Quantitative Aptitude PYQs

Calculation:

The logic follows here is:

⇒ 225 + 1³ = 226

⇒ 226 + 2² = 230

⇒ 230 + 3³ = 257

⇒ 257 + 4² = 273

⇒ 273 + 5³ = 398

∴ 230 is the wrong term.

2 × 13 = 26, 

26 ×  11 = 286,

286 ×  7 = 2002, 

2002 ×  5 = 10010,

10010 ×  3 = 30030.

The wrong term is 2004.

The series follows the following pattern:

30 × 0.5 + 1 = 16

16 × 1 + 2 = 18

18 × 1.5 + 3 = 30

30 × 2 + 4 = 64

64 × 2.5 + 5 = 165

∴ The wrong term in the series is 26.

Common Calculation

Let, Pants sold in Shop A is x.

Then, shirts sold in A = [4/3]x

Shop B sold 10 more shirts than pants

Let pants sold in B = y

→ shirts sold in B = y + 10

Pants in B is 17 more than in A

→ y =x + 17

⇒ x = y – 17

Total pants in A, B, and C = 163

Let pants sold in C = z

So: [x + y + z] = 163    

Shop C total items = 90

Let shirts in C = a

Then: [a + z ] = 90 ---------à (II)

Pants in C = 25% more than shirts

→ z = 1.25a

z = 1.25a,

So, a + z = 90

⇒ a + 1.25a = 90

⇒ 2.25a = 90

⇒ a = 40, z = [1.25 × 40] = 50

So, x + y = 113

Or, y – 17 + y = 113

Or, y = [130/2] = 65

So, x = 65 – 17 = 48

Now, Shirts sold in A = [4/3] × 48 = 64

Shirts sold in B = y + 10=75

Shirts in D is 5 less than in B

→ Shirts sold in D = y + 10 − 5 = y + 5 = 65 + 5 = 70

Ratio of shirts : pants in D = 7 : 6

So, Number of pants sold in D is 70 × 6 / 7 = 60

 

Calculation

Total items in A + B = [n + 22]

Items in A = 64 + 48 = 112

Items in B = 75 + 65 = 140

→ Total = 112 + 140 = 252

So, n + 22 = 252

⇒ n = 230

⇒8n + 22 = [(8 × 230) + 22] = 1840 + 22 = 1862

Common Calculation

Let, Pants sold in Shop A is x.

Then, shirts sold in A = [4/3]x

Shop B sold 10 more shirts than pants

Let pants sold in B = y

→ shirts sold in B = y + 10

Pants in B is 17 more than in A

→ y =x + 17

⇒ x = y – 17

Total pants in A, B, and C = 163

Let pants sold in C = z

So: [x + y + z] = 163    

Shop C total items = 90

Let shirts in C = a

Then: [a + z ] = 90 ---------à (II)

Pants in C = 25% more than shirts

→ z = 1.25a

z = 1.25a,

So, a + z = 90

⇒ a + 1.25a = 90

⇒ 2.25a = 90

⇒ a = 40, z = [1.25 × 40] = 50

So, x + y = 113

Or, y – 17 + y = 113

Or, y = [130/2] = 65

So, x = 65 – 17 = 48

Now, Shirts sold in A = [4/3] × 48 = 64

Shirts sold in B = y + 10=75

Shirts in D is 5 less than in B

→ Shirts sold in D = y + 10 − 5 = y + 5 = 65 + 5 = 70

Ratio of shirts : pants in D = 7 : 6

So, Number of pants sold in D is 70 × 6 / 7 = 60

 

Calculation

Watches in D = Average of pants in A and C

→ A pants = 48, C pants = 50

→ Average = (48 + 50)/2 = 49

→ D watches = 49

→ C watches = 49 + 25 = 74

Common Calculation

Let, Pants sold in Shop A is x.

