A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is:

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.

According to question ,

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