বিসিএস, ব্যাংক, প্রাথমিক শিক্ষক ও সকল সরকারি চাকরির বিগত সালের প্রশ্ন ও অধ্যায়ভিত্তিক নির্ভুল সমাধান
Solution:
Let,
The capacity of the tank in gallons is x gallons.
ATQ,
(x/2) - 8 = x/10
⇒ (x - 16)/2 = x/10
⇒ 10(x - 16) = 2x
⇒ 10x - 160 = 2x
⇒ 10x - 2x = 160
⇒ 8x = 160
∴ x = 160/8
= 20 gallons
Let:
Work done by A and B together in 1 hour =
(1/x) + (1/(x + 5)) = (2x + 5)/(x² + 5x)
Given: Both together can fill in 6 hours, so:
1 / [(2x + 5)/(x² + 5x)] = 1/6
⇒ (x² + 5x)/(2x + 5) = 6
⇒ x² + 5x = 12x + 30
⇒ x² - 7x - 30 = 0
x² - 10x + 3x - 30 = 0
x(x - 10) + 3(x - 10) = 0
(x - 10)(x + 3) = 0
Therefore:
∴ A alone can fill the reservoir in: 10 hours
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
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
