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Quantitative Aptitude - Test 5


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25 Questions MCQ Test SSC CGL Tier 1 Mock Test Series | Quantitative Aptitude - Test 5

Quantitative Aptitude - Test 5 for SSC 2022 is part of SSC CGL Tier 1 Mock Test Series preparation. The Quantitative Aptitude - Test 5 questions and answers have been prepared according to the SSC exam syllabus.The Quantitative Aptitude - Test 5 MCQs are made for SSC 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Quantitative Aptitude - Test 5 below.
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Quantitative Aptitude - Test 5 - Question 1

A is thrice as fast as B and is therefore able to finish a work in 40 days less than that of B. Find the time in which they can do it working together.

Detailed Solution for Quantitative Aptitude - Test 5 - Question 1

Given,
Ratio of time taken by A and B = 1 : 3
∴ B takes 3 days to finish a unit work while A takes 1 day to finish the same work
The difference of time is 2 days
Given,
Difference of time is 40 days
∴ Time taken by B to complete the work = [(3/2) × 40] = 60 days
∴ A takes 20 days to finish a work
⇒ Work in 1 day by A = 1/20
⇒ Work in 1 day by B = 1/60
⇒ Work in 1 day by (A+B) = [(1/20) + (1/60)] = 4/60
∴ A and B will take days to complete the work = 15 days

Quantitative Aptitude - Test 5 - Question 2

Area of the circle inscribed in a square of diagonal 4 cm is

Detailed Solution for Quantitative Aptitude - Test 5 - Question 2

Let, the side of square be a
Given,
Diagonal of square (d) = 4 cm
⟹ Side of square = Diameter of inscribed circle
Using Pythagoras theorem:
⟹ d2 = a2 + a2
⟹ (4)2 = 2a2
⟹ a = 2√2cm
∴ Radius of circle = √2cm
⟹ Area of circle = π × r2
∴ Area of circle = π × (√2)2 = 2π

Quantitative Aptitude - Test 5 - Question 3

The original price of a TV set is Rs. 4,000.If the price is discounted by 10% and then raised by 5% for service contract, the price charged by the shopkeeper is

Detailed Solution for Quantitative Aptitude - Test 5 - Question 3

Original price of a TV set = Rs. 4,000
∴ after 10% discount price will be = [4000 - (10/100) × 4000] = Rs. 3600
Given,
Increase in service contract = 5%
∴ The raised 5% service contract on new price will be = (5/100) × 3600 = Rs. 180
∴ Final selling price = 3600 + 180 = Rs. 3780

Quantitative Aptitude - Test 5 - Question 4

A certain sum of money was divided between A, B and C in the ratio 1 : 3 : 5.If A received Rs. 500 the sum divided was

Detailed Solution for Quantitative Aptitude - Test 5 - Question 4

Let, the distributed amount among A, B and C are x, 3x and 5x respectively
Given,
‘A’ received amount = Rs. 500
∴ x = 500
⟹ ‘B’ received amount = Rs. (500 × 3) = Rs. 1500
⟹ ‘C’ received amount = Rs. (500 × 5) = Rs. 2500
⟹ Sum of money = Rs. (500 + 1500 + 2500) = Rs. 4500

Quantitative Aptitude - Test 5 - Question 5

By selling a bag at Rs. 300, profit of 10% is made. The selling price of the bag, when it is sold at 15% profit would be

Detailed Solution for Quantitative Aptitude - Test 5 - Question 5

Given,
S.P1 = Rs.300, Profit1 = 10% and Profit2 = 15%
We know that,

Where, S.P = Selling Price, C.P = Cost Price

⟹ C.P = Rs. 272.72
⟹ ProfitProfit%/100 × C.P
⟹ Profit2 = 15/100 × 272.72
⟹ Profit2 ≈ Rs. 41
⟹ SP2 = C.P + Profit2
⟹ SP2 = 272.72 + 41
∴ Selling price of the bag will be = Rs. 313.72

Quantitative Aptitude - Test 5 - Question 6

The weights of two iron balls are 5 kg and 7 kg. What is the percentage weight of the 1st ball with respect to 2nd ball.

