Quantitative Aptitude PYQs

Follow BODMAS rule to solve this question, as per the order given below:

Step-1: Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket,

Step-2: Any mathematical 'Of' or 'Exponent' must be solved next,

Step-3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step-4: Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Now,

Calculations:

Considering the following question

25% of 88 × ? ÷ 2 = 66

 ⇒ ¼ × 88 × ? ÷ 2 = 66

⇒ 22 × ? ÷ 2 = 66

⇒ 11 × ? = 66

∴ ? = 6

Concept used:

Follow BODMAS rule to solve this question, as per the order given below:

Calculation:

90 × 1/3 + 49 ÷ 7 – 12 ÷ 3 = ?

⇒ 90 × 1/3 + 7 – 4 = ?

⇒ 30 + 7 – 4 = ?

⇒ 37 – 4 = ?

⇒ ? = 33

∴ The value of ? is 33

\({8^{\frac{2}{3}}} × \frac{7}{2} + ;\sqrt {49} ; - ;\sqrt[3]{{729}}\) = ?

⇒\({({2^3})^{\frac{2}{3}}} × \frac{7}{2} + 7 - 9\) = ?

 ⇒ \({2^{3 × }}^{\frac{2}{3}} × \frac{7}{2} + 7 - 9\) = ?

⇒ 2² × (7/2) + 7 - 9 = ?

⇒ 14 + 7 - 9 = ?

⇒ 21 - 9 = ?

⇒ ? =  12

∴ The required value of "?" is 12.

Given:

Speed₁ = 10 km/hr

Speed₂ = 20 km/hr

Formula Used:

Speed = Distance/Time

Average speed = Total distance/Total Time

Calculation:      

Let's assume that the distance is d km

Time₁ = d/10 hour

Time₂ = d/20 hour

Total time = d/10 + d/20

Total distance = d + d = 2d km

Average speed = \(\frac{2d}{\frac{d}{10}+\frac{d}{20}}\)

Average speed = \(2d \times \frac{20}{3d}\)

Average speed = 40/3 km/hr

Average speed = \(13\frac{1}{3}\) km/hr

Average speed is \(13\frac{1}{3}\) km/hr

The correct option is 1 i.e. \(13\frac{1}{3}\) km/hr

Given:

X and Y can complete a piece of work in 30 days and 12 days respectively

They started the work while working on alternate days, starting from X

Concept Used:

Work done = efficiency × time

Calculation:

Total work = LCM of (30,12) = 60 unit

Efficiency of X = 60/30 = 2 unit/day

Efficiency of Y = 60/12 = 5 unit/day

While working on alternate days,

In 2 days total work done = 2 + 5 = 7 units

Now multiplying with 8

So, in (8 × 2) = 16 days total work done = (7 × 8) = 56 units

On 17^th day X will work, so work done = 56 + 2 = 58 units

Remaining work = 60 - 58 = 2 units, which will be done by Y

Y will do the 2 unit work in = 2/5 days

So, the total work will be completed in 17 + 2/5 = 17\(\frac{2}{5}\) days

∴ The correct answer is option 3

General Solution:

Given:

Hotel A: Rooms = 39, Guests = 78

Hotel B: Rooms = 50, Guests = 105

Hotel C: Rooms = 45, Guests = 100

Hotel D: Rooms = 45, Guests = 117

Hotel E: Rooms = 60, Guests = 150

Calculations:

⇒ Total rooms = 39

⇒ Group P rooms = 2/3 × 39 = 26

⇒ Group Q rooms = 39 − 26 = 13

⇒ Group P guests = 52 ⇒ avg in P = 52 ÷ 26 = 2

⇒ Total guests = 78 ⇒ Group Q guests = 78 − 52 = 26

⇒ Avg in Q = 26 ÷ 13 = 2

Hence, the correct answer is 2.

General Solution:

Given:

Hotel A: Rooms = 39, Guests = 78

Hotel B: Rooms = 50, Guests = 105

Hotel C: Rooms = 45, Guests = 100

Hotel D: Rooms = 45, Guests = 117

Hotel E: Rooms = 60, Guests = 150​

Calculations:

⇒ Total rooms = 45

⇒ Deluxe rooms = 5/9 × 45 = 25

⇒ Standard rooms = 45 − 25 = 20

⇒ Total guests = 100 ⇒ Deluxe guests = 60% × 100 = 60

⇒ Standard guests = 100 − 60 = 40

⇒ Avg per Standard room = 40 ÷ 20 = 2

Hence, the correct answer is 2

General Solution:

Given:

Hotel A: Rooms = 39, Guests = 78

Hotel B: Rooms = 50, Guests = 105

Hotel C: Rooms = 45, Guests = 100

Hotel D: Rooms = 45, Guests = 117

Hotel E: Rooms = 60, Guests = 150

Calculations:

⇒ B avg = 105 ÷ 50 = 2.1 = 21/10

⇒ E avg = 150 ÷ 60 = 2.5 = 5/2

⇒ Ratio = (21/10) : (5/2) = (21/10) × (2/5) = 42/50 = 21/25

Hence, the correct answer is 21 : 25

General Solution:

Given:

Hotel A: Rooms = 39, Guests = 78

Hotel B: Rooms = 50, Guests = 105

Hotel C: Rooms = 45, Guests = 100

Hotel D: Rooms = 45, Guests = 117

Hotel E: Rooms = 60, Guests = 150

Calculations:

Hotel B revenue:

= (Room charge × Rooms) + (Guest fee × Guests)

= (1200 × 50) + (300 × 105)

= 60,000 + 31,500

= ₹91,500

Hotel C revenue:

= (1500 × 45) + (250 × 100)

= 67,500 + 25,000

= ₹92,500

Difference = 92,500 – 91,500 = ₹1,000

Hence, the correct answer is ₹1,000.

