Question

a does 8/15 of the given work in 8 days and the remaining work is finished with the assistance of B in 4 days . how long will B take to do the work alone​

Answer 1

Answer:

20 days

Step-by-step explanation:

In 8 days A completes = (8/15) of the given work

In 1 day A completes = (8/15) ÷ 8 = (8/15) × (1/8) = 1/15 of the given work

i.e A's 1 day work = 1/15

Remaining work done by A with the assistance of B = 1 - Work done by A in 8 days

= 1 - (8/15)

Taking LCM

= (15 - 8)/15

= 7/15

i.e Remaining work done by A with the assistance of B = 7/15

Given

Remaining work is finished by A with the assistance of B in 4 days

We know that

Number of Days worked × (A's 1 day work + B's 1 day work) = Remaining work done by A with the assistance of B

⇒4(1/15 + B) = 7/15

⇒ (1/15) + B = (7/15) ÷ 4

⇒ (1/15) + B = (7/15) × (1/4)

⇒ (1/15) + B = 7/60

⇒ B = (7/60) - (1/15)

Taking LCM

⇒ B = (7 - 4)/60

⇒ B = 3/60

⇒ B = 1/20

i.e B's 1 day work = 1/20

So B alone takes 20 days to complete the work.