Quantitative Aptitude PYQs

Common Calculation

Shop A produced = 120

Shop A sold = 2× unsold

Let unsold = x ⇒ sold = 2x

So, total = x + 2x = 3x ⇒ 3x = 120 ⇒ x = 40, sold = 80

Shop B:

Produced = A + 20 = 120 + 20 = 140

Unsold in B = 25% more than unsold in A = 40 + 25% of 40 = 40 + 10 = 50

Sold = 140 - 50 = 90

Shop C:

Produced = 33.33% less than A = 120 - (1/3 × 120) = 120 - 40 = 80

Now:

Total unsold in A + B = 40 + 50 = 90

Sold in C = (2/3) × 90 = 60

So, Unsold = 80 - 60 = 20

Shop D:

Unsold = 2 × unsold in C = 2 × 20 = 40

Produced = 12.5% more than produced in C = 80 + 12.5% of 80 = 80 + 10 = 90

Sold = 90 - 40 = 50

 

Calculation

Number of items unsold in A is 40

Number of items produced in B is 140

Percentage = (40 / 140) × 100 = 28.57%

Common Calculation

Shop A produced = 120

Shop A sold = 2× unsold

Let unsold = x ⇒ sold = 2x

So, total = x + 2x = 3x ⇒ 3x = 120 ⇒ x = 40, sold = 80

Shop B:

Produced = A + 20 = 120 + 20 = 140

Unsold in B = 25% more than unsold in A = 40 + 25% of 40 = 40 + 10 = 50

Sold = 140 - 50 = 90

Shop C:

Produced = 33.33% less than A = 120 - (1/3 × 120) = 120 - 40 = 80

Now:

Total unsold in A + B = 40 + 50 = 90

Sold in C = (2/3) × 90 = 60

So, Unsold = 80 - 60 = 20

Shop D:

Unsold = 2 × unsold in C = 2 × 20 = 40

Produced = 12.5% more than produced in C = 80 + 12.5% of 80 = 80 + 10 = 90

Sold = 90 - 40 = 50

Calculation

A sold = 80, B sold = 90

⇒ Difference a = 90 - 80 = 10

C sold = 60

⇒ 60 = 2y ⇒ y = 30

a + y = 10 + 30 = 40

Common Calculation

Shop A produced = 120

Shop A sold = 2× unsold

Let unsold = x ⇒ sold = 2x

So, total = x + 2x = 3x ⇒ 3x = 120 ⇒ x = 40, sold = 80

Shop B:

Produced = A + 20 = 120 + 20 = 140

Unsold in B = 25% more than unsold in A = 40 + 25% of 40 = 40 + 10 = 50

Sold = 140 - 50 = 90

Shop C:

Produced = 33.33% less than A = 120 - (1/3 × 120) = 120 - 40 = 80

Now:

Total unsold in A + B = 40 + 50 = 90

Sold in C = (2/3) × 90 = 60

So, Unsold = 80 - 60 = 20

Shop D:

Unsold = 2 × unsold in C = 2 × 20 = 40

Produced = 12.5% more than produced in C = 80 + 12.5% of 80 = 80 + 10 = 90

Sold = 90 - 40 = 50

Calculation

D produced = 90

⇒ E produced = 90 + 33.33% of 90 = 90 + 30 = 120

Sold : Unsold = 3:1 ⇒ Total = 4 parts

So, Unsold in E = (1/4) × 120 = 30

D unsold = 40

⇒ Total unsold in D and E = 40 + 30 = 70

Given:

Downstream distance = 120 km, Time taken = 2.5 hours

Speed ratio of boat and stream = 7:5

Upstream distance = d - 24 km, Time taken = 7.5 hours

Formula used:

Speed downstream = (Speed of boat + Speed of stream)

Speed upstream = (Speed of boat - Speed of stream)

Speed = Distance / Time

Calculations:

Speed downstream = 120 km / 2.5 hours = 48 km/h

Let the speed of the boat = 7x and speed of stream = 5x

⇒ Speed downstream = 7x + 5x = 12x

⇒ 12x = 48

⇒ x = 4

Speed of boat = 7x = 7 × 4 = 28 km/h

Speed of stream = 5x = 5 × 4 = 20 km/h

Now, Speed upstream = Speed of boat - Speed of stream = 28 - 20 = 8 km/h

Distance upstream = d - 24 km, Time taken = 7.5 hours

Speed upstream = (d - 24) / 7.5

⇒ 8 = (d - 24) / 7.5

⇒ 8 × 7.5 = d - 24

⇒ 60 = d - 24

⇒ d = 84 km

Now, the time taken to cover d km in still water is given by:

Time = Distance / Speed of boat

Time = 84 km / 28 km/h = 3 hours

∴ The time taken by the boat to cover d km in still water is 3 hours.

Calculation

P and Q start a business.

P's investment is ₹2000 more than Q's.

P invests for 8 months, Q for 12 months.

Total profit at the end of the year = ₹6300.