Detailed Solution for Quantitative Aptitude - Test 5 - Question 6

We know that,
Percentage weight of 1st ball with respect to 2nd ball will be = 5/7 × 100 = 71 3/7 %

Quantitative Aptitude - Test 5 - Question 7

A Bus travels at the speed of 40 km/hr, then the distance covered by it in 5 second is

Detailed Solution for Quantitative Aptitude - Test 5 - Question 7

Given,
Speed of bus = 40 km/hr = (100/9) m/s
Time = 5 s
We know that,
Distance = Speed × time
∴ Distance = (100/9) × 5 = 55.55 m

Quantitative Aptitude - Test 5 - Question 8

Find the value of 

Detailed Solution for Quantitative Aptitude - Test 5 - Question 8

Quantitative Aptitude - Test 5 - Question 9

 

The value of 

Detailed Solution for Quantitative Aptitude - Test 5 - Question 9

On solving,

Quantitative Aptitude - Test 5 - Question 10

∆XYZ and ∆PQR are two similar triangles and the perimeter of ∆XYZ and ∆PQR are 160 cm and 40 cm respectively. If length of PQ = 20 cm, then length of XY is

Detailed Solution for Quantitative Aptitude - Test 5 - Question 10

Let, length of XY be x
Given,
Perimeter (P1) of ∆XYZ = 160 cm
Perimeter (P2) of ∆PQR = 40 cm
∵ ∆XYZ and ∆PQR are similar

Quantitative Aptitude - Test 5 - Question 11

If the length of a chord of a circle is equal to that of the radius of the circle, then the angle subtended, in radians, at the center of the circle by chord is

Detailed Solution for Quantitative Aptitude - Test 5 - Question 11

Given,
Radius of circle = r
Chord length = radius of circle = r
Draw a perpendicular line of length x from center O

Using Pythagoras theorm,
OA2 = Aa2 + Oa2
⇒ r2 = (r/2)2 + x2
⇒ x2 = 3r2/4
⇒ x = √3/2 r
Take any one triangle so formed
⟹ cos θ = √3/2
⟹ θ = π/6
∴ The angle subtended by the chord at the center = 2 × π/6 = π/3

Quantitative Aptitude - Test 5 - Question 12

The value of (sin60° - cosec2 45°) + (cot2 30° + tan45°)

Detailed Solution for Quantitative Aptitude - Test 5 - Question 12

We know that,
sin 60° = √3/2
cosec 45° = √2
cot 30° = √3
tan 45° = 1
Putting these values in the given equation,

⟹ [(3/4) – 2] + [3 + 1] = 11/4

Quantitative Aptitude - Test 5 - Question 13

The average salary of male employees in a firm was Rs. 6000 and that of females was Rs. 5600. The mean salary of all the employees was Rs. 5800. What is the % of female employees?

Detailed Solution for Quantitative Aptitude - Test 5 - Question 13

Let, the number of males be ‘m’ and number of females be ‘n’
Salaries of male employees be (x1, x2, x3,…….xm)
Salaries of females employees be (y1, y2, y3,………yn)
Given,
Average salary of males = Rs.6000
⟹ m/n = 1
⟹ m = n  ----(iii)

Quantitative Aptitude - Test 5 - Question 14

If x +1 = √3, then the value of x2+2√3

Detailed Solution for Quantitative Aptitude - Test 5 - Question 14

Given,
x = √3-1
Put the value of x in given equation
⇒ x2 + 2√3 = (√3 - 1)2 + 2√3
⇒ 3 + 1 - 2√3 + 2√3 = 4

Quantitative Aptitude - Test 5 - Question 15

The cube of 55 is

Detailed Solution for Quantitative Aptitude - Test 5 - Question 15

We can write,
(55)= (50 + 5)3
We know that,
(a + b)3 = (a)3 + (b)3 + 3 × (a × b) (a + b)
⟹ (50 + 5)= (50)3 + (5)3 + 3 × (50 × 5) (50 + 5)
⟹ (50 + 5)3 = (125000) + (125) + 3 × 250 × 55
∴ (50 + 5)3 = 166375

Quantitative Aptitude - Test 5 - Question 16

In ∆PQR, ∠Q is right angle, S is the mid-point of the side PR. If PQ = 4 cm, QR = 6 cm, then the length of PS is

Detailed Solution for Quantitative Aptitude - Test 5 - Question 16

Using Pythagoras's theorem,
⇒ PR2 = PQ2 + QR2
⇒ PR2 = 42 + 62
⇒ PR = √52 cm = 2√13
⇒ PS = PR/2 = √13

Quantitative Aptitude - Test 5 - Question 17

The diagonals of two squares are in the ratio 5 : 7. The ratio of their area is

Detailed Solution for Quantitative Aptitude - Test 5 - Question 17

Let, the diagonal of two squares be d1 and d2. And their sides and area be a1 and a2 & A1 and A2 respectively