General Solution:

Given:

Hotel A: Rooms = 39, Guests = 78

Hotel B: Rooms = 50, Guests = 105

Hotel C: Rooms = 45, Guests = 100

Hotel D: Rooms = 45, Guests = 117

Hotel E: Rooms = 60, Guests = 150

Calculations:

⇒ Rooms in F = average of A & C = (39 + 45) ÷ 2 = 42

⇒ Guests in F = 20% more than B = 1.2 × 105 = 126

⇒ Avg in F = 126 ÷ 42 = 3

⇒ Avg in A = 78 ÷ 39 = 2

⇒ Difference = 3 − 2 = 1

Hence, the correct answer is 1

Given:

A and B have equal principal = P each.

A invests at 8% SI for 2 years.

B invests at 14% SI for 2 years.

Total interest earned together = Rs. 3,520

Simple Interest formula: SI = (P × R × T) / 100

Calculate interest of each:

Interest by A:

SI_A = (P × 8 × 2) / 100 = 16P / 100 = 0.16P

Interest by B:

SI_B = (P × 14 × 2) / 100 = 28P / 100 = 0.28P

Total interest:

0.16P + 0.28P = 0.44P

Given:

0.44P = 3,520

Solve for P:

P = 3,520 / 0.44

P = 3,520 ÷ 0.44

P = 8,000

So, B’s principal = Rs. 8,000

Hence, the correct answer is Rs. 8,000

Given:

Pens = 40% more than Pencils

Erasers = 25% less than Pens

Total (Pens + Pencils + Erasers) = 690

Formula used:

Pens = Pencils × 1.4

Erasers = Pens × 0.75

Total = Pencils + Pens + Erasers

Calculations:

Let Pencils = x

⇒ Pens = 7/5 × x

⇒ Erasers = 0.75 × Pens = 3/4 × (7/5 x) = 21/20 × x

⇒ Total = x + 7/5 x + 21/20 x

⇒ Total = (20/20 + 28/20 + 21/20) x = 69/20 × x

⇒ 69/20 × x = 690

⇒ x = 690 × 20 ÷ 69 = 200 (Pencils)

⇒ Erasers = 21/20 × x = 21/20 × 200 = 21 × 10 = 210

Hence, the correct answer is 210.

Given,

The ratio of the present ages of Vishal and Himanshu is 5 : 7.

The difference between their ages is 6 years

Calculations: 

Let the present age of Vishal and Himanshu be 5X and 7X respectively.

Given that

7X - 5X = 6

⇒ 2X = 6

⇒ X = 3

Then  Vishal present age is

⇒ X = 5(3) = 15

∴ The required answer is 15 years

Given:

Length of rectangle = 8 cm

Breadth of rectangle =7 cm

Formula:

Perimeter of square  = 4 × a

Perimeter of rectangle = 2 × (L + B)

Calculations:

Perimeter of a square = 2 × perimeter of a rectangle

Perimeter of a square = 4 × side

Perimeter of a rectangle = 2(length + breadth)

Given Rectangle of length = 8 cm and breadth = 7 cm

Perimeter of a rectangle = 2(8 + 7) = 2 × 15 = 30 cm

So, Perimeter of a square = 4 × side = 2 × perimeter of a rectangle

⇒ 4 × side = 2 × 30

⇒ Side = 15 cm

∴ Side of the square is 15 cm

The series follows the following pattern:

3 × 2 = 6

6 × 3 = 18

18 × 5 = 90

90 × 7 = 630

630 × 11 = 6930

∴ The wrong term in the series is 590.

The series follows the following pattern:

7 + 2² = 11

11 + 4² = 27

27 + 6² = 63

63 + 8² = 127

127 + 10² = 227

∴ The wrong term in the series is 61.

The series follows the following pattern:

11 + 2 = 13

13 + 3 = 16

16 + 5 = 21

21 + 7 = 28

28 + 11 = 39

∴ The wrong term in the series is 37.

The series follows the following pattern 

36 × 0.5 = 18

18 × 1 = 18 

18 × 1.5 = 27

27 × 2 = 54 

54 × 2.5 = 135 

∴ The wrong number in the series is 19.

The series follows the following pattern:

2880 ÷ 2 = 1440

1440 ÷ 3 = 480

480 ÷ 4 = 120

120 ÷ 5 = 24

24 ÷ 6 = 4

∴ The wrong term in the series is 1400.

Given:

The average score of X and Y is 41.5

The average score of Y and  Z is 62.5

The average score of Z and X is 54.95

Formula used:

Total Sum = Average × No of terms

Calculation:

Total score of X and Y = 41.5 × 2

X + Y = 83  -------(1)

Total score of Y and Z = 62.5 × 2

Y + Z = 125  -------(2)

Total score of Z and X = 54.95 × 2

Z + X = 109.9  --------(3)

By adding equations (1), (2) and (3)

2 (X + Y + Z) = 83 + 125 + 109.9

X + Y + Z = 317.9/2

X + Y + Z = 158.95   ---------(4)

Subtracting equation (3) from (4),

X + Y + Z - (Z + X) = 158.95 - 109.9

Y = 49.05

Score of W = Y + 19.45 marks

= 68.5

\(\therefore\) The correct answer is 68.5.