A does 1/2 work as B and C does 1/2 work as much as A and B together. If C alone can finish the work in 40 days the all will finish the work in?
A. 30 days
B. 13 1/2 days
C. 15 days
D. 20 days
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C alone can finish the work in 40 days.
(A + B)can do it in 20 days
(A + B)s 1 days wok = 1/20.
As 1 days work : Bs 1 days Work = 1/2 : 1 = 1:2.
A's 1 day's work = (1/20) * (1/3) = (1/60). [Divide 1/20 in the raio 1:2] Bs 1 days work = (1/20) * (2/3) = 1/30
(A+B+c)S 1 day's work = (1/60) + (1/30) + (1/40) = 9/120 = 3/40
All the three together will finish it in 40/3 = 13 and 1/3 days.
C can finish the work in 40 days.
One day work of C = 1/40
Now,
A = 1/2 B
B = 2A
And,
C = 1/2 ( A + B)
C = 1/2 ( A + 2A) = 3/2 A =
3/2 A = C
3/2 A = 1/40
A = 1/60
B = 2 A = 2 * 1/60 = 1/30
One day work of A, B and C together,
= 1/60 + 1/30 + 1/40 = 9/120
Thus, they all together can finish the work,
= 10/9 = 13.33 days (Approx).