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.
a) 12 days
b) 5 days
c) 7.5 days
d) 10 days
e) None of these
Sol:
Time taken by A alone to complete the work = x
days
Time taken by B alone to complete the work = (x
+ 5) days
Time taken by C alone to complete the work =
x/2 days
1/A + 1/B + 1/C = 1/4
1/x + 1/(x + 5) + 2/x = 1/4
3/x + 1/(x + 5) = 1/4
(3x + 15 + x)/(x2 + 5x) = 1/4
4x + 15 = (x2 + 5x)/4
16x + 60 = x2 + 5x
x2 – 11x – 60 = 0
x2 – 15x + 4x – 60 = 0
x(x – 15) + 4(x – 15) = 0
x = 15, -4
Time taken by A alone to complete the work = 15
days
Time taken by C alone to complete the work =
15/2 days
1/A + 1/C = 1/15 + 2/15 = 3/15 = 1/5 = 5 days
