A, B and C together can complete a work in 12 days and A and B together can complete the same work in 24 days and the ratio of the efficiency of B and C is 2:5. A, B and C started the work and worked for 6 days. After 6 days, A and B left the work and C completed the remaining work. Find the time taken by C to complete the remaining work.<\/p>\n\n\n\n
a) 24 days<\/p>\n\n\n\n
b) 12 days<\/strong><\/p>\n\n\n\n c) 8 days<\/p>\n\n\n\n d) 20 days<\/p>\n\n\n\n e) 15 days<\/p>\n\n\n\n Sol:<\/p>\n\n\n\n 1\/A + 1\/B + 1\/C = 1\/12<\/p>\n\n\n\n 1\/A + 1\/B = 1\/24<\/p>\n\n\n\n 1\/C = 1\/12-1\/24 = 1\/24<\/p>\n\n\n\n Time taken by C alone to complete the work =<\/p>\n\n\n\n 24 days<\/p>\n\n\n\n Time taken by B alone to complete the work = 24<\/p>\n\n\n\n * 5\/2 = 60 days<\/p>\n\n\n\n 1\/A + 1\/60 = 1\/24<\/p>\n\n\n\n 1\/A = 1\/40<\/p>\n\n\n\n Time taken by A alone to complete the work = 40<\/p>\n\n\n\n days<\/p>\n\n\n\n LCM of 40, 60, 24 = 120<\/p>\n\n\n\n Total work = 120 units<\/p>\n\n\n\n A = 120\/40 = 3 units per day<\/p>\n\n\n\n B = 120\/60 = 2 units per day<\/p>\n\n\n\n C = 120\/24 = 5 units per day<\/p>\n\n\n\n A, B and C work for 6 days<\/p>\n\n\n\n Work completed by A, B and C together =<\/p>\n\n\n\n (3+2+5)*6 = 60 units<\/p>\n\n\n\n Remaining work = 120 \u2013 60 = 60 units<\/p>\n\n\n\n Time taken by C to complete the remaining work<\/p>\n\n\n\n = 60\/ 5 = 12 days<\/p>\n","protected":false},"excerpt":{"rendered":" A, B and C together can complete a work in 12 days and A and B together can complete the same work in 24 days and the ratio of the efficiency of B and C is 2:5. A, B and C started the work and worked for 6 days. 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