3. 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 will A alone take to finish the work
Given :
- A and B can do a piece of work in 12 days , B and C in 15 days , C and A in 20 days
To find :
- How much time will A alone take to finish the work
Solution :
Given,
- A and B = 1/12
- B ans C = 1/15
- C and A = 1/20
Now , we have to add we get,
- 2(A + B + C)
→ 1/12 + 1/15 + 1/20
→ 5 + 4 + 3 / 60 (lcm of 12 , 15 and 20)
→ 12/60
→ 1/5
A + B + C (one days work) = 1/5 × 2 = 1/10
Finding how much time will A alone take to finish the work
→ A work = 1/10 - 1/15
→ 3 - 2 / 30
→ 1/30
Hence , 30 days will A alone take to finish the work
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.