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Question

যদি প্রতি 10মিনিট 3 বার গোলাবষন করে 6টি কামান 60ঘন্টায কোন দূগ ভাঙতে পারে তবে 5 মিনিটে 2বার গোলা বষণ করে যে সংখ্যাক কামান ঐ দূগকে ভাঙ্গতে

Translation:- If 6 cannons by firing 3 times every 10 minutes can break a fort in 60 hrs then how many cannons will be needed to break it by firing 2 times every 5 minutes?

Answer 1

The 6 cannons fire at a rate of 3 shots every 10 minutes, or 18 shots per hour. If we multiply this by 60 we get that each cannon fires 1080 shots over the 60 hours, for a total of 6480 shots to bring down the fort. Let's assume this to be constant, and also that 60 hours is a constant. Using the same process as before, we see that $n$ cannons firing at a rate of 2 shots every 5 minutes shoot of 24 shots per hour, for a total of 1440 shots over the 60 hours. We then divide the number of shots needed (6480) by the number of shots each cannon makes (1440) to get 4.5 cannons. We obviously cannot have half a cannon, so we round up to get 5 cannons $$ $$ (Note that this solution assumes 60 hours is constant, as the translation of the original question does not seem to specify)

Answer 2

As total time for second case is not given we assume it to be the same 60 hrs.

Now,

10 mins------3 times----6 cannons

So,1 min-----3 times-----6/10 cannons

So,1 min-----1 time------6*3/10 cannons

So,5 min-----1 time------18*5/10 cannons

So,5 min-----2 times-----90/10*2 cannons=9/2 cannons=4.5 =5 cannons approximately.