ans: 48.
If S = speed, and N = number of compartments, then according to the question,
S = 42 – k x $\sqrt{N}$ ; where k is a constant of the proportionality.
From the question, putting N = 9 and S = 24 from the above equation, we have
24 = 42 – k x $\sqrt{9}$
=> 24 = 42 – k x $\sqrt{9}$
=> 3k = 18
=> k = 6
Now, we need to know: what value of N makes S go to zero?
0 = 42 – 6 x $\sqrt{N}$
=> 6 $\sqrt{N}$ = 42
=> $\sqrt{N}$ = 7
=> N = 7$^{2}$ = 49
Now it is clear that with 49 compartments, the train speed is 0 i.e the train does not move. Therefore, it would move if there were one fewer compartments. Thus, 49 – 1 = 48 is the maximum number of compartments the engine can pull and still move.
ans: 1400 gallon.
If cost price = 100 then
At 7.5% 1055, selling price = (100 – 7.5) = 92.5 Tk.
At, 10% less, cost price = (100 — 10) = 90 Tk.
At 20% gain, selling price = (100 + 20) = 120 Tk.
Now,
When selling price 100, cost price = 90 Tk.
When selling price 120, cost price = $\frac{90\times 120}{100}$ = 108 Tk.
Difference of selling price (108 – 92.5) = 15.5 Tk.
When difference is 15.5 the cost price 100 Tk.
When difference is 31 the cost price $\frac{100\times 31}{15.5}$ = 200 Tk
