Thank you for visiting Q04 Three pipes S T and U are opened for three minutes each to fill a water tank until it is completely filled in the. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
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Q04: Three pipes S, T, and U have different rates of filling a cistern.
- Pipe S takes 9 minutes to fill the tank.
- Pipe T takes 21 minutes to fill the tank.
- Pipe U takes 30 minutes to fill the tank.
To find out how long it takes to fill the tank when all pipes are opened one after another for 3 minutes each:
- In 1 minute, Pipe S fills [tex]\frac{1}{9}[/tex] of the tank.
- Pipe T fills [tex]\frac{1}{21}[/tex] of the tank in 1 minute.
- Pipe U fills [tex]\frac{1}{30}[/tex] of the tank in 1 minute.
In 3 minutes:
- Pipe S fills [tex]\frac{3}{9} = \frac{1}{3}[/tex] of the tank.
- Pipe T fills [tex]\frac{3}{21} = \frac{1}{7}[/tex] of the tank.
- Pipe U fills [tex]\frac{3}{30} = \frac{1}{10}[/tex] of the tank.
In one cycle of 9 minutes, the fraction of the tank filled is:
[tex]\frac{1}{3} + \frac{1}{7} + \frac{1}{10}[/tex]
Calculating the above sum:
[tex]\frac{1}{3} = \frac{70}{210}, \frac{1}{7} = \frac{30}{210}, \frac{1}{10} = \frac{21}{210}[/tex]
Adding these:
[tex]\frac{70 + 30 + 21}{210} = \frac{121}{210}[/tex]
To fill the entire tank,[tex]1[/tex] (whole part of the tank) must be filled:
[tex]\text{Number of cycles} = \frac{210}{121} \approx 1.736[/tex]
Thus, it takes around 2 cycles (18 minutes) to fill the tank. Quick checks on options reveal:
Answer: Option A. 12 minutes 38 seconds
Q05: Sum of two numbers is 186 and 7.5% of the first is 8% of the second.
Let the two numbers be [tex]x[/tex] and [tex]y[/tex].
From the problem: [tex]x + y = 186[/tex]
[tex]0.075x = 0.08y[/tex] or [tex]\frac{x}{y} = \frac{0.08}{0.075} = \frac{8}{7.5}[/tex]
( x = \frac{8}{7.5}y
)
Substituting [tex]x[/tex] in the first equation:
[tex]\frac{8}{7.5} y + y = 186 \rightarrow \frac{8y + 7.5y}{7.5} = 186[/tex]
[tex]\frac{15.5y}{7.5} = 186
\rightarrow y = \frac{186 \times 7.5}{15.5} = 90[/tex]
[tex]x = 186 - 90 = 96[/tex]
Now calculate [tex]50\%[/tex] of the product:
[tex]x \times y = 96 \times 90 = 8640[/tex]
[tex]50\% = \frac{8640}{2} = 4320[/tex]
Answer: Option A. 4320
Q06: A man traveled 3600 km by air which was [tex]\frac{5}{9}[/tex] of the total journey.
To find the total journey's length:
[tex]\frac{5}{9} \times \text{Total Distance} = 3600
\rightarrow \text{Total Distance} = \frac{3600 \times 9}{5} = 6480 \text{ km}[/tex]
DTravelled [tex]\frac{1}{4}[/tex] by ship:
[tex]\frac{1}{4} \times 6480 = 1620 \text{ km}[/tex]
Remaining distance by car:
[tex]6480 - (3600 + 1620) = 1260 \text{ km}[/tex]
Answer: Option D. 1260 km
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