একটি চৌবাচ্চা দুটি নল দিয়ে যথাক্রমে 2ও3 ঘন্টা চৌবাচ্চাটি পূর্ণ হয় । অপর একটি নল চৌবাচ্চা টিকে খালি করে । যদি তিনটি নল একসঙ্গে খুলে দেওয়া হয়, তবে চৌবাচ্চাটি 7/24 অংশ পূর্ণ হয় 30মিনিটে। তবে খালি করা নল দিয়ে চৌবাচ্চাটি কতক্ষণে খালি হবে?
Answers
Given :- A basin is filled with two tubes for 2 and 3 hours respectively. Another tube empties the tub. If the three tubes are opened together, the tub is filled with 7/24 parts in 30 minutes. But how long will the full cistern be emptied with the emptied tube ?
Solution :-
given that,
→ All three tubes filled (7/24) part in = 30 minutes
so,
→ All three tubes fill whole basin in = 30 * (24/7) = (720/7) minutes = (720/7) * (1/60) = (12/7) hours .
now,
→ LCM of 2, 3 and (12/7) = 12 litres = Let total capacity of basin .
then,
→ Efficiency of filling tubes = 12/2 and 12/3 = 6 litres / hour and 4 litres / hour .
Let us assume that, efficiency of empty tube is x litres / hour .
A/q,
→ (12/7)[6 + 4 - x] = 12
→ (10 - x) = 7
→ x = 10 - 7
→ x = 3 litres / hour .
therefore,
→ Time taken by empty tube to empty the full basin = 12 / 3 = 4 hours (Ans.)
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