A can do some work in 24 days, b can do it in 32 days and c can do it in 60 days. They start working together. A left after 6 days and b left after working for 8 days. How many more days are required to complete the whole work?
Answers
Answer:
16 1/4 days
Step-by-step explanation:
A can do the work in 24 days
B in 32 days
C in 60 days
Here is the fraction of work each can do in a single day:
A - 1/24 of the work
B - 1/32 of the work
C = 1/60 of the work
In a single day, together the three cover the following fraction of the work:
1/24 + 1/32 + 1/60 = (20 + 15 + 8)/ 480 = 43/480
Therefore, after 6 days when A leaves, the work done is:
43/480 × 6 = 43/80
The fraction of work left:
80/80 - 43/80 = 37/80
B and C then work 2 days together before B leaves on the 8th day. The work done on these 2 days is:
Fraction of B + Fraction of C done in a single day × 2
1/32 + 1/60 = (15+8)/480 = 23/480
There in the two days they cover ⇒ 23/480 × 2 = 23/240
The total work covered in the 8 days, therefore is:
43/80 + 23/120 = 35/48
So far 35/48 of the work is done, after 8 days C is alone. He is left with
48/48 - 35/48 = 13/48 of the work
C covers 1/60 of the work in a day, therefore how many days will he take to cover 13/48?
13/48 ÷ 1/60 = 13/48 ×60/1 = 13/4 × 5/1 = 65/4
= 16 1/4
Therefore C requires 16 and a quarter more days to complete the work.