Then, shirts sold in A = [4/3]x

Shop B sold 10 more shirts than pants

Let pants sold in B = y

→ shirts sold in B = y + 10

Pants in B is 17 more than in A

→ y =x + 17

⇒ x = y – 17

Total pants in A, B, and C = 163

Let pants sold in C = z

So: [x + y + z] = 163    

Shop C total items = 90

Let shirts in C = a

Then: [a + z ] = 90 ---------à (II)

Pants in C = 25% more than shirts

→ z = 1.25a

z = 1.25a,

So, a + z = 90

⇒ a + 1.25a = 90

⇒ 2.25a = 90

⇒ a = 40, z = [1.25 × 40] = 50

So, x + y = 113

Or, y – 17 + y = 113

Or, y = [130/2] = 65

So, x = 65 – 17 = 48

Now, Shirts sold in A = [4/3] × 48 = 64

Shirts sold in B = y + 10=75

Shirts in D is 5 less than in B

→ Shirts sold in D = y + 10 − 5 = y + 5 = 65 + 5 = 70

Ratio of shirts : pants in D = 7 : 6

So, Number of pants sold in D is 70 × 6 / 7 = 60

 

Calculation

Shirts earn Rs. 500, pants Rs. 400

We calculate shirt revenue and pant revenue across A–D

Shirts Total: A: 64, B: 75, C: 40 , D: 70

→ Total = 64 + 75 + 40 + 70 = 249

Pants Total: A: 48, B: 65 , C: 50 , D: 60

→ Total = 48 + 65 + 50 + 60 = 223

Revenue: Shirt revenue = 249 × 500 = Rs. 124500

Pant revenue = 223 × 400 = Rs. 89200

Difference = 124500 − 89200 = 35300

Common Calculation

Let, Pants sold in Shop A is x.

Then, shirts sold in A = [4/3]x

Shop B sold 10 more shirts than pants

Let pants sold in B = y

→ shirts sold in B = y + 10

Pants in B is 17 more than in A

→ y =x + 17

⇒ x = y – 17

Total pants in A, B, and C = 163

Let pants sold in C = z

So: [x + y + z] = 163    

Shop C total items = 90

Let shirts in C = a

Then: [a + z ] = 90 ---------à (II)

Pants in C = 25% more than shirts

→ z = 1.25a

z = 1.25a,

So, a + z = 90

⇒ a + 1.25a = 90

⇒ 2.25a = 90

⇒ a = 40, z = [1.25 × 40] = 50

So, x + y = 113

Or, y – 17 + y = 113

Or, y = [130/2] = 65

So, x = 65 – 17 = 48

Now, Shirts sold in A = [4/3] × 48 = 64

Shirts sold in B = y + 10=75

Shirts in D is 5 less than in B

→ Shirts sold in D = y + 10 − 5 = y + 5 = 65 + 5 = 70

Ratio of shirts : pants in D = 7 : 6

So, Number of pants sold in D is 70 × 6 / 7 = 60

 

Calculation

m= Difference between shirts in C and pants in D

→ C shirts = 40, D pants = 60

So, m = 60 – 40 = 20

⇒ 7m = 7 × 20 = 140

Common Calculation

Let, Pants sold in Shop A is x.

Then, shirts sold in A = [4/3]x

Shop B sold 10 more shirts than pants

Let pants sold in B = y

→ shirts sold in B = y + 10

Pants in B is 17 more than in A

→ y =x + 17

⇒ x = y – 17

Total pants in A, B, and C = 163

Let pants sold in C = z

So: [x + y + z] = 163    

Shop C total items = 90

Let shirts in C = a

Then: [a + z ] = 90 ---------à (II)

Pants in C = 25% more than shirts

→ z = 1.25a

z = 1.25a,

So, a + z = 90

⇒ a + 1.25a = 90

⇒ 2.25a = 90

⇒ a = 40, z = [1.25 × 40] = 50

So, x + y = 113

Or, y – 17 + y = 113

Or, y = [130/2] = 65

So, x = 65 – 17 = 48

Now, Shirts sold in A = [4/3] × 48 = 64

Shirts sold in B = y + 10=75

Shirts in D is 5 less than in B

→ Shirts sold in D = y + 10 − 5 = y + 5 = 65 + 5 = 70

Ratio of shirts : pants in D = 7 : 6

So, Number of pants sold in D is 70 × 6 / 7 = 60

 

