Mix Test - 2

Given,

Speed of car \(=45\) km/hr

To convert speed from km/hr in m/s we multiply it with \(\frac{5}{18}\).

\(\therefore\) Speed of car \(=45 \times \frac{5} {18}=\frac{25}{2}\) m/s

Time taken \(=50 \) s

As we know,

Speed \(= \frac{\text{Distance}}{\text{Time}}\)

Distance \(=\) Speed \(\times\) Time

\(\therefore\) Distance \(=\frac{25}{2} \times 50\)

\(=25 \times 25\)

\(=625 \) m

So, the distance travelled is \(625\) m.

Hence, the correct option is (B).

Given,

Length \(=100\) m

Breadth \(=0.2\) m 

Height \(=0.15\) m

As we know,

Volume of the cuboid \(=\) Length \(\times\) Breadth \(\times\) Height 

Volume of the cuboid \(=100 \times 0.2 \times 0.15=3\) m\(^{3}\)

Hence, the correct option is (A).

Let the number be \(x\).

According to the question,

\(64 \%\) of \(x+76 \%\) of \(x=84\)

\(\Rightarrow \frac{64}{100} x+\frac{76}{100} x=84 \)

\(\Rightarrow \left(\frac{64+76}{100}\right) x=84 \)

\(\Rightarrow \frac{140}{100} x=84 \)

\(\Rightarrow x= \frac{84 \times 100}{140}\)

\(\Rightarrow x=60 \)

\(\therefore40 \%\) of \(60=\frac{40}{100} \times 60=24\)

Hence, the correct option is (A).

Given,

Radius \(r = 21\) cm

\(\pi=\frac{22}{7}\)

As we know,

Area of the circle \(=\pi r^{2}\)

Area of the circle \(=\frac{22}{7} \times 21 \times 21\)

\(=22 \times 3 \times 21\) 

\(=1386\) cm\(^{2}\)

Hence, the correct option is (D).

Given,

Principal \(=\) Rs. \(35000\)

Time \(=2\) years

Rate of interest \(=12 \%\) per annum

As we know,

Simple Interest \(=\frac{P \times R \times T}{100}\)

Where, \(P=\) Principal, \(R=\) Rate of interest and \(T=\) Time period.

Simple Interest \(=\frac{(35000 \times 12 \times 2)}{100}=\) Rs. \(8400\)

\(\therefore\) The simple interest is Rs. \(8400\).

Hence, the correct option is (D).

Given,

Cost price \((CP)=\) Rs. \(200\)

Selling Price \((SP)=\) Rs. \(198\)

As we know,

Loss \(=\) Selling Price \(-\) Cost Price

Loss \(=\) Rs. \((200 - 198)=\) Rs. \(2\)

Loss \(\%=(\frac{\text{Loss}}{CP}) \times 100\)

Loss \(\%=(\frac{2}{200}) \times 100= 1 \%\)

Hence, the correct option is (B).

Given, 

\(P \%\) of \(P\) is \(36\).

\(\therefore \frac{P}{100} \times P=36\)

\(\Rightarrow \frac{P^2}{100}=36\)

\(\Rightarrow P^{2}=36 \times 100\)

\(\Rightarrow P^{2}=3600\)

\(\Rightarrow P=\sqrt{3 600}\)

\(\Rightarrow P=60\)

\(\therefore\) The value of \(P\) is \(60\).

Hence, the correct option is (B).

Given,

The cost price of a Hard disk \(\text{(CP)}=\) Rs. \(3200\)

The selling price of a Hard disk \(\text{(SP)}=\) Rs. \(3300\)

As we know,

Profit \(\%=\frac{(\text {SP}-\text {CP})}{\text {CP} } \times 100 \)

\(\Rightarrow\) Profit \(\%=\frac{(3300-3200) }{ (3200)} \times 100 \)

\(\Rightarrow\) Profit \( \%=\frac{100} { 3200} \times 100=3.125 \%\)

\(\therefore\) Profit Percentage is \(3.125 \%\).

Hence, the correct option is (B).

Total distance covered \(=10\) km \(+10 \) km \(=20 \) km

Time taken \(=2 \frac{1}{2}=\frac{5}{2}\) hours

As we know,

Speed \(=\frac{\text { Distance }}{\text { Time }}\)

Speed \(=\frac{20}{\frac{5}{2}}\) 

\(=\frac{20 \times 2}{5}\) km/hr 

\(=8\) km/hr 

Hence, the correct option is (C).

Given,

Principal \((P)=\) Rs. \(700\)

Rate \((R)=5 \%\)

Time \((T)=4\) years

As we know,

Simple Interest \(=\frac{(P \times R \times T)}{100}\)

Simple Interest \(=\frac{(700 \times 5 \times 4)}{100}\)

\(=7 \times 20\)

\(=\) Rs. \(140\)

\(\therefore\) The simple interest obtained is Rs. \(140\).

Hence, the correct option is (D).