বিগত সালের প্রশ্ন ও প্রশ্ন ব্যাংক
বিসিএস, ব্যাংক, প্রাথমিক শিক্ষক ও সকল সরকারি চাকরির বিগত সালের প্রশ্ন ও অধ্যায়ভিত্তিক নির্ভুল সমাধান
Let, Capacity larger jar = x
Say 20 litters of water poured into each jar, because the same amount of water stored for a while in smaller jar
So x×1/4 = 20
Or, x = 80
Total water of larger jar after pouring the water of smaller jar = 20 + 20 = 40
So, the fraction is = 40/80 = 1/2
A pipe can fill up an empty tank in 14 minutes. Another pipe flows out 12 liters of water per minute. If the two pipes are opened together and the empty tank is filled up in 98 minutes, how much water does the tank contain?
Solution:
মনে করি, ট্যাংকটি খালি হয় x মিনিটে।
প্রশ্নমতে, (1/14) - (1/x) = 1/98
⇒ (1/14) - (1/98) = 1/x
⇒ 6/98 = 1/x
⇒ 3/49 = 1/x
⇒ x = 49/3
অপর নল দ্বারা ট্যাংকটি 49/3 মিনিটে পুরো খালি হয়।
∴ ট্যাংকটির ধারণক্ষমতা = (49/3) × 12 = 196 লিটার
Solution:
Let, after x minutes pipe A must be turned off.
Part fill by (A + B ) in 1 minutes = (1/20+ 1/30) = 1/12
Part fill by (A + B ) in x minutes = x/12
Then, pipe B does the job = (15 - x) minutes
In (15 - x) minutes Pipe B can fill the tank (15 - x) part
ATQ,
x/12 + (15 - x)/30 = 1
⇒ (5x + 30 - 2x)/60 = 1
⇒ 3x + 30 = 60
⇒ 3x = 30
⇒ x = 10
Solution:
চৌবাচ্চাটি 1 ঘণ্টায় পূর্ণ হয় =(1/4) - (1/9) অংশ = (9 - 4)/36 অংশ = 5/36
চৌবাচ্চাটির 5/36 অংশ পূর্ণ হয় = 1 ঘণ্টায়
চৌবাচ্চাটির 1 অংশ পূর্ণ হয় = (1 × 36 )/5 ঘণ্টায় =36/5 = 7.2 ঘণ্টায়
Solution:
Pump A can empty the pool in 3 hours therefore the rate at which it empties is 1/3 pool/hour
Pump b can empty the pool in 2 hours therefore the rate at which it empties is 1/2 pool/hour.
If they work together, the resulting rate is the addition of both rates (1/3 +1/2)pool/hour
= 5/6 pool/hour
So, time taken by both pipe to empty the pool = 6/5 hr
= (6/5) × 60 minutes
= 72 minutes
Solution:
A, B and C together can fill
in one hour = 1/6 in two hours = 2/6 = 1/3
the remaining part is = 1 - 1/3 = 2/3
in 6 hours, A and B can do = 2/3
so, in one hour A and B can do = 2/(3 × 6) = 2/18
so, C can do in one hour = (A, B and C in one hour) - (A and B in one hour)
= 1/6 - 2/18
= 1/18
hence, C take 18 hours to fill the tank