Chain Rule: Formulas, Shortcuts and Solved Examples — MCQs with Answers (Set 3)

Assume every man builds the wall at the same rate. 10 men build 82 metres in 4 days. More men and more days each let you build more wall, so length is directly proportional to both. So length = (4 x 15) / (10 x 4) x 82 = 123 metres. Check: 123 x 10 x 4 = 4920, and 82 x 4 x 15 = 4920, which match.

Assume every man builds the wall at the same rate. 25 men build 44 metres in 3 days. More men and more days each let you build more wall, so length is directly proportional to both. So length = (25 x 15) / (25 x 3) x 44 = 220 metres. Check: 220 x 25 x 3 = 16500, and 44 x 25 x 15 = 16500, which match.

Assume every man builds the wall at the same rate. 4 men build 60 metres in 5 days. More men and more days each let you build more wall, so length is directly proportional to both. So length = (14 x 12) / (4 x 5) x 60 = 504 metres. Check: 504 x 4 x 5 = 10080, and 60 x 14 x 12 = 10080, which match.

Assume every man builds the wall at the same rate. 6 men build 32 metres in 5 days. More men and more days each let you build more wall, so length is directly proportional to both. So length = (15 x 17) / (6 x 5) x 32 = 272 metres. Check: 272 x 6 x 5 = 8160, and 32 x 15 x 17 = 8160, which match.

Assume every man builds the wall at the same rate. 20 men build 85 metres in 16 days. More men and more days each let you build more wall, so length is directly proportional to both. So length = (32 x 14) / (20 x 16) x 85 = 119 metres. Check: 119 x 20 x 16 = 38080, and 85 x 32 x 14 = 38080, which match.

Assume every man builds the wall at the same rate. 9 men build 36 metres in 16 days. More men and more days each let you build more wall, so length is directly proportional to both. So length = (18 x 4) / (9 x 16) x 36 = 18 metres. Check: 18 x 9 x 16 = 2592, and 36 x 18 x 4 = 2592, which match.

Assume every man builds the wall at the same rate. 4 men build 54 metres in 9 days. More men and more days each let you build more wall, so length is directly proportional to both. So length = (31 x 6) / (4 x 9) x 54 = 279 metres. Check: 279 x 4 x 9 = 10044, and 54 x 31 x 6 = 10044, which match.

Assume every man builds the wall at the same rate. 4 men build 66 metres in 11 days. More men and more days each let you build more wall, so length is directly proportional to both. So length = (6 x 11) / (4 x 11) x 66 = 99 metres. Check: 99 x 4 x 11 = 4356, and 66 x 6 x 11 = 4356, which match.

Assume every man builds the wall at the same rate. 11 men build 67 metres in 19 days. More men and more days each let you build more wall, so length is directly proportional to both. So length = (33 x 19) / (11 x 19) x 67 = 201 metres. Check: 201 x 11 x 19 = 42009, and 67 x 33 x 19 = 42009, which match.

Assume every man builds the wall at the same rate. 20 men build 77 metres in 4 days. More men and more days each let you build more wall, so length is directly proportional to both. So length = (40 x 16) / (20 x 4) x 77 = 616 metres. Check: 616 x 20 x 4 = 49280, and 77 x 40 x 16 = 49280, which match.

Assume every man builds the wall at the same rate. 7 men build 98 metres in 17 days. More men and more days each let you build more wall, so length is directly proportional to both. So length = (34 x 17) / (7 x 17) x 98 = 476 metres. Check: 476 x 7 x 17 = 56644, and 98 x 34 x 17 = 56644, which match.

Assume each of the labourers works at the same rate. 28 labourers finish the work in 15 days, so the job needs 28 x 15 = 420 worker-days of effort. Fewer days available means more labourers are needed, so days and workers are inversely proportional. For 20 days, workers needed = 420 / 20 = 21. Check: 21 x 20 = 420, which equals the same 420 worker-days.

Assume each of the women works at the same rate. 10 women finish the work in 24 days, so the job needs 10 x 24 = 240 worker-days of effort. Fewer days available means more women are needed, so days and workers are inversely proportional. For 16 days, workers needed = 240 / 16 = 15. Check: 15 x 16 = 240, which equals the same 240 worker-days.

