A and B can do a piece of work in 12 days, B and C in 15 days, C and A in 20 days. How much time will A alone take to finish the work
Answers
Answer:
30 days.
Step-by-step explanation:
2(A+B+C) 1 DAY WORK=1 UPON 12 + 1 UPON 15 +1 UPON 20.
2(A+B+C)1 DAY WORK=12 UPON 60=1 UPON 5.
(A+B+C)1 DAY WORK=1 UPON 5INTO2=1 UPON 10.
A'S 1 DAY WORK=(A+B+C)1 DAY WORK-(B+C)1 DAY WORK.
A'S 1 DAY WORK=1 UPON 10-1 UPON 15.
A'S 1 DAY WORK=1 UPON 30.
NO. OF DAYS=1 UPON 1 DAY WORK.
NO. OF DAYS=1/1 UPON 30.
NO. OF DAYS=30 DAYS.
ANS=A ALONE WILL COMPLETE THE WORK IN 30 DAYS.
THANK YOU.
Given:
A and B can do a piece of work in = 12 days
Work done by A and B in 1 day = 1/12
B and C can do a piece of work in = 15 days
Work done by B and C in 1 day = 1/15
A and C can do a piece of work in = 20 days
Work done by A and C in 1 day = 1/20
Solution:
On adding A, B and C we get,
2(A+B+C)’s one day work
= 1/12 + 1/15 + 1/20
= (5+4+3)/60 (by taking LCM for 12, 15 and 20 which is 60)
= 12/60
= 1/5
A+B+C one day work = 1/(5×2) = 1/10
Knowing that:
Work A can do in 1 day
= (A+B+C)’s 1 day work – (B+C)’s 1 day work
= 1/10 – 1/15
= (3-2)/30 (by taking LCM for 10 and 15 which is 30)
= 1/30
Answer:
∴ A alone can finish the work in = 1/(1/30) = 30days.