Quantitative Aptitude PYQs

General solution:

 

Company A:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (22/100) = 660

Number of metallic products manufactured = 1200 ×  (17/100) = 204

Number of non- metallic products manufactured = (660 - 204) = 456

Company B:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (18/100) = 540

Number of metallic products manufactured = 1200 ×  (13/100) = 156

Number of non- metallic products manufactured = (540 - 156) = 384

Company C:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (24/100) = 720

Number of metallic products manufactured = 1200 ×  (20/100) = 240

Number of non- metallic products manufactured = (720 - 240) = 480

Company D:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (16/100) = 480

Number of metallic products manufactured = 1200 ×  (26/100) = 312

Number of non- metallic products manufactured = (480 - 312) = 168

Company E:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (20/100) = 600

Number of metallic products manufactured = 1200 ×  (24/100) = 288

Number of non- metallic products manufactured = (600 - 288) = 312

 

Solution:

 Number of metallic products manufactured by company C = 240 ×  (150/100) = 360

Number of non metallic products manufactured by company C = 480 ×  (80/100) = 384

Number of products manufactured = (360 + 384) = 744

General solution:

 

Company A:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (22/100) = 660

Number of metallic products manufactured = 1200 ×  (17/100) = 204

Number of non- metallic products manufactured = (660 - 204) = 456

Company B:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (18/100) = 540

Number of metallic products manufactured = 1200 ×  (13/100) = 156

Number of non- metallic products manufactured = (540 - 156) = 384

Company C:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (24/100) = 720

Number of metallic products manufactured = 1200 ×  (20/100) = 240

Number of non- metallic products manufactured = (720 - 240) = 480

Company D:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (16/100) = 480

Number of metallic products manufactured = 1200 ×  (26/100) = 312

Number of non- metallic products manufactured = (480 - 312) = 168

Company E:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (20/100) = 600

Number of metallic products manufactured = 1200 ×  (24/100) = 288

Number of non- metallic products manufactured = (600 - 288) = 312

 

Solution:

Number of metallic products manufactured by company D = 312

Number of non metallic products manufactured by company D = 168

(312 + x)/(168 - x) = 2/1

312 + x = 336 - 2x

3x = 24

x = 8

General solution:

 

Company A:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (22/100) = 660

Number of metallic products manufactured = 1200 ×  (17/100) = 204

Number of non- metallic products manufactured = (660 - 204) = 456

Company B:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (18/100) = 540

Number of metallic products manufactured = 1200 ×  (13/100) = 156

Number of non- metallic products manufactured = (540 - 156) = 384

Company C:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (24/100) = 720

Number of metallic products manufactured = 1200 ×  (20/100) = 240

Number of non- metallic products manufactured = (720 - 240) = 480

Company D:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (16/100) = 480

Number of metallic products manufactured = 1200 ×  (26/100) = 312

Number of non- metallic products manufactured = (480 - 312) = 168

Company E:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (20/100) = 600

Number of metallic products manufactured = 1200 ×  (24/100) = 288

Number of non- metallic products manufactured = (600 - 288) = 312

 

Solution:

Number of metallic products made by company A = 204

Number of metallic products made by company B = 156

Total nonmetallic in all the companies = (3000 - 1200) = 1800

Required percentage = (204 + 156) = 360/1800 ×  100 = 20%

General solution:

 

Company A:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (22/100) = 660

Number of metallic products manufactured = 1200 ×  (17/100) = 204

Number of non- metallic products manufactured = (660 - 204) = 456

Company B:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (18/100) = 540

Number of metallic products manufactured = 1200 ×  (13/100) = 156

Number of non- metallic products manufactured = (540 - 156) = 384

Company C:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (24/100) = 720

Number of metallic products manufactured = 1200 ×  (20/100) = 240

Number of non- metallic products manufactured = (720 - 240) = 480

Company D:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (16/100) = 480

Number of metallic products manufactured = 1200 ×  (26/100) = 312

Number of non- metallic products manufactured = (480 - 312) = 168

Company E:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (20/100) = 600

Number of metallic products manufactured = 1200 ×  (24/100) = 288

Number of non- metallic products manufactured = (600 - 288) = 312

 

