Quantitative Ability Test

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Quantitative Ability Test - 9

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Weekly Quiz Competition

Question 1
4 / -1

The concentration of petrol in three different mixtures of petrol and kerosene 1/2 , 3/5 and 4/5 , is respectively. If 2 ltr, 3 ltr and 1 ltr liquid is withdrawn from these mixtures respectively and mixed together then the ratio of petrol and kerosene in the new mixture is :

A
4 : 5

B
3 : 2

C
3 : 5

D
2 : 3

Solution

The concentration of petrol in the mixture of kerosene and petrol 1/2 , 3/5 and 4/5

it means that petrol and kerosene ratio=1:1, 3:2,4:1 respectively

matrix 1: make them equal

and the ratio of taken out mixtures 2:3:1

matrix 1:

matrix 10:

36:24

the ratio of petrol and kerosene in the mixture is 3:2
Question 2
4 / -1

A train travels 300 km at an equal speed . If the speed of train increased by 5km/ hr then it takes 2 less in completion of the total journey then the original speed of the train is

A
25 km/hr

B
20 km/hr

C
28 km/hr

D
30 km/hr

Solution

If real speed of train = x

300/x - 300 / x+5 =2

by putting the value of each option calculate the value of x(hit and trial method)

x = 25 kmph
Question 3
4 / -1

A sum of Rs. 221 is divided among X, Y and Z such that X gets Rs. 52 more than Y. Y gets Rs. 26 more than Z. The ratio of the shares of X, Y and Z respectively is :

A
9 : 5 : 3

B
9 : 3 : 5

C
5 : 9 : 3

D
10 : 6 : 5

Solution

x =y +52
z =y -26
x +y +z =221
=> y +52 +y +y -26 =221
=> 3y =221 -26 =195
=> y =195/3 =65
x=65 +52 =117
z =65 -26 =39
x:y:z =117 : 65 :39
=9 : 5: 3
Question 4
4 / -1

Total price of a horse and its cart is Rs. 8000 . If the horse sold on 10% profit and cart on 10% loss, thus he earns 2.5% as profit, then the cost price of the horse is :

A
3000

B
3500

C
40000

D
5000

Solution

Horse \(+\) Cart 8000

CP of horse \(=\frac{5}{8} \times 8000=5000\)
Question 5
4 / -1

The cost of the two types of pulses is Rs.\(15\) and Rs. \(20\) per \(\mathrm{kg}\), respectively. If both the pulses are mixed together in the ratio of \(2: 3\), then what should be the price of the mixed variety of pulses per \(\mathrm{kg}\)?

A
Rs. \(22\) per \(\mathrm{kg}\)

B
Rs. \(30\) per \(\mathrm{kg}\)

C
Rs. \(10\) per \(\mathrm{kg}\)

D
Rs. \(18\) per \(\mathrm{kg}\)

Solution

Let the cost of the mixed variety of pulse be Rs. \(x\).

As per the Alligation rule:

\(2: 3=(20-x):(x-15)\)

\(\Rightarrow 2 x+3 x=60+30\)

\(\Rightarrow 5 x=90\)

\(\Rightarrow x=18\)

The price of the mixed variety of pulses should be 18 Rs. per\(\mathrm{kg}\).
Question 6
4 / -1

The length of a line AB is 2 unit. It divides in two parts on point C such as then the AC²= AB*CB . , length of CB is :

A
3+√5unit

B
3√5 unit

C
2-√5 unit

D
√3 unit

Solution

\(A C^{2}=A B \times C B\)
\(x^{2}=2(2-x)\)
\(x^{2}+2 x-4=0\)
By the formula of Shridharacharya \(x=\frac{-2 \pm \sqrt{4-4(1)(-4)}}{2}\)
\(x=\sqrt{5}-1\)
So. \(B C=2-x=2-(\sqrt{5}-1)=3 \sqrt{5}\)
Question 7
4 / -1

If \(\cot \theta=\frac{b}{a}\) then \(\cos \theta-\sin \theta=?\)

A
b-a

B

\(\sqrt{b^{2}-a^{2}}\)

C
\(\frac{b-a}{\sqrt{a^{2}+b^{2}}}\)

D
\(\frac{b+a}{\sqrt{a^{2}+b^{2}}}\)

