Question

A and B can do a piece of work in 10 hours B and C in 12 hour and C and A in 15 hours how long will detect if they work together? how long with each take to complete the work independently​

Answer 1

Solution :-

A and B can do a piece of work in 10 hours.

(A + B)'s one hour work = 1/10

B and C in 12 hour

(B + C)'s one hour work = 1/12

C and A in 15 hours

(A + C)'s one hour work = 1/15

Now,

Adding the total's one hour work = 1/10 + 1/12 + 1/15

=> (A + B + B + C + C + A) = (6 + 5 + 4)/60

=> 2(A + B + C)= 15/60

=> ( A + B + C) = 15/(60 × 2) = 1/8

They work together can do it in 8 days.

1/A = 1/8 - 1/12

=> 1/A = (3 - 2)/24

=> 1/A = 1/24

=> A = 24

A alone do it in 24 days .

1/B = 1/8 - 1/15

=> 1/B (15 - 8)/120

=> 1/B = 7/120

=> B = 120/7 = 17 (approx.)

B alone do it in 17 days .

1/C = 1/8 - 1/10

=> 1/C = (5 - 4)/40

=> 1/C = 1/40

=> C = 40

C alone do it in 40 days.

Answer 2

Answer:

A = 24 days

B = 17 days

C = 40 days

Step-by-step explanation:

A and B can do work in 10 Hrs.

» A and B's work in one hour = 1/10

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B and C can do work in 12 Hrs.

» B and C's work in one hour = 1/12

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A and C can do work in 15 Hrs.

» A and C's work in one hour = 1/15

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A.T.Q

Adding total time of one hour

» (A+B+B+C+C+A) = 1/10 + 1/12 + 1/15

» 2(A+B+C) = 15/60

» A+B+C = 1/8

A's Work:

» 1/A = 1/8 - 1/10

» 1/A = 1/24

» A = 24 days

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B's Work:

» 1/B = 1/8 - 1/15

» 1/B = 7/120

» B = 120/7

» B = 17 days (Approximately)

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C's Work:

» 1/C = 1/8 - 1/10

» 1/C = 1/40

» C = 40 days

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A completes work in 24 days.

B completes work in 17 days.

C completes work in 40 days.