a is twice as efficient as b and b is thrice as efficient as c who can finish a job alone in 24 days. if a b and c work on alternate days with a starting first in how many days will the job finished?
Answers
Step-by-step explanation:
- Answer: If A, B and C work alternatively, with A starting first.. then the job will be finished in 20/3days i.e 6 2/3days.
Given:
A is twice as efficient as B
B is thrice as efficient as C
C can finish a job alone in 24 days.
To Find:
if a, b, and c work on alternate days with A starting first in how many days will the job be finished?
Solution:
As given,
⇒ C can finish a job alone in 24 days.
⇒ And B is thrice efficient as C so B will finish work in 24/3 days i.e. 8 days.
⇒ A is twice as efficient as B so A will finish work in 8/2 days i.e. 4 days
Therefore,
Work done by A in one day = 1/4
Work done by B in one day = 1/8
Work done by C in one day = 1/24
Now consider the condition when they three work for three consecutive days, the work done will be:
= 1/24 + 1/8 + 1/4
= (1+3+6)/24
= 10/24
after 6 days,
work done will be 20/24
so 1 - 20/24 i.e. 4/24 = 1/6 of work is remaining.
As for the seventh day, A will work so he will complete 1/4 of the work, but only 1/6 work is remaining.
Hence, the work will be finished in 7 days.