Given,

Using Pythagoras theorm in any one triangle
⇒ d12 = a12 + a12
⇒ d12 = 2a12


Similarly,

∴ The ratio of both squares

 

Quantitative Aptitude - Test 5 - Question 18

The angle of elevation of a ladder leaning against a wall is 30° and the foot of the ladder is 5 m away from the wall. The length of the ladder is

Detailed Solution for Quantitative Aptitude - Test 5 - Question 18

Let, the length of the ladder be ‘l’ which is QR

 

Use trigonometric method in given triangle PQR
⇒ cos θ = Base/Hypotenuse 
⇒ cos 30° = 5/l
⇒ l = 10/√3 m

Quantitative Aptitude - Test 5 - Question 19

The product of two numbers is 1800 and their HCF is 15. The numbers are

Detailed Solution for Quantitative Aptitude - Test 5 - Question 19

Let, the two numbers are 15x and 15y
Given,
⇒ (15x) × (15y) = 1800
⇒ xy = 8
Value of co-primes of x and y are (1, 8)
∴ The two numbers are (1 × 15, 8 × 15) = (15, 120)

Quantitative Aptitude - Test 5 - Question 20

The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 2% per annum is Rs. 3. The sum (in Rs.) is:

Detailed Solution for Quantitative Aptitude - Test 5 - Question 20

Let, the sum of the money be x. CI is compound interest and SI is Simple interest

Given,
CI – SI = 3

Quantitative Aptitude - Test 5 - Question 21

In a mixture of 20 litres, the ratio of milk to water is 3 : 2. Another 2 litres of water is added to the mixture. The ratio of milk to water in new mixture is

Detailed Solution for Quantitative Aptitude - Test 5 - Question 21

Let, the milk be in given mixture is 3x and water be in given mixture is 2x
According to question,
⇒ 3x + 2x = 20
⇒ x = 4
∴ the milk in given mixture is 12 litres and the water be in given mixture is 8 litres
After adding 2 litres of water in the given mixture, the quantity of water will be (8 + 2) = 10 litres
∴ Ratio of milk to water in new mixture = 12/10 = 6/5 = 6 : 5

Quantitative Aptitude - Test 5 - Question 22

Direction: The pie chart given below represents the modes of transport for 1400 officers of the Staff Selection Commission, Kolkata. Study the chart and answer the following questions.

Question: The number of officers who go to office by Bus is

Detailed Solution for Quantitative Aptitude - Test 5 - Question 22

∵ Total number of officers = 1400
∵ Percentage of officer who go to office by Bus = 20%
∴ Number of officers who go to office by Bus = 20% of 1400 = 280

Quantitative Aptitude - Test 5 - Question 23

Direction: The pie chart given below represents the modes of transport for 1400 officers of the Staff Selection Commission, Kolkata. Study the chart and answer the following questions.

Question: The number of officers who go to office by Metro Rail is

Detailed Solution for Quantitative Aptitude - Test 5 - Question 23

∵ Total number of officers = 1400
∵ Percentage of officer who go to office by Metro Rail = 8%
∴ Number of officers who go to office by Metro Rail = 8% of 1400 = 112
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Quantitative Aptitude - Test 5 - Question 24

Direction: The pie chart given below represents the modes of transport for 1400 officers of the Staff Selection Commission, Kolkata. Study the chart and answer the following questions.

Question: Write down the difference of officers availing train and the officers availing car as mode of transport?

Detailed Solution for Quantitative Aptitude - Test 5 - Question 24

∵ Total number of officers = 1400
∵ Percentage of officer using Cars = 21%
∵ Percentage of officer using trains = 36%
∴ required difference = 36% of 1400 – 21% of 1400 = 15% of 1400 = 210

Quantitative Aptitude - Test 5 - Question 25

Direction: The pie chart given below represents the modes of transport for 1400 officers of the Staff Selection Commission, Kolkata. Study the chart and answer the following questions.

Question: The ratio of two - wheelers and trains being used as modes of transport is

Detailed Solution for Quantitative Aptitude - Test 5 - Question 25

∵ Total number of officers = 1400
∵ Percentage of officer using two - wheelers = 15%
∵ Percentage of officer using trains = 36%
∴ Required ratio = (15% of 1400) : (36% 0f 1400) = 15 : 36 = 5 : 12

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