Calculation

Shirts in E = 20 more than shirts in C

→ Shirts in E = 40 + 20 = 60

Pants in E = same as in B = 65

Total items in E = 60 + 65 = 125

Given:

A, B, and C can complete a work in 16, 24, and 32 days respectively

They all started the work together, but B left after working 3 days

C left 5 days before the completion of the work

Concept Used:

Work done = efficiency × time

Calculation:

Total work = LCM of (16, 24, 32) = 96 units

The efficiency of A = 96/16 = 6 unit/day

The efficiency of B = 96/24 = 4 unit/day

The efficiency of C = 96/32 = 3 unit/day

Let, the work get completed in T days

According to the question,

⇒ 6T + 4 × 3 + 3 × (T - 5) = 96

⇒ 6T + 12 +3T - 15 = 96

⇒ 9T = 99

⇒ T = 11 days

∴ The work is completed in 11 days

Shortcut Trick

Sum = Difference × (100/rate)² [Only for two years]

Here, Difference = Rs. 4.20, Rate = 5%, 

Sum = (4.20) × (100/5)² = Rs. 1680

∴ The sum of money is Rs. 1680.

Traditional method:

Given:

The difference between simple interest and compound interest is Rs. 4.20

Total time period = 2 years

Rate = 5%

Formula used:

S.I = (PRT)/100

Where S.I = Simple interest, P = Principal, R = Rate, T = Time

C.I = P[{1 + (r/100)}ⁿ - 1]

Where C.I = Compound interest, P = Pricipal, r = rate, n = time period

Calculation:

Let, the sum be P

Here, T = 2 years, R = 5%

So, S.I = (P × 5 × 2)/100 = (P/10)

Again, n = 2 years, r = 5%

So, C.I = P[{1 + (5/100)}² - 1]

⇒ C.I = P[{1 + (1/20)}² - 1]

⇒ C.I = P[(441/400) - 1]

⇒ C.I = P[41/400]

Now, according to the question, we can say,

P[41/400] - (P/10) = 4.2

⇒ P[(41/400) - (1/10)] = 4.2

⇒ P[(41 - 40)/400] = 4.2

⇒ P[1/400] = 4.2

⇒ P = 4.2 × 400 = 1680

∴ The sum of money is Rs. 1680.

Given:

Length of train A = 120 meters

Speed of train = 90 km/h

Speed of train B = 30 m/s

Formula used:

Time = distance/speed

Relative speed = (sum of the length of train 1 and 2) / (sum of the speed of train 1 and 2)

Calculation:

Speed of train A = 90 × (5/18) = 25 m/s

Let the length of the platform be x meters.

⇒ (120 + x)/25 = 40

⇒ 120 + x = 1000

⇒ x = 1000 – 120

⇒ x = 880 meters

Speed of train B = 30 m/s

Let the length of train B be y meters

⇒ (y + 880)/30 = 55

⇒ y + 880 = 1650

⇒ y = 1650 – 880

⇒ y = 770 meters

∴ Required time = (120 + 770) / (25 + 30)

⇒ 890/55

⇒ \(16\frac{2}{{11}}\) seconds

Given:

Distance covered by boat in upstream = 200 km

Distance covered by boat in downstream = 300 km

Formula used:

Time = distance/speed

Calculation:

Let the speed of stream be s km/h

Upstream speed = (5 – s) km/h

Downstream speed = (5 + s) km/h

According to question:

200/(5 – s) = 300/(5 + s)

⇒ 200(5 + s) = 300(5 – s)