Solution:

Number of metallic products manufactured by company A = 204

Number of defective metallic products manufactured by company A= 204/3 = 68

Number of non - metallic products manufactured by company A = 456

Number of defective non - metallic products manufactured by company A = 456/4 = 114

Number of non - defective products manufactured by company A = (204 - 68) + (456 - 114) = (136 + 342) = 478

General solution:

 

Company A:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (22/100) = 660

Number of metallic products manufactured = 1200 ×  (17/100) = 204

Number of non- metallic products manufactured = (660 - 204) = 456

Company B:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (18/100) = 540

Number of metallic products manufactured = 1200 ×  (13/100) = 156

Number of non- metallic products manufactured = (540 - 156) = 384

Company C:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (24/100) = 720

Number of metallic products manufactured = 1200 ×  (20/100) = 240

Number of non- metallic products manufactured = (720 - 240) = 480

Company D:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (16/100) = 480

Number of metallic products manufactured = 1200 ×  (26/100) = 312

Number of non- metallic products manufactured = (480 - 312) = 168

Company E:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (20/100) = 600

Number of metallic products manufactured = 1200 ×  (24/100) = 288

Number of non- metallic products manufactured = (600 - 288) = 312

 

Solution:

Number of metallic products manufactured by company D = 312

NUmber of metallic products manufactured by company E = 288

Number of metallic products manufactured by company D = 168

Number of metallic products manufactured by company E = 312

Required ratio = (312 + 288): (168 + 312) = (600:480) = 5: 4

Shortcut Trick

Total Casting Votes = 80% of 25000 = 20000.

Ratio of votes (A : B : C) = 8 : 7 : 5. Total ratio units = 8 + 7 + 5 = 20 units.

Value of 1 unit = 20000 ÷ 20 = 1000 votes.

Winner is A (8 units) and Second runner-up is C (5 units).

Difference (A − C) = (8 − 5) × 1000 = 3000 votes.

∴ The correct answer is A, 3000.

Alternate Method

Given → Total Voters = 25000 | Non-voters = 20% | Ratio A:B:C = 8:7:5.
Formulas: Casting Votes = Total × (100 − Non-voter%) ÷ 100 | Difference = (Ratio Diff ÷ Total Ratio) × Total Casting.

⇒ Casting Votes = 25000 − (20% of 25000) = 25000 − 5000 = 20000.
⇒ Ratio components: A = 8x, B = 7x, C = 5x.
⇒ 8x + 7x + 5x = 20x = 20000 ⇒ x = 1000.
⇒ Winner is A because he has the highest ratio (8 units).
⇒ Second runner-up is C (5 units).

Note:

B is the first runner-up.
⇒ Difference = A − C = 8000 − 5000 = 3000.

∴ The correct answer is A, 3000.

Additional Information

Election Terminology

Winner: The candidate with the maximum number of votes. Runner-up: The candidate with the second-highest votes. Second Runner-up: The candidate with the third-highest votes.

Ratio Distribution

To find an individual share: Share = (Individual Ratio ÷ Sum of Ratios) × Total Quantity.

Shortcut Trick

Circumference 44 cm → Radius = 7 cm (Standard circle ratio 7 : 44).

Length = 2 × 7 + 2 = 16 cm.

Breadth = Area ÷ Length = 192 ÷ 16 = 12 cm.

Side of Triangle = Breadth − 8 = 12 − 8 = 4 cm.

Perimeter = 3 × 4 = 12 cm.

∴ The correct answer is 12 cm.

Alternate Method

Given: Area of rectangle = 192 cm², Circumference of circle = 44 cm.

Formula Used: Circumference = 2πr; Area = L × B; Perimeter of Triangle = 3a.

