24 men complete the work in 16 days
⇒ Work that 16 men complete in 12 days = (16/24) x (12/ 16) = 1/2 part of work in 12 days.

32 women complete the work in 24 days
∴ Work that 16 women complete in 14 days = (16/32) x (14/24) = 7/24 part of work in (12 + 2) = 14 days.

So, the remaining part of the work which done by (sixteen men + sixteen women) and required additional no. of men in 2 days = 1 - (1/2 + 7/24) = 1/2 - 7/24 = 5/24 (part)

Correct Option: B

24 men complete the work in 16 days
⇒ Work that 16 men complete in 12 days = (16/24) x (12/ 16) = 1/2 part of work in 12 days.

32 women complete the work in 24 days
∴ Work that 16 women complete in 14 days = (16/32) x (14/24) = 7/24 part of work in (12 + 2) = 14 days.

So, the remaining part of the work which done by (sixteen men + sixteen women) and required additional no. of men in 2 days = 1 - (1/2 + 7/24) = 1/2 - 7/24 = 5/24 (part)

Now, in 2 days 5/24 part part of the work is done by (24 x 16)/ 2 x (5/ 24) = 40 men
∴ Required additional no. of men = 40 - 16 =24.

(A + B +)'s 2 h work = 1/8 + 1/12 = 5/24
(A + B)'s 8 h work = (5 x 8)/(24 x 2) = 5/6
Work done by A in 9th h = 1/8
Total work done upto 9th h = 5/6 + 1/8 = 23/24

Correct Option: A

(A + B +)'s 2 h work = 1/8 + 1/12 = 5/24
(A + B)'s 8 h work = (5 x 8)/(24 x 2) = 5/6
Work done by A in 9th h = 1/8
Total work done upto 9th h = 5/6 + 1/8 = 23/24
Remaining wok = 1/24
B's 1 h work = 1/12
B can do 1/24 of the work = (1/24) x 12 = 1/2 h
So, both can finish the job in 9¹/₂ h.

Let us assume that each soldiers eats one unit of food per day. Thus, total units of food at the beginning will be 1000 x 30 = 30000. After 10 days the 100 soldiers would have eaten 1000 x 10 = 10000 units of food. Thus, food left after 10 days equals 20000 units. Now, there are a total of 2000 soldiers who eat one unit of food everyday.

Now, 30 x 1000 = 1000 x 10 + 2000 x D (here, D is number of days food will last)

Correct Option: D

Let us assume that each soldiers eats one unit of food per day. Thus, total units of food at the beginning will be 1000 x 30 = 30000. After 10 days the 100 soldiers would have eaten 1000 x 10 = 10000 units of food. Thus, food left after 10 days equals 20000 units. Now, there are a total of 2000 soldiers who eat one unit of food everyday.

Now, 30 x 1000 = 1000 x 10 + 2000 x D (here, D is number of days food will last)
⇒ 30000 - 10000 = 2000 x D
∴ D = 20000/2000 = 10 days

Using formula M₁D₁T₁W₁ = M₂D₂T₂W₂
M₁ = 15, M₂ = 10, D₁ = 16, D₂ = ?
T₁ = 5, T₂ = 8, W₁ = 15, W₂ = 12

Correct Option: B

Using formula M₁D₁T₁W₁ = M₂D₂T₂W₂
M₁ = 15, M₂ = 10, D₁ = 16, D₂ = ?
T₁ = 5, T₂ = 8, W₁ = 15, W₂ = 12
Now, 15 x 16 x 5 x 15 = 10 x D₂ x 8 x 12
D₂ = (15 x 16 x 5 x 15)/(10 x 8 x 12)
= (15 x 15)/12 = 75/4 = 18³/₄ days

Efficiency of A = 100/10 = 10%
Efficiency of B = 100/24 = 4.16%
Efficiency of (A+B+C) = 100/6 = 16.66%

Efficiency of C = (16.66) - (10 + 4.16) = 2.5%

Correct Option: B

Efficiency of A = 100/10 = 10%
Efficiency of B = 100/24 = 4.16%
Efficiency of (A+B+C) = 100/6 = 16.66%

Efficiency of C = (16.66) - (10 + 4.16) = 2.5%
Number of days required by C alone to finish the work = 100/2.5 = 40 days