⇒ 1000 + 200s = 1500 – 300s

⇒ -500 = - 500s

⇒ s = 1 km/h

∴ Speed of stream is 1 km/h

Common Calculation

Given:

Total Balls Manufactured = 640

Formula:

Total Balls = Total × Percentage/100

Blue Balls = Total Balls × Blue Parts / Total Parts

Green Balls = Total Balls × Green Parts / Total Parts

Calculation:

⇒ May Total Balls = 10% of 640 = (10/100) × 640 = 64

⇒ Blue Balls in May = (5/8) × 64 = 40

⇒ Green Balls in May = (3/8) × 64 = 24

⇒ June Total Balls = 15% of 640 = (15/100) × 640 = 96

⇒ Blue Balls in June = (7/12) × 96 = 56

⇒ Green Balls in June = (5/12) × 96 = 40

⇒ July Total Balls = 20% of 640 = (20/100) × 640 = 128

⇒ Blue Balls in July = (5/8) × 128 = 80

⇒ Green Balls in July = (3/8) × 128 = 48

⇒ August Total Balls = 25% of 640 = (25/100) × 640 = 160

⇒ Blue Balls in August = (3/8) × 160 = 60

⇒ Green Balls in August = (5/8) × 160 = 100

⇒ September Total Balls = 30% of 640 = (30/100) × 640 = 192

⇒ Blue Balls in September = (7/12) × 192 = 112

⇒ Green Balls in September = (5/12) × 192 = 80

Given:

Blue Balls (June) = 56

Blue Balls (September) = 112

Green Balls (May) = 24

Green Balls (July) = 48

Formula:

Required Percentage

= [(First Quantity − Second Quantity)/Second Quantity] × 100

Calculation:

⇒ Total Blue Balls (June & September) = 56 + 112 = 168

⇒ Total Green Balls (May & July) = 24 + 48 = 72

⇒ Difference = 168 – 72 = 96

⇒ Required Percentage = (96/72) × 100 = 133(1/3)%

∴ Answer = 133(1/3)%

Common Calculation

Given:

Total Balls Manufactured = 640

Formula:

Total Balls = Total × Percentage/100

Blue Balls = Total Balls × Blue Parts / Total Parts

Green Balls = Total Balls × Green Parts / Total Parts

Calculation:

⇒ May Total Balls = 10% of 640 = (10/100) × 640 = 64

⇒ Blue Balls in May = (5/8) × 64 = 40

⇒ Green Balls in May = (3/8) × 64 = 24

⇒ June Total Balls = 15% of 640 = (15/100) × 640 = 96

⇒ Blue Balls in June = (7/12) × 96 = 56

⇒ Green Balls in June = (5/12) × 96 = 40

⇒ July Total Balls = 20% of 640 = (20/100) × 640 = 128

⇒ Blue Balls in July = (5/8) × 128 = 80

⇒ Green Balls in July = (3/8) × 128 = 48

⇒ August Total Balls = 25% of 640 = (25/100) × 640 = 160

⇒ Blue Balls in August = (3/8) × 160 = 60

⇒ Green Balls in August = (5/8) × 160 = 100

⇒ September Total Balls = 30% of 640 = (30/100) × 640 = 192

⇒ Blue Balls in September = (7/12) × 192 = 112

⇒ Green Balls in September = (5/12) × 192 = 80

Given:

Green Balls (August & September)

Blue Balls (May, June & July)

Formula:

Required Ratio

= First Quantity : Second Quantity

Calculation:

⇒ Green Balls in August and September = 100 + 80 = 180

⇒ Blue Balls in May, June and July = 40 + 56 + 80 = 176

⇒ Required Ratio = 180 : 176 = 45 : 44

∴ Answer = 45 : 44

Common Calculation

Given:

Total Balls Manufactured = 640

Formula:

Total Balls = Total × Percentage/100

Blue Balls = Total Balls × Blue Parts / Total Parts

Green Balls = Total Balls × Green Parts / Total Parts

Calculation:

⇒ May Total Balls = 10% of 640 = (10/100) × 640 = 64

⇒ Blue Balls in May = (5/8) × 64 = 40

⇒ Green Balls in May = (3/8) × 64 = 24

⇒ June Total Balls = 15% of 640 = (15/100) × 640 = 96

⇒ Blue Balls in June = (7/12) × 96 = 56

⇒ Green Balls in June = (5/12) × 96 = 40

⇒ July Total Balls = 20% of 640 = (20/100) × 640 = 128

⇒ Blue Balls in July = (5/8) × 128 = 80

⇒ Green Balls in July = (3/8) × 128 = 48

⇒ August Total Balls = 25% of 640 = (25/100) × 640 = 160

⇒ Blue Balls in August = (3/8) × 160 = 60

⇒ Green Balls in August = (5/8) × 160 = 100

⇒ September Total Balls = 30% of 640 = (30/100) × 640 = 192

⇒ Blue Balls in September = (7/12) × 192 = 112

⇒ Green Balls in September = (5/12) × 192 = 80

 

Given:

Blue Balls in August = 60

Blue Balls in September = 112

Transferred Blue Balls = 20

Formula:

New Quantity

= Original Quantity ± Transferred Balls

Required Ratio

= New Blue Balls in August : New Blue Balls in September

Calculation:

⇒ New Blue Balls in August = 60 + 20 = 80

⇒ New Blue Balls in September = 112 – 20 = 92

⇒ Required Ratio = 80 : 92 = 20 : 23

∴ Answer = 20 : 23

Common Calculation

Given:

Total Balls Manufactured = 640

Formula:

Total Balls = Total × Percentage/100

Blue Balls = Total Balls × Blue Parts / Total Parts

Green Balls = Total Balls × Green Parts / Total Parts

Calculation:

⇒ May Total Balls = 10% of 640 = (10/100) × 640 = 64

⇒ Blue Balls in May = (5/8) × 64 = 40

⇒ Green Balls in May = (3/8) × 64 = 24

⇒ June Total Balls = 15% of 640 = (15/100) × 640 = 96

⇒ Blue Balls in June = (7/12) × 96 = 56

⇒ Green Balls in June = (5/12) × 96 = 40

⇒ July Total Balls = 20% of 640 = (20/100) × 640 = 128

⇒ Blue Balls in July = (5/8) × 128 = 80

⇒ Green Balls in July = (3/8) × 128 = 48

⇒ August Total Balls = 25% of 640 = (25/100) × 640 = 160

⇒ Blue Balls in August = (3/8) × 160 = 60

⇒ Green Balls in August = (5/8) × 160 = 100

⇒ September Total Balls = 30% of 640 = (30/100) × 640 = 192

⇒ Blue Balls in September = (7/12) × 192 = 112

⇒ Green Balls in September = (5/12) × 192 = 80

 

Given:

Balls Manufactured during June, July and August

Balls Manufactured during May and September

Formula:

Average

= Sum of Quantities/Number of Quantities

Required Difference

= First Average − Second Average

Calculation:

⇒ Average Balls Manufactured during June, July and August = (96 + 128 + 160)/3 = 384/3 = 128

⇒ Average Balls Manufactured during May and September = (64 + 192)/2 = 256/2 = 128

⇒ Required Difference = 128 – 128 = 0

∴ Answer = 0

Common Calculation

Given:

Total Balls Manufactured = 640

Formula:

Total Balls = Total × Percentage/100

Blue Balls = Total Balls × Blue Parts / Total Parts

Green Balls = Total Balls × Green Parts / Total Parts

Calculation:

⇒ May Total Balls = 10% of 640 = (10/100) × 640 = 64

⇒ Blue Balls in May = (5/8) × 64 = 40

⇒ Green Balls in May = (3/8) × 64 = 24

⇒ June Total Balls = 15% of 640 = (15/100) × 640 = 96

⇒ Blue Balls in June = (7/12) × 96 = 56

⇒ Green Balls in June = (5/12) × 96 = 40

⇒ July Total Balls = 20% of 640 = (20/100) × 640 = 128

⇒ Blue Balls in July = (5/8) × 128 = 80

⇒ Green Balls in July = (3/8) × 128 = 48

⇒ August Total Balls = 25% of 640 = (25/100) × 640 = 160

⇒ Blue Balls in August = (3/8) × 160 = 60

⇒ Green Balls in August = (5/8) × 160 = 100

⇒ September Total Balls = 30% of 640 = (30/100) × 640 = 192

⇒ Blue Balls in September = (7/12) × 192 = 112

⇒ Green Balls in September = (5/12) × 192 = 80

Given:

Green Balls in August = 100

Blue Balls in June = 56

Blue Balls in July = 80

Formula:

Required Percentage

= (Required Quantity/Base Quantity) × 100

Calculation:

⇒ Total Blue Balls in June and July = 56 + 80 = 136

⇒ Green Balls in August = 100

⇒ Required Percentage = (100/136) × 100 = 73.53% ≈ 73.5%

∴ Answer = 73.5%

Given:

Total population of the village = x

2/7 of them are graduates

Remaining are non-graduates

30% of non-graduates = 2100

25% of graduates are employed

42.85% of non-graduates are unemployed

Formula used:

Number of non-graduates = Total population - Number of graduates

Number of unemployed graduates = 75% of graduates

Number of employed non-graduates = 57.15% of non-graduates

Calculations:

Let the total population be x.

Number of graduates:

2/7 of x = 2x/7

Number of non-graduates:

Remaining = x - 2x/7 = 5x/7

Given 30% of non-graduates = 2100:

0.3 × 5x/7 = 2100

⇒ 1.5x/7 = 2100

⇒ 1.5x = 2100 × 7

⇒ 1.5x = 14700

⇒ x = 14700 / 1.5

⇒ x = 9800

Total population = 9800

Number of graduates:

2/7 of 9800 = 2/7 × 9800 = 2800

Number of non-graduates:

5/7 of 9800 = 5/7 × 9800 = 7000

Number of employed graduates:

25% of 2800 = 0.25 × 2800 = 700

Number of unemployed graduates:

75% of 2800 = 0.75 × 2800 = 2100

Number of unemployed non-graduates:

42.85% of 7000 = 0.4285 × 7000 = 2999.5 ≈ 3000

Number of employed non-graduates:

Remaining non-graduates after accounting for unemployed non-graduates:

Total non-graduates - Unemployed non-graduates = 7000 - 3000 = 4000

Difference between unemployed graduates and employed non-graduates:

Difference = 2100 - 4000

∴ The difference between unemployed graduates and employed non-graduates is 1900.

Given:

Average weight initially = 9.5 kg

5 dogs with average weight 6.5 kg leave and 4 dogs with average weight 12.5 kg join the group

Average increases by 3 kg

Formula used:

Average = sum of observations / no. of observations

Calculation:

Let the no. of dogs be x

According to question,

(9.5x - 5 × 6.5 + 4 × 12.5) / x - 5 + 4 = 12.5

⇒ (9.5x - 32.5 + 50) / x- 1 = 12.5

⇒ 9.5x + 17.5 / x - 1 = 12.5

⇒ 9.5x + 17.5 = (x - 1) × 12.5

⇒ 12.5x - 9.5x = 17.5 + 12.5

⇒ 3x = 30

⇒ x = 10

∴ The number of dogs initially in the group is 10.

Let the investments of A and B be ₹4x and ₹5x, respectively.

A and B invested their amounts for 12 months, while C invested for 12 – 7 = 5 months

Ratio of profits = 4x × 12: 5x × 12: 18000 × 5 = 48x:60x:90000

Given profit ratio = 8:10:5

Therefore, 48x/8 = 90000/5

Or, 6x = 18000

So, x = 3000

Investment of B = 5x = 5 × 3000 = ₹ 15,000