⇒ 2 × (22/7) × r = 44

⇒ r = 7 cm

⇒ Length (L) = 2r + 2 = 2(7) + 2 = 16 cm

⇒ Breadth (B) = Area ÷ L = 192 ÷ 16 = 12 cm

⇒ Side of triangle (a) = B − 8 = 12 − 8 = 4 cm

⇒ Perimeter = 3 × a = 3 × 4 = 12 cm

∴ The correct answer is 12 cm.

Additional Information

Equilateral Triangle Properties

All sides are equal (a) and Area = (√3/4) × a². Height h = (√3/2) × a.

Circle Relations

Area = πr². For r = 7, Circumference = 44 and Area = 154.

Rectangle Perimeter

Perimeter = 2(L + B). Diagonal d = √(L² + B²).

Combining statements I and II:

Suppose quantities of milk and honey initially were 5a and 4a respectively.

According to the given statements

(4a + 9) = 45

⇒ a = 9

⇒ Quantity of milk initially = 45 litres

Quantity of honey initially = 36 litres

Now,

(45 + x) : 45 = 7 : 5

⇒ x = 18

∴ Statements I and II together are required to answer the question.

Statement I: 

Number of males in town B is 11520 which is 80% of the number of females in town A.

⇒ Number of females in town A = 11520/0.8 = 14400

There are 4880 more males in town A as compared to town B.

Number of males in town A = 11520 + 4880 = 16400

⇒ Total population of town A = 14400 + 16400 = 30800

Statement II: 

The ratio of number of males and females in town A is 41 : 36 and difference of number of males and females is 2000.

Suppose number of males and females in town A are 41x and 36x respectively.

⇒ 41x – 36x = 2000

⇒ 5x = 2000

⇒ x = 400

⇒ Total population of town A = 41x + 36x = 77x = 30800

∴ Either statement I or statement II alone is sufficient to answer the question.

Statement I:

Volume of the cuboid = lbh

Let length be 3x, breadth be 4x, height be 2x

5184 = 3x × 4x × 2x

⇒ 5184 = 24x³

⇒ 216 = x³

⇒ x = 6

Length = 18 cm, Breadth = 24 cm, Height = 12 cm

Total Surface Area of cuboid = 2 (lb + bh + hl)

⇒ 2 × (18 × 24 + 24 × 12 + 12 × 18)

⇒ 2 × (432 + 288 + 216)

⇒ 1872 cm²

Statement II:

Total surface area of the upper and lower faces of the cuboid is 864 cm²

2lb = 864

⇒ lb = 432

height (h) = 12 cm

Now,

Total Surface Area of cuboid = 2 (lb + bh + hl)

We can’t find the total surface area as we do not have the values of length and breadth.

∴ Statement I alone is sufficient to answer the question.

General solution:

 

City

Number of persons (Male + Female) living in city = 3000 ×  (18/100) = 540

Difference between number of (Male - Females) = 60

M + F = 540

M - F = 60

2M = 600

M = 300

F = 240

 

City B:

 

Number of persons (Male + Female) living in city = 3000 ×  (20/100) = 600

Difference between number of (Male - Females) = 100

M + F = 600

M - F = 100

2M = 700

M = 350

F = 250

 

City C:

 

Number of persons (Male + Female) living in city = 3000 ×  (22/100) = 660

Difference between number of (Male - Females) = 100

M + F = 660

M - F = 100

2M = 760

M = 380

F = 280

 

City D:

 

Number of persons (Male + Female) living in city = 3000 ×  (15/100) = 450

Difference between number of (Male - Females) = 50

M + F = 450

M - F = 50

2M = 500

M = 250

F = 200

 

City E:

 

Number of persons (Male + Female) living in city = 3000 ×  (25/100) = 750

Difference between number of (Male - Females) = 210

M + F = 750

M - F = 210

2M = 960

M = 480

F = 270

 

Solution:

