A, B and C together can complete a work in 4 days. A alone can complete a work in x days and B alone can complete the same work in (x + 5) days and C alone can complete the work in x\/2 days. Find the time taken by A and C together to complete the work.<\/p>\n\n\n\n
a) 12 days<\/p>\n\n\n\n
b) 5 days<\/strong><\/p>\n\n\n\n c) 7.5 days<\/p>\n\n\n\n d) 10 days<\/p>\n\n\n\n e) None of these<\/p>\n\n\n\n Sol:<\/p>\n\n\n\n Time taken by A alone to complete the work = x<\/p>\n\n\n\n days<\/p>\n\n\n\n Time taken by B alone to complete the work = (x<\/p>\n\n\n\n + 5) days<\/p>\n\n\n\n Time taken by C alone to complete the work =<\/p>\n\n\n\n x\/2 days<\/p>\n\n\n\n 1\/A + 1\/B + 1\/C = 1\/4<\/p>\n\n\n\n 1\/x + 1\/(x + 5) + 2\/x = 1\/4<\/p>\n\n\n\n 3\/x + 1\/(x + 5) = 1\/4<\/p>\n\n\n\n (3x + 15 + x)\/(x2 + 5x) = 1\/4<\/p>\n\n\n\n 4x + 15 = (x2 + 5x)\/4<\/p>\n\n\n\n 16x + 60 = x2 + 5x<\/p>\n\n\n\n x2 \u2013 11x \u2013 60 = 0<\/p>\n\n\n\n x2 \u2013 15x + 4x \u2013 60 = 0<\/p>\n\n\n\n x(x \u2013 15) + 4(x \u2013 15) = 0<\/p>\n\n\n\n x = 15, -4<\/p>\n\n\n\n Time taken by A alone to complete the work = 15<\/p>\n\n\n\n days<\/p>\n\n\n\n Time taken by C alone to complete the work =<\/p>\n\n\n\n 15\/2 days<\/p>\n\n\n\n 1\/A + 1\/C = 1\/15 + 2\/15 = 3\/15 = 1\/5 = 5 days<\/p>\n","protected":false},"excerpt":{"rendered":" A, B and C together can complete a work in 4 days. A alone can complete a work in x days and B alone can complete the same work in (x + 5) days and C alone can complete the work in x\/2 days. 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