Question

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

Answer 1

Answer:

they take together complete tha work 8 day

A take =24 day

B take= 17 1/7 day

c take= 40 day

Answer 2

Explanation:

Given :-

A and B can do a piece of work in 10 hours by B and C 12 hours and C and A in 15 hours.

To find :-

i)How long will they take if they work together ?

ii)How long will each take to complete the work independently ?

Solution :-

Given that :

A work completed by A and B = 10 hours

The work completed by both A and B in one hour = 1/10

A+ B = 1/10 -----(1)

The work completed by B and C = 12 hours

The work completed by both B and C in one hour = 1/12

B+C = 1/12 -----(2)

The work completed by C and A = 15 hours

The work completed by both C and A in one hour = 1/15

C+A = 1/15 -----(3)

On adding (1),(2)&(3) then

A+B+B+C+C+A = (1/10)+(1/12)+(1/15)

=> 2A+2B+2C = (1/10)+(1/12)+(1/15)

LCM of 10 , 12 and 15 = 60

=> 2A+2B+2C =(6+5+4)/60

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

=> 2(A+B+C) = 1/4

=> A+B+C = (1/4)/2

=> A+B+C = 1/(4×2)

=> A+B+C = 1/8----------(4)

They work together they will complete the work in one hour = 1/8

They work together,they will complete the work in 8 hours .

Now,

A can do the work independently in one hour

= (A+B+C)-(B+C)

From (4) and (2)

=> (1/8)-(1/12)

LCM of 8 and 12 = 24

=> (3-2)/24

=> 1/24

A can do the work in one hour = 1/24

A can do the work in 24 hours independently.

B can do the work in one hour independently

= (A+B+C)-(A+C)

From (4) and (3)

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

LCM of 8 and 15 = 120

=> (15-8)/120

=> 7/120

B can do the work in one hour = 7/120

B can do the work independently in 120/7 hours or 17 1/7 hours

C can do the work independently in one hour

= (A+B+C) -(A+B)

From (4)&(1)

=> (1/8)-(1/10)

LCM of 8 and 10 = 40

=> (5-4)/40

=> 1/40

C can do the work in hour is 1/40

C can do the work in 40 hours independently.

Answer:-

i)If they week together then they will take 8 hours to complete the work.

ii)

• A can complete the work in 24 days independently.

• B can complete the work in 120/7 hours or 17 1/7 hours independently.

• C can do complete the work in 40 hours independently.