Number of males below the age of 25 in city D = 250 ×  (20/100) = 50

Number of males below the age of 25 in city E = 480 ×  (25/100) = 120

Number of females below the age of 25 in city D = 200 ×  (40/100) = 80

Number of females below the age of 25 in city E = 270 ×  (33.33/100) = 90

Required sum = (50 + 120 + 80 + 90) = 340

General solution:

 

City A 

Number of persons (Male + Female) living in city = 3000 ×  (18/100) = 540

Difference between number of (Male - Females) = 60

M + F = 540

M - F = 60

2M = 600

M = 300

F = 240

 

City B:

 

Number of persons (Male + Female) living in city = 3000 ×  (20/100) = 600

Difference between number of (Male - Females) = 100

M + F = 600

M - F = 100

2M = 700

M = 350

F = 250

 

City C:

 

Number of persons (Male + Female) living in city = 3000 ×  (22/100) = 660

Difference between number of (Male - Females) = 100

M + F = 660

M - F = 100

2M = 760

M = 380

F = 280

 

City D:

 

Number of persons (Male + Female) living in city = 3000 ×  (15/100) = 450

Difference between number of (Male - Females) = 50

M + F = 450

M - F = 50

2M = 500

M = 250

F = 200

 

City E:

 

Number of persons (Male + Female) living in city = 3000 ×  (25/100) = 750

Difference between number of (Male - Females) = 210

M + F = 750

M - F = 210

2M = 960

M = 480

F = 270

 

Solution:

Number of males living in city B = 350

Number of females living in city B = 250

Number of males having two wheelers in city B = 350 ×  3/7 = 150

Number of females having two wheelers in city B = 250 ×  2/5 = 100

Number of females having four wheelers in city B = (350 - 150) = 200

Number of females having four wheelers in city B = (250 - 100) = 150

Required difference = (200 ×  4/5 - 150) = (160 - 150) = 10

General solution:

 

City A 

Number of persons (Male + Female) living in city = 3000 ×  (18/100) = 540

Difference between number of (Male - Females) = 60

M + F = 540

M - F = 60

2M = 600

M = 300

F = 240

 

City B:

 

Number of persons (Male + Female) living in city = 3000 ×  (20/100) = 600

Difference between number of (Male - Females) = 100

M + F = 600

M - F = 100

2M = 700

M = 350

F = 250

 

City C:

 

Number of persons (Male + Female) living in city = 3000 ×  (22/100) = 660

Difference between number of (Male - Females) = 100

M + F = 660

M - F = 100

2M = 760

M = 380

F = 280

 

City D:

 

Number of persons (Male + Female) living in city = 3000 ×  (15/100) = 450

Difference between number of (Male - Females) = 50

M + F = 450

M - F = 50

2M = 500

M = 250

F = 150

 

City E:

 

Number of persons (Male + Female) living in city = 3000 ×  (25/100) = 750

Difference between number of (Male - Females) = 210

M + F = 750

M - F = 210

2M = 960

M = 480

F = 270

 

 

Solution:

Number of males living in the city C = 380

Number of females living in the city C = 280

(380 + x)/(280 + (x - 50)) = 3/2

(760 + 2x) = ( 690 + 3x)

x = 70

General solution:

 

City A 

Number of persons (Male + Female) living in city = 3000 ×  (18/100) = 540

Difference between number of (Male - Females) = 60

M + F = 540

M - F = 60

2M = 600

M = 300

F = 240

 

City B:

 

Number of persons (Male + Female) living in city = 3000 ×  (20/100) = 600

Difference between number of (Male - Females) = 100

M + F = 600

M - F = 100

2M = 700

M = 350

F = 250

 

City C:

 

Number of persons (Male + Female) living in city = 3000 ×  (22/100) = 660

Difference between number of (Male - Females) = 100

M + F = 660

M - F = 100

2M = 760

M = 380

F = 280

 

City D:

 

Number of persons (Male + Female) living in city = 3000 ×  (15/100) = 450

Difference between number of (Male - Females) = 50

M + F = 450

M - F = 50

2M = 500

M = 250

F = 150

 

