C

1003197407

Level: 
C
A hose can fill the garden pool in \( 20 \) hours. The owners bought a pump that guarantees filling the pool in \( 8 \) hours. However, a crack appeared in the pool's shell which can drain all the water from the full pool within \( 5 \) days. How long will it take to fill the pool with the hose and the pump at the same time as the water runs off through the crack?
exactly \( 6 \) hours
approximately \( 5.7 \) hours
approximately \( 5.5 \) hours
approximately \( 6.8 \) hours

1003197406

Level: 
C
Each of two companies should deliver the same amount of raw material. While inspecting it was found out that the company \( A \) delivered \( 150\,\mathrm{kg} \) and the company \( B \) delivered \( 194\,\mathrm{kg} \). At the moment of inspection, company \( A \) has to deliver yet three times more than what is left to be delivered by company \( B \). Choose the equation which does NOT correspond to the described situation.
\( 3(x-150)=x-194 \), where \( x \) represents the total planned delivery of both companies.
\( x-150=3(x-194) \), where \( x \) represents the total planned delivery of both companies.
\( 150+3x=194+x \), where \( x \) represents the amount of raw material which is left to be delivered by company \( B \).
\( 150+x=194+\frac x3 \), where \( x \) represents the amount of raw material which is left to be delivered by company \( A \).

1003197405

Level: 
C
Nine people travel by bus. The same number of people gets off the bus at each of three bus stops and then so many people get in to double the number of remaining bus passengers. After the third bus stop there are \( 30 \) people in the bus. How many passengers get off at each bus stop?
\( 3 \)
\( 2 \)
\( 1 \)
\( 6 \)

1003197404

Level: 
C
The stock of the monitored company lost \( 12\,\% \) of its value during a week. Its fall continued over the next week, and the value declined by another \( 4\,\% \). Let’s denote the original value of the stock by an \( x \). From the following possibilities, choose the expression that gives the value of the stock at the end of the monitored term.
\( 0.96\cdot0.88x \)
\( (0.96+0.88)x \)
\( 0.04\cdot0.12x \)
\( [1-(0.04+0.12)]x \)

1003197403

Level: 
C
An express train of length \( 150\,\mathrm{m} \) travels at the constant speed of \( 144\,\mathrm{kph} \). On a parallel track in the opposite direction travels a freight train of length \( 240\,\mathrm{m} \) at the constant speed of \( 90\,\mathrm{kph} \). How long does it take for trains to pass each other?
\( 6\,\mathrm{s} \)
\( 1.\overline{6}\,\mathrm{s} \)
\( 7.\overline{2} \)
\( 26\,\mathrm{s} \)

1003197402

Level: 
C
Paul rides the bike at a constant speed of \( 18\,\mathrm{kph} \). Eighteen minutes after Paul starts his trip, Tom takes the same route on a motorbike at an average speed of \( 40\,\mathrm{kph} \). How far behind Paul will Tom be after \( 12 \) minutes of his ride?
\( 1\,\mathrm{km} \)
\( 60\,\mathrm{km} \)
\( 14\,\mathrm{km} \)
after \( 12 \) minutes of ride Tom will be in front of Paul

1003197401

Level: 
C
A man on a bike rides to a distant city at an average speed of \( 24\,\mathrm{kph} \). He will end the trip \( 12 \) minutes earlier, if he increases his average speed by \( 1\,\mathrm{kph} \). How distant is the city?
\( 120\,\mathrm{km} \)
\( 115.2\,\mathrm{km} \)
\( 300\,\mathrm{km} \)
\( 125\,\mathrm{km} \)

1003124806

Level: 
C
We should fence the land in a shape of an equilateral triangle. Choose the function that describes the dependence of the fenced land area \( S \) (in square meters) on the length \( d \) (in meters) of the fence used.
\( S=\frac{\sqrt3}{36} d^2 \)
\( S=\frac{\sqrt3}{18} d^2 \)
\( S=\frac{\sqrt3}4 d^2 \)
\( S=\frac1{36} d^2 \)

1003124805

Level: 
C
On a spool of mass \( 0.5\,\mathrm{kg} \) is winded an aluminium wire of length \( 100\,\mathrm{m} \). Choose the function that describes the dependence of a mass of the spool with the wire \( m \) (in kilograms) on a diameter of the wire \( d \) (in millimetres). Wire density is \( 2\,700\frac{kg}{m^3} \). \[ \] Hint: The density of an object is defined as the ratio of the mass and the volume of the object.
\( m=\frac{27\pi}{400} d^2+0.5 \)
\( m= 67 500\pi d^2+0.5 \)
\( m=\frac{27\pi}{400} d^2-0.5 \)
\( m=\frac{27\pi}{200} d^2+0.5 \)

1003124804

Level: 
C
In the centre of a square shaped square there is a water fountain. The fountain has a square ground plan with the side length \( 4.5\,\mathrm{m} \). The square should be paved with cobblestones of size \( 25\,\mathrm{cm} \times 25\,\mathrm{cm} \). Choose the function that describes the dependence of the number of cobblestones needed (\( n \)) on the length of the square (\( a \)) given in meters.
\( n=16a^2-324 \)
\( n=\frac{a^2}{625}-324 \)
\( n=16a^2-625 \)
\( n=\frac{a^2}{16}-324 \)
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