A can complete a work in 10 days, B, 15 days and C, in 20 days, A and C worked together for 2 days, after which B was replaced in place of A. In how many days did the work complete ? / A किसी कार्य को 10 दिन , B , 15 दिन और C ,20 दिन में पूरा कर सकता है A तथा C ने मिलकर 2 दिन कार्य किया तत्पश्चात A के स्थान पर B को कार्य करने के लिए लगा दिया गया । कुल मिलाकर कार्य कितने दिन में पूरा हुआ ?
12
10
6
8
solution : -
In 1 day A completes = 1/10 part of the work
In 1 day B completes = 1/15 part of the work
In 1 day C completes = 1/20 part of the work
In 1 day A and C together complete = (1/10) + (1/20)
= (2+1)/20
= 3/20 part of the work
∴ In 2 days A and C together complete = 2× 3/20
= 3/10 part of the work
∴ The amount of work left = 1-3/10
= 10-3/10
= 7/10 part of the work
In 1 day B and C together complete = (1/15)+(1/20)
= (4+3)/60
= 7/60 part of the work
7/60 part of the work is done within 1 day
∴ 1 part of the work is done in (60/7) days
∴ 7/10 part of the work is completed in = (60/7)×(7/10)
= 6 days.
∴ B and C will together complete the remaining work in 6 days.
In 1 day A,B,C together do =(1/10)+(1/15)+(1/20)
= (6+4+3)/60
= 13/60 part of the work
13/60 part of the work is completed in 1 day
∴ 1 part of the work is completed in = (60/13)
= 4+(8/13) days
∴ They altogether complete the work in 4 whole of 8/13 days
If according to the question A and C worked together for 2 days AND then B replaced A then, the work would be completed within (6+2)
= 8 days
So, the answer is 8 days.
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