City E:

 

Number of persons (Male + Female) living in city = 3000 ×  (25/100) = 750

Difference between number of (Male - Females) = 210

M + F = 750

M - F = 210

2M = 960

M = 480

F = 270

 

 

Solution:

Number of males living in city C = 380

Number of males living in city E = 480

Average number of males living in city C and E = (380 + 480)/2 = 430

Number of males living in city F = (430 + 20) = 450

Number of females living in city A = 240

Number of females living in city C = 280

Average number of females living in city A and C = (240 + 280)/2 = 260

Number of females living in city F = (260 + 40) = 300

Required sum = (450 + 300) = 750

General solution:

 

City A 

Number of persons (Male + Female) living in city = 3000 ×  (18/100) = 540

Difference between number of (Male - Females) = 60

M + F = 540

M - F = 60

2M = 600

M = 300

F = 240

 

City B:

 

Number of persons (Male + Female) living in city = 3000 ×  (20/100) = 600

Difference between number of (Male - Females) = 100

M + F = 600

M - F = 100

2M = 700

M = 350

F = 250

 

City C:

 

Number of persons (Male + Female) living in city = 3000 ×  (22/100) = 660

Difference between number of (Male - Females) = 100

M + F = 660

M - F = 100

2M = 760

M = 380

F = 280

 

City D:

 

Number of persons (Male + Female) living in city = 3000 ×  (15/100) = 450

Difference between number of (Male - Females) = 50

M + F = 450

M - F = 50

2M = 500

M = 250

F = 150

 

City E:

 

Number of persons (Male + Female) living in city = 3000 ×  (25/100) = 750

Difference between number of (Male - Females) = 210

M + F = 750

M - F = 210

2M = 960

M = 480

F = 270

 

Solution:

Number of males living in city A =300

Number of males living in city B = 350

Number of females living in city C = 280

Number of females living in city E = 270

Required ratio = (300 + 350): (280 + 270) = (650: 550) = 13: 11

General solution:

 

City A 

Number of persons (Male + Female) living in city = 3000 ×  (18/100) = 540

Difference between number of (Male - Females) = 60

M + F = 540

M - F = 60

2M = 600

M = 300

F = 240

 

City B:

 

Number of persons (Male + Female) living in city = 3000 ×  (20/100) = 600

Difference between number of (Male - Females) = 100

M + F = 600

M - F = 100

2M = 700

M = 350

F = 250

 

City C:

 

Number of persons (Male + Female) living in city = 3000 ×  (22/100) = 660

Difference between number of (Male - Females) = 100

M + F = 660

M - F = 100

2M = 760

M = 380

F = 280

 

City D:

 

Number of persons (Male + Female) living in city = 3000 ×  (15/100) = 450

Difference between number of (Male - Females) = 50

M + F = 450

M - F = 50

2M = 500

M = 250

F = 150

 

City E:

 

Number of persons (Male + Female) living in city = 3000 ×  (25/100) = 750

Difference between number of (Male - Females) = 210

M + F = 750

M - F = 210

2M = 960

M = 480

F = 270

 

 

Solution:

Number of literate people in each city if males = 70% and females = 60% literate in all cities.

City A: Literate Males = 210, Literate Females = 144,

Total Literate People = 354

City B: Literate Males = 245, Literate Females = 150,

Total Literate People = 395

City C: Literate Males = 266, Literate Females = 168,

Total Literate People = 434

City D: Literate Males = 175, Literate Females = 120,

Total Literate People = 295

City E: Literate Males = 336, Literate Females = 162,

Total Literate People = 498

Literacy rate in each city = Literate people as a percentage of the total population of the city

City A: Literacy Rate = 65.56%

City B: Literacy Rate = 65.83%

City C: Literacy Rate = 65.76%

City D: Literacy Rate = 65.56%

City E: Literacy Rate = 66.40%

City E has the highest literacy rate with approximately 66.40%.

