Question

A can complete a specific work in a similar time in which b and c together can do it. In the event that a and b together could do it in 10 days and c alone in 50 days, at that point b alone could do it in.

Answer 1

Answer:

b can alone do the work in 25 days

Thanks.

Answer 2

Answer:

B can do the work alone in 25 days

Step-by-step explanation:

Let A take x days to complete the work alone

Let B take y days to complete the work alone

Given: C takes 50 days to complete the work alone

The fraction of work completed by A in 1 day = 1/x .......(i)

The fraction of work completed by B in 1 day = 1/y      ..(ii)

The fraction of work completed by C in 1 day = 1/50   ..(iii)

ATQ

A and B complete the work in 10 days

=> Fraction of work completed by A and B together in 1 day = 1/10

=> 1/x + 1/y = 1/10 ......(iv)

Also given that A can do the same work done by B and C in the same time.

Fraction of work done by B and C together in 1 day = 1/y + 1/50

Fraction of work done by A in 1 day = 1/x

=> 1/x = 1/y + 1/50       ..(v)

From (iv),

1/x = 1/10 - 1/y ...........(vi)

Equating (v) and (vi),

1/y + 1/50 = 1/10 - 1/y

=> (y + 50)/50y = (y - 10)/10y

=> (y + 50)/5 = (y - 10)

=> y + 50 = 5y - 50

=> 4y = 100

=> y = 25

B will take 25 days to complete the work alone.

Substituting the value of y in (vi), we get:

x = 50/3

Verification:

Fraction of work done by A in 1 day = 1/x = 3/50

Fraction of work done by B in 1 day = 1/y = 1/25

Fraction of work done by C in 1 day = 1/50

Fraction of work done by B and C together in 1 day

= 1/25 + 1/50 = 2/50 + 1/50

= 3/50

= Fraction of work done by A in 1 day  √

The statement: "A can complete a specific work in a similar time in which B and C together can do it" has been verified.