Question

A can do a piece of work in 100 days, b and c together can do the same work in 20 days. if b can do the work in same time as that of c and a together then how long c alone can do the same work?

Answer 1

A can do a piece of work in 100 days

⇒ 1 day = 1/100

⇒ 1/a = 1/100

B and C can do the work in 20 days

⇒ 1 day = 1/20

⇒ 1/b + 1/c = 1/20

B can do the work in the same time as C and A

⇒ 1/b = 1/c + 1/100

⇒ 1/b - 1/c = 1/100

1/b + 1/c = 1/20 ------------- [ 1 ]

1/b - 1/c = 1/100 ------------- [ 2 ]

[ 1 ] + [ 2 ]:

2/b = 3/50

3b = 100

b = 100/3

FInd c:

1/b + 1/c = 1/20 -----------[ From [1] ]

3/100 + 1/c = 1/20

1/c = 1/20 - 3/100

1/c = 1/50

Number of days c need:

1/c = 1/50

c = 50 days

Answer: C needs 50 days

Answer 2

A's 1 day's work = 1/ 100

1/ A = 1/ 100

(B + C)' 1 day's work = 1/ 20

1/ B + 1/ C = 1/ 20

C's 1 day's work

1/ C = (1/ 20) - 1/ B ------(1)

B can do the work in same time as
(C + A) can do .

1/ B = 1 / C + 1/ A

1/ B = 1/20 - 1/ B + 1/ 100

1/ B + 1/B = 120/ 2000

2/ B = 3/ 50 => B = 100/ 3

from (1)

1/ C = 1/ 20 - 1/ B

1/ C = 1/ 20 - ( 1/ 100/ 3)

1/ C = 1/ 20 - 3/ 100

1/C = 40 / 2000 = 1/ 50

1 / C = 1/ 50 => C = 50 days

Answer:
-------------

C alone can finish the same work in 50days