Shortcut Trick

Area of rectangle = 1260 m². Factors of 1260 with difference 12: 42 × 30.

Length (x) = 42 m, Breadth (x − 12) = 30 m.

Perimeter of rectangle = 2 × (42 + 30) = 144 m.

Cost of fencing = Perimeter × Rate = 144 m × ₹15 per m = ₹2160.

∴ The correct answer is ₹2160.

Alternate Method

Given: Area of rectangular field = 1260 m², Length = x, Breadth = x − 12. Rate = ₹15/m.

Formula Used: Area = Length × Breadth; Perimeter of rectangle = 2(l + b).

⇒ x(x − 12) = 1260

⇒ x² − 12x − 1260 = 0

⇒ x² − 42x + 30x − 1260 = 0

⇒ (x − 42)(x + 30) = 0 ⇒ x = 42 m (Length), Breadth = 30 m

⇒ Perimeter of rectangular field = 2(42 + 30) = 144 m

⇒ Since Perimeters are equal, Fencing length of semi-circular garden = 144 m

⇒ Total Cost = 144 × 15 = ₹2160

∴ The correct answer is ₹2160.

Additional Information

Perimeter of Semi-circle

The total perimeter includes the curved arc and the diameter: P = πr + 2r or r(π + 2).

Cost of Fencing

Total Cost is calculated by multiplying the boundary length (Perimeter) by the rate per unit length.

Area of Semi-circle

The region enclosed is half that of a full circle: Area = (πr²) ÷ 2.

Shortcut Trick

Rate = 10%. Multiplying factors: 3 years = 1.331, 4 years = 1.4641.

CI₁ = 5000 × (1.331 − 1) = 5000 × 0.331 = 1655.

CI₂ = A × (1.4641 − 1) = 0.4641A.

Difference: 0.4641A − 1655 = 2986 ⇒ 0.4641A = 4641 ⇒ A = 10000.

∴ The correct answer is ₹10000.

Alternate Method

Given: Principal₁ = ₹5000, Time₁ = 3 years, Principal₂ = ₹A, Time₂ = 4 years, Rate = 10%.

Formula: CI = P[(1 + R/100)ⁿ − 1]

⇒ CI₁ = 5000[(1 + 10/100)³ − 1]

⇒ CI₁ = 5000[1.1³ − 1] = 5000[1.331 − 1] = 5000 × 0.331 = 1655

⇒ CI₂ = A[(1.1)⁴ − 1] = A[1.4641 − 1] = 0.4641A

⇒ CI₂ − CI₁ = 2986

⇒ 0.4641A − 1655 = 2986

⇒ 0.4641A = 2986 + 1655 = 4641

⇒ A = 4641 ÷ 0.4641 = 10000

∴ The correct answer is ₹10000.

Additional Information

Compound Interest Formula

The amount A = P(1 + r/100)ⁿ. Compound Interest CI = Amount − Principal.

Successive Percentage Method

For 10% rate: 2 years effective rate = 21%, 3 years = 33.1%, 4 years = 46.41%.

Difference between CI and SI

For 2 years, Difference = P(R/100)². For 3 years, Difference = P(R/100)² × (3 + R/100).

Considering the above series,

123, 184, 219, 235, 243, ?

The logic of the series can be explained as:

123 + (128/2 = 64) = 187

187 + (64/2 = 32) = 219

219 + (32/2 = 16) = 235

235 + (16/2 = 8) = 243

By observing the pattern, we can write

⇒ 243 + (8/2 = 4) = ?

⇒ ? = 247

∴ The value of ? is 247.

Considering the above series,

13, 13, 14, 18, 45, 61, ?

The logic of the series can be explained as:

13 + 0² = 13

13 + 1³ = 14

14 + 2² = 18

18 + 3³ = 45

45 + 4² = 61

By observing the pattern, we can write

⇒ 61 + 5³ = ?

⇒ ? = 186

∴ The value of ? is 186.