According to given question,
10 men, can complete a work in 18 days by working 6 hours a day.
1 men, can complete a work in 18 days by working 6 x 10 hours a day.
1 men, can complete a work in 1 days by working 6 x 10 x 18 hours a day.

Correct Option: C

According to given question,
10 men, can complete a work in 18 days by working 6 hours a day.
1 men, can complete a work in 18 days by working 6 x 10 hours a day.
1 men, can complete a work in 1 days by working 6 x 10 x 18 hours a day.

Let required amount of coal be y metric tonnes .
9 engines consumes 24 metric tonnes of coal in 8 hours a day.
More engines, more amount of coal (direct proportion)
If 3 engines of first type consume 1 unit, then 1 engine will consume 1/3 unit which is its the rate of consumption.
If 4 engines of second type consume 1 unit, then 1 engine will consume 1/4 unit which is its the rate of consumption
More rate of consumption, more amount of coal (direct proportion)
More hours, more amount of coal(direct proportion)

Correct Option: D

Let required amount of coal be y metric tonnes
9 engines consumes 24 metric tonnes of coal in 8 hours a day.
More engines, more amount of coal (direct proportion)
If 3 engines of first type consume 1 unit, then 1 engine will consume 1/3 unit which is its the rate of consumption.
If 4 engines of second type consume 1 unit, then 1 engine will consume 1/4 unit which is its the rate of consumption
More rate of consumption, more amount of coal (direct proportion)
More hours, more amount of coal(direct proportion)
Now we have , 9 × ( 1 / 3 ) × 8 × y = 8 × ( 1 / 4 ) × 13 × 24
⇒ 3 × 8 × y = 8 × 6 × 13
⇒ 3 × y = 6 × 13 ⇒ y = 2 x 13 = 26 metric tonnes

As per the given question ,
Food of 150 men for 45 days = 150 × 45 = 6750 unit
After 10 days , Food of 150 men for 150 × 10 = 1500 unit
And after 10 days remaining men = 150 - 25 = 125
and remaining food = 6750 - 1500 = 5250 unit
Let D be the number of days for which the remaining food .

Correct Option: C

As per the given question ,
Food of 150 men for 45 days = 150 × 45 = 6750 unit
After 10 days , Food of 150 men for 150 × 10 = 1500 unit
And after 10 days remaining men = 150 - 25 = 125
and remaining food = 6750 - 1500 = 5250 unit
Let D be the number of days for which the remaining food .
So, 125 × D = 5250
⇒ D = 5250 /125 = 42 days

Here , M₁ = 9
D₁ = 12
H₁ = 5
W₁ = 1
And M₂ = 4
D₂ = 30
H₂ = x
W₂ = 2
We know that ,

Correct Option: A

Here , M₁ = 9
D₁ = 12
H₁ = 5
W₁ = 1
And M₂ = 4
D₂ = 30
H₂ = x
W₂ = 2
We know that ,

As we know from the given question,
P men working P hours per day in P days can do P units of a work.
1 men working P hours per day in P days can do P / P units of a work.
1 men working 1 hours per day in P days can do P /P x P units of a work.
1 men working 1 hours per day in 1 days can do P /P x P x P units of a work.
Q men working 1 hours per day in 1 days can do P x Q /P x P x P units of a work.
Q men working Q hours per day in 1 days can do P x Q x Q /P x P x P units of a work.

Correct Option: B

As we know from the given question,
P men working P hours per day in P days can do P units of a work.
1 men working P hours per day in P days can do P / P units of a work.
1 men working 1 hours per day in P days can do P /P x P units of a work.
1 men working 1 hours per day in 1 days can do P /P x P x P units of a work.
Q men working 1 hours per day in 1 days can do P x Q /P x P x P units of a work.
Q men working Q hours per day in 1 days can do P x Q x Q /P x P x P units of a work.
Q men working Q hours per day in Q days can do P x Q x Q x Q/P x P x P units of a work.
Q men working Q hours per day in Q days can do Q³/P² units of a work.