more hours per day both need fewer days, so days is inversely proportional to each of them. With 11 men working 6 hours a day, days needed = 1716 / (11 x 6) = 26. Check: 11 x 6 x 26 = 1716, which equals the same 1716 man-hours.

Assume every man works at the same rate each hour. 11 men working 5 hours a day for 8 days do 11 x 5 x 8 = 440 man-hours of work in total. More men or more hours per day both need fewer days, so days is inversely proportional to each of them. With 11 men working 8 hours a day, days needed = 440 / (11 x 8) = 5. Check: 11 x 8 x 5 = 440, which equals the same 440 man-hours.

Assume every man works at the same rate each hour. 13 men working 4 hours a day for 15 days do 13 x 4 x 15 = 780 man-hours of work in total. More men or more hours per day both need fewer days, so days is inversely proportional to each of them. With 12 men working 5 hours a day, days needed = 780 / (12 x 5) = 13. Check: 12 x 5 x 13 = 780, which equals the same 780 man-hours.

Assume every man works at the same rate each hour. 4 men working 12 hours a day for 10 days do 4 x 12 x 10 = 480 man-hours of work in total. More men or more hours per day both need fewer days, so days is inversely proportional to each of them. With 16 men working 10 hours a day, days needed = 480 / (16 x 10) = 3. Check: 16 x 10 x 3 = 480, which equals the same 480 man-hours.

Assume every man works at the same rate each hour. 4 men working 12 hours a day for 22 days do 4 x 12 x 22 = 1056 man-hours of work in total. More men or more hours per day both need fewer days, so days is inversely proportional to each of them. With 16 men working 11 hours a day, days needed = 1056 / (16 x 11) = 6. Check: 16 x 11 x 6 = 1056, which equals the same 1056 man-hours.

Assume every man works at the same rate each hour. 19 men working 5 hours a day for 24 days do 19 x 5 x 24 = 2280 man-hours of work in total. More men or more hours per day both need fewer days, so days is inversely proportional to each of them. With 8 men working 5 hours a day, days needed = 2280 / (8 x 5) = 57. Check: 8 x 5 x 57 = 2280, which equals the same 2280 man-hours.

Assume every man works at the same rate each hour. 19 men working 12 hours a day for 21 days do 19 x 12 x 21 = 4788 man-hours of work in total. More men or more hours per day both need fewer days, so days is inversely proportional to each of them. With 12 men working 7 hours a day, days needed = 4788 / (12 x 7) = 57. Check: 12 x 7 x 57 = 4788, which equals the same 4788 man-hours.

Assume every man works at the same rate each hour. 8 men working 12 hours a day for 10 days do 8 x 12 x 10 = 960 man-hours of work in total. More men or more hours per day both need fewer days, so days is inversely proportional to each of them. With 6 men working 8 hours a day, days needed = 960 / (6 x 8) = 20. Check: 6 x 8 x 20 = 960, which equals the same 960 man-hours.

Assume every man works at the same rate each hour. 20 men working 5 hours a day for 24 days do 20 x 5 x 24 = 2400 man-hours of work in total. More men or more hours per day both need fewer days, so days is inversely proportional to each of them. With 6 men working 5 hours a day, days needed = 2400 / (6 x 5) = 80. Check: 6 x 5 x 80 = 2400, which equals the same 2400 man-hours.

Assume every man works at the same rate each hour. 15 men working 10 hours a day for 12 days do 15 x 10 x 12 = 1800 man-hours of work in total. More men or more hours per day both need fewer days, so days is inversely proportional to each of them. With 20 men working 6 hours a day, days needed = 1800 / (20 x 6) = 15. Check: 20 x 6 x 15 = 1800, which equals the same 1800 man-hours.

Assume every man works at the same rate each hour. 10 men working 9 hours a day for 16 days do 10 x 9 x 16 = 1440 man-hours of work in total. More men or more hours per day both need fewer days, so days is inversely proportional to each of them. With 8 men working 6 hours a day, days needed = 1440 / (8 x 6) = 30. Check: 8 x 6 x 30 = 1440, which equals the same 1440 man-hours.

Assume every man works at the same rate each hour. 6 men working 12 hours a day for 14 days do 6 x 12 x 14 = 1008 man-hours of work in total. More men or more hours per day both need fewer days, so days is inversely proportional to each of them. With 16 men working 7 hours a day, days needed = 1008 / (16 x 7) = 9. Check: 16 x 7 x 9 = 1008, which equals the same 1008 man-hours.

Assume every man builds the wall at the same rate. 14 men build 99 metres in 12 days. More men and more days each let you build more wall, so length is directly proportional to both. So length = (7 x 8) / (14 x 12) x 99 = 33 metres. Check: 33 x 14 x 12 = 5544, and 99 x 7 x 8 = 5544, which match.

Assume every man builds the wall at the same rate. 24 men build 84 metres in 5 days. More men and more days each let you build more wall, so length is directly proportional to both. So length = (11 x 20) / (24 x 5) x 84 = 154 metres. Check: 154 x 24 x 5 = 18480, and 84 x 11 x 20 = 18480, which match.

Assume every man builds the wall at the same rate. 7 men build 98 metres in 19 days. More men and more days each let you build more wall, so length is directly proportional to both. So length = (19 x 19) / (7 x 19) x 98 = 266 metres. Check: 266 x 7 x 19 = 35378, and 98 x 19 x 19 = 35378, which match.