Question

A and B can do a piece of work in 10 days, B and C in 15
days and C and A in 20 days. They all work at it for 6
days, and then A leaves, and B and C go on together for
4 days more. If B then leaves, how long will C take to
complete the work?​

Answer 1

Answer:

C can complete the work in 10 Days

Step-by-step explanation:

The part of work A and B can do in aday is 1/10

The part of work B and C can do in aday is /15

1hecpart I of work C and Ai can do in aday i is 1/20

They all worked for 6days

So the part of work the all can do in aday is

2 (A + B+C ) Can do part of the work 1/10+1/20+ 1 /15 =( 6+3+4)/60 =13/60

So (A+B+C )Can do a part of the work in a day is 13/120

In 6 days they cover 6 ×13 /120

= 13/20

Balance of work is 1-- 13/20 =7/20

B and C together do part of work is day is 1/15

In 4 days B and C do part of WORK is 4/15

B LEAVES

BALANCE OF WORK =7/20 --4/15

=21-- 16 /60 =

5/60

=1/12

C HAS TO COMPLETE THE WORK OF 1/12

No of days C needs to complete the work is

1/12 /120 = 1/12 × 120 =10 days

C COMPLETES THE WORK IN 10 DAYAS

Answer 2

A + B do 1/10 of work; B+ C do 1/15, C + A do 1/20 so 2 (A+ B + C) do 1/10 + 1/15+1/20 = 13/60 of the work. So A + B + C do 13/120 of work in a day. If all work for 6 days, 13*6/120 = 78/120 or 39/60 th of work will be completed, leaving 21/60 or 7/20 of work to be completed. B and C working together will complete 4*1/15 = 4/15 of the work leaving (7/20 - 4/15) = 5/60 = 1/12 of work yet to be completed.

A + B + C do 13/120 of work a day and A + B do 1/10 of work. So C does 13/120 - 1/10 = 1/120 of the work. So to complete 1/12 work, C will take (1/12)/(1/120) = 10 days.