Solution

\(\cot \theta=\frac{b}{a}=\frac{\text { base }}{\text { perpendicular }}\)
hypotenuse \(^{2}=\) base \(^{2}+\) per pendicular \(^{2}\)
\(h=\sqrt{a^{2}+b^{2}}\)
\(\frac{b}{\sqrt{a^{2}+b^{2}}}-\frac{a}{\sqrt{a^{2}+b^{2}}}=\frac{b-a}{\sqrt{a^{2}+b^{2}}}\)
Question 8
4 / -1

A, B and C together earn Rs. 1450 and spend 60%, 65% and 70% of their income. If the ratio of their savings is 14 : 21 : 15 then the income of B is :

A
500

B
600

C
450

D
750

Solution

Suppose salary of A,B and C is x,y and z respectively

their spending percentage 60%,65% and 70% respectively which means

theirs saving percentage 40%, 35% and 30%.

and saving ratio's14:21:15

\(x=\frac{40 x}{100}=14 \Rightarrow x=35\)

\(y=\frac{35 x}{100}=21 \Rightarrow y=60\)

\(z \cdot \frac{30 z}{100}=15 \Rightarrow z=50\)

\begin{equation}\begin{array}{llll}

\mathrm{x} & \vdots & \mathrm{y} & = & \mathrm{z} \\

35 & : & 60 & = & 50 \\

7 & : & 12 & = & 10

\end{array}\end{equation}
Question 9
4 / -1

The fare of an autorickshaw is equal to the sum of a constant price and the fare of distance travelled. If total fare of 10 km distance is Rs. 85 and 15 km is Rs.120 then the fare of 25 km distance is

A
175

B
190

C
180

D
225

Solution

Suppose Constant price \(=x\) Price of distance travelled per kilometre \(=y\) \(x+10 y=85-(1)\)
\(x+15 y=120-(2)\)
Solveing equation 182 \(x=15 . y=7\)
for \(25 \mathrm{km}\) total fare \(15+25 \times 7 \Rightarrow 15+175\)
\(=190\)
Question 10
4 / -1

An aeroplaneflews in north from an airport at 1000 km/hr. At the same time another aeroplaneflews from the same airport in west at 1200 km/hr. The distance between both aeroplane after 1 1/2 hris :

A
300 km

B
300√71km

C
300√61 km

D
600 km

Solution

Distance travel by first aeroplane in \(1 \frac{1}{2}\) hr in north \(O A=1000 \times \frac{3}{2}=1500\)
Distance travel by Second aero plane in \(\frac{3}{2}\) hr in west \(O A=1200 \times \frac{3}{2}=1800\)
In right angle \(\Delta A O B\) \(A B^{2}=O A^{2}+O B^{2}\)
\(=(1500)^{2}+(1800)^{2}\)
\(\Rightarrow 2250000+3240000\)
\(\Rightarrow 5490000\)
\(\Rightarrow A B=\sqrt{5490000}=300 \sqrt{61}\)
Distance between both aero plane \(=300 \sqrt{61}\)

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Re-Attempt Weekly Quiz Competition

Quantitative Ability Test - 9

Result

Quantitative Ability Test - 9

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SHARING IS CARING

Question 1

4 : 5

3 : 2

3 : 5

2 : 3

Solution

Question 2

25 km/hr

20 km/hr

28 km/hr

30 km/hr

Solution

Question 3

9 : 5 : 3

9 : 3 : 5

5 : 9 : 3

10 : 6 : 5

Solution

Question 4

3000

3500

40000

5000

Solution

Question 5

Rs. \(22\) per \(\mathrm{kg}\)

Rs. \(30\) per \(\mathrm{kg}\)

Rs. \(10\) per \(\mathrm{kg}\)

Rs. \(18\) per \(\mathrm{kg}\)

Solution

Question 6

3+√5unit

3√5 unit

2-√5 unit

√3 unit

Solution

Question 7

b-a

\(\sqrt{b^{2}-a^{2}}\)

\(\frac{b-a}{\sqrt{a^{2}+b^{2}}}\)

\(\frac{b+a}{\sqrt{a^{2}+b^{2}}}\)

Solution

Question 8

500

600

450

750

Solution

Question 9

175

190

180

225

Solution

Question 10

300 km

300√71km

300√61 km

600 km

Solution

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