Let B will take N days to complete the remaining job.
According to the question
(1/A) + (1/B) = 1/24 and 1/A = 1/32
∴ 1/B = (1/24) - (1/32) = 1/96
⇒ B = 96 days

According to the question,
8[(1/A) + (1/B)] + N x (1/B) = 1

Correct Option: C

Let B will take N days to complete the remaining job.
According to the question
(1/A) + (1/B) = 1/24 and 1/A = 1/32
∴ 1/B = (1/24) - (1/32) = 1/96
⇒ B = 96 days

According to the question,
8[(1/A) + (1/B)] + N x (1/B) = 1
⇒ 8 x (1/24) + (N/96) = 1
⇒ (1/3) + (N/96) = 1
⇒ N/96 = 1 -1/3
∴ N = (2 x 96)/3 = 64
Hence, B complete the remaining job in 64 days

Let N men are allowed to go off,
M₁= 90, D₁ = 25, D₂ = 15
W₁ = 2/3, W₂ = 1 - (2/3) = 1/3
M₂ = 90 - N
According to the formula, M₁D₁W₂ = M₂D₂W₁
⇒ (90 x 25) (1/3) = (90 - N) x 15 x (2/3)

Correct Option: B

Let N men are allowed to go off,
M₁= 90, D₁ = 25, D₂ = 15
W₁ = 2/3, W₂ = 1 - (2/3) = 1/3
M₂ = 90 - N
According to the formula, M₁D₁W₂ = M₂D₂W₁
⇒ (90 x 25) (1/3) = (90 - N) x 15 x (2/3)
⇒ 90 x 25 x (1/3) = 10(90 - N)
⇒ 75 = 90 - N
∴ N = 90 - 75 = 15

Given, M₁= 20, M₂ = 25, T₁ = 5, T₂ = 10, D₁ = 10 and D₂ = ?
According to the formula,
M₁T₁D₁= M₂T₂D₂

Correct Option: A

Given, M₁= 20, M₂ = 25, T₁ = 5, T₂ = 10, D₁ = 10 and D₂ = ?
According to the formula,
M₁T₁D₁= M₂T₂D₂
⇒ 20 x 5 x 10 = 25 x 10 x D₂
∴ D₂ = 20 x 5 x 10/25 x 10 = 4 days

Work done by A and B in 1 day
= (1/8) + (1/12) = 5/24
2 day's work of A and B = 10/24
After 2 day's A left the work
∴ Remaining work = 1 - (10/24) = 14/24
One day work of B and C together = (1/12) + (1/15) = 9/60
So, the number of days required by B and C to finish work
= (14/24) / (9/60) = (14/24) x (60/9) = 35/9

Correct Option: A

Work done by A and B in 1 day
= (1/8) + (1/12) = 5/24
2 day's work of A and B = 10/24
After 2 day's A left the work
∴ Remaining work = 1 - (10/24) = 14/24
One day work of B and C together = (1/12) + (1/15) = 9/60
So, the number of days required by B and C to finish work
= (14/24) / (9/60) = (14/24) x (60/9) = 35/9
∴ Total days to complete the work = 2 + (35/9) = 53/9 = 5⁸/₉ days

(A + B)'s 2 day's work = 2 x (1/3) = 2/3
Remaining work = 1 - (2/3) = 1/3
A will complete 1/3 work in 2
A will complete 1 work in 6

Correct Option: B

(A + B)'s 2 day's work = 2 x (1/3) = 2/3
Remaining work = 1 - (2/3) = 1/3
A will complete 1/3 work in 2
A will complete 1 work in 6
A's 1 days work = 1/6
B's 1 day's work = (1/3) - (1/6) = 1/6
∴ B will take 6 days to complete the work alone.