Assume each of the labourers works at the same rate. 65 labourers finish the work in 18 days, so the job needs 65 x 18 = 1170 worker-days of effort. Fewer days available means more labourers are needed, so days and workers are inversely proportional. For 6 days, workers needed = 1170 / 6 = 195. Check: 195 x 6 = 1170, which equals the same 1170 worker-days.

Assume each of the workers works at the same rate. 37 workers finish the work in 13 days, so the job needs 37 x 13 = 481 worker-days of effort. Fewer days available means more workers are needed, so days and workers are inversely proportional. For 37 days, workers needed = 481 / 37 = 13. Check: 13 x 37 = 481, which equals the same 481 worker-days.

Assume each of the men works at the same rate. 80 men finish the work in 20 days, so the job needs 80 x 20 = 1600 worker-days of effort. Fewer days available means more men are needed, so days and workers are inversely proportional. For 40 days, workers needed = 1600 / 40 = 40. Check: 40 x 40 = 1600, which equals the same 1600 worker-days.

Assume each of the women works at the same rate. 13 women finish the work in 40 days, so the job needs 13 x 40 = 520 worker-days of effort. Fewer days available means more women are needed, so days and workers are inversely proportional. For 5 days, workers needed = 520 / 5 = 104. Check: 104 x 5 = 520, which equals the same 520 worker-days.

Assume each of the labourers works at the same rate. 70 labourers finish the work in 31 days, so the job needs 70 x 31 = 2170 worker-days of effort. Fewer days available means more labourers are needed, so days and workers are inversely proportional. For 35 days, workers needed = 2170 / 35 = 62. Check: 62 x 35 = 2170, which equals the same 2170 worker-days.

Assume each of the men works at the same rate. 21 men finish the work in 30 days, so the job needs 21 x 30 = 630 worker-days of effort. Fewer days available means more men are needed, so days and workers are inversely proportional. For 15 days, workers needed = 630 / 15 = 42. Check: 42 x 15 = 630, which equals the same 630 worker-days.

Assume each of the men works at the same rate. 23 men finish the work in 21 days, so the job needs 23 x 21 = 483 worker-days of effort. Fewer days available means more men are needed, so days and workers are inversely proportional. For 23 days, workers needed = 483 / 23 = 21. Check: 21 x 23 = 483, which equals the same 483 worker-days.

Assume each of the women works at the same rate. 27 women finish the work in 32 days, so the job needs 27 x 32 = 864 worker-days of effort. Fewer days available means more women are needed, so days and workers are inversely proportional. For 16 days, workers needed = 864 / 16 = 54. Check: 54 x 16 = 864, which equals the same 864 worker-days.

Assume each of the men works at the same rate. 41 men finish the work in 20 days, so the job needs 41 x 20 = 820 worker-days of effort. Fewer days available means more men are needed, so days and workers are inversely proportional. For 10 days, workers needed = 820 / 10 = 82. Check: 82 x 10 = 820, which equals the same 820 worker-days.

Assume each of the women works at the same rate. 60 women finish the work in 20 days, so the job needs 60 x 20 = 1200 worker-days of effort. Fewer days available means more women are needed, so days and workers are inversely proportional. For 8 days, workers needed = 1200 / 8 = 150. Check: 150 x 8 = 1200, which equals the same 1200 worker-days.

Assume each of the women works at the same rate. 23 women finish the work in 16 days, so the job needs 23 x 16 = 368 worker-days of effort. Fewer days available means more women are needed, so days and workers are inversely proportional. For 23 days, workers needed = 368 / 23 = 16. Check: 16 x 23 = 368, which equals the same 368 worker-days.

Assume each of the workers works at the same rate. 23 workers finish the work in 10 days, so the job needs 23 x 10 = 230 worker-days of effort. Fewer days available means more workers are needed, so days and workers are inversely proportional. For 23 days, workers needed = 230 / 23 = 10. Check: 10 x 23 = 230, which equals the same 230 worker-days.