Profit share of P is 16x, where

x=152 – 50 = 225 – 50 = 175

So, P's share = 16 × 175 =₹2800

Total profit = 6300

⇒Q’s share = 6300 – 2800 =3500

Let investment of Q = ₹y

→ Then P’s investment = ₹(y + 2000)

So:

P = (y+2000) ×8

Q = y×12

Profit ratio = P : Q = 2800 : 3500 = 4 : 5

So:

[ (y+2000) × 8 ]/ 12y = 4/5

So, [(5 × 8) (y + 2000)] = 4 × 12y

⇒ 40y + 80000 = 48y

⇒ 80000 = [48y − 40y] = 8y

⇒ y = 80000/8 = 10,000

Investment of Q = 10,000

Calculation

Speed of Train E is 25% greater than Train B

→ Speed of E = 1.25B

Speed of Train F is 25% greater than Train A

→ Speed of F = 1.25A

Sum of speed of Train A and B = 108 km/h

→ A + B =108

Trains E and F cross each other in 96 seconds while moving in opposite directions

Ratio of lengths of E : F = 3 : 2

→ Let lengths be: E = 3x, F = 2x

→ So total distance to cross = 5x

Time = 96 seconds

So, (A + B) =108 ---------Equation (1)

Then:

Speed of E = 1.25b

Speed of F = 1.25a

So relative speed when they cross each other =

[1.25a + 1.25b] = 1.25(a + b) =1.25 × 108 = 135 km/h = [135 × [5/18] = 37.5 m/s

Distance=Speed × Time = 37.5 × 96 = 3600 meters

But distance = E + F = 5x

So, 5x=3600

⇒ x = 3600 / 5 = 720

Train F = 2x = 2 × 720 = 1440 meters

Calculation

Quantity I:

Daughter’s age after 5 years = 30

So, current age = 30 – 5 =25

Son = Daughter − 4 = 25 − 4=21

Mother = 2 × Daughter = 2 × 25 = 50

Father = Mother + 6 = 50 + 6 = 56

Now add all the ages:

Father + Mother + Daughter + Son = 56 + 50 + 25 + 21 = 152

Average age of 4 family members = [152/4] = 38 years

Quantity II:

C = 30

B = C + 3 = 30 + 3 = 33

A = B + 5 = 33 + 5 = 38

D = A + 2 = 38 + 2 = 40

Now average of C and D = [30 + 40] / 2 = 70/2 = 35 year

Quantity I = 38 years

Quantity II = 35 years

Quantity I > Quantity II.

Given:

m is a perfect square less than 50

n is a perfect cube greater than 50 but less than 100

The difference between m² and n² is 1695

Another number, o, is a perfect square smaller than m and more than 20, but the difference between m and o is more than the difference between m and n

p is a two-digit perfect square less than o

Formula used:

Perfect square: m = x²

Perfect cube: n = y³

Difference between squares: a² - b² = (a - b)(a + b)

Calculations:

Let m be a perfect square less than 50, so m can be 1, 4, 9, 16, 25, 36, or 49.

Let n be a perfect cube greater than 50 but less than 100. The perfect cubes between 50 and 100 are 64 and 125. So, n = 64.

We are given that the difference between m² and n² is 1695:

m² - n² = 1695

Using the difference of squares formula:

(m - n)(m + n) = 1695

Substitute n = 64:

(m - 64)(m + 64) = 1695

Let’s try different values for m (perfect squares less than 50) and see which one satisfies this equation.

For m = 49:

(49 - 64)(49 + 64) = (-15)(113) = -1695

This satisfies the equation. So, m = 49 and n = 64.

Next, we need to find the value of o, which is a perfect square smaller than m and more than 20. o must be a perfect square between 20 and 49. The possible values for o are 25 and 36. Since the difference between m and o is more than the difference between m and n, we choose o = 25 because the difference between m and 25 is 24, while the difference between m and n is 15.

Finally, p is a two-digit perfect square less than o. The perfect squares less than 25 are 1, 4, 9, 16. The largest two-digit perfect square less than 25 is 16, so p = 16.

Now, let’s compute the quantities:

Quantity I: m + n + 2p = 49 + 64 + 2 × 16 = 49 + 64 + 32 = 145

Quantity II: m + 2n + o = 49 + 2 × 64 + 25 = 49 + 128 + 25 = 202

Conclusion:

Quantity I = 145

Quantity II = 202

The relation between the magnitudes of Quantity I and Quantity II is that Quantity II is greater than Quantity I.

Given:

A and B together can finish the task in 20 days

B and C together can complete the task in 40 days

A and C together can complete the task in 30 days

Worker D is twice as efficient as C

Worker E has double the efficiency of B

Formula used:

Work done = Efficiency × Time

Efficiency of workers can be represented as the reciprocal of the time taken by them to complete the task alone.

Calculations:

Let the amount of work done by A, B, C, D, and E in one day be denoted by A, B, C, D, and E, respectively.

From the given information:

1. A + B = 1/20 (because they finish the task in 20 days)
2. B + C = 1/40 (because they finish the task in 40 days)
3. A + C = 1/30 (because they finish the task in 30 days)

Now, let's solve for A, B, and C's individual efficiencies (work rates):

From equations (1) and (2), subtract equation (2) from equation (1):

(A + B) - (B + C) = 1/20 - 1/40

⇒ A - C = (2 - 1) / 40

⇒ A - C = 1/40

So, A = C + 1/40.

Now, substitute A = C + 1/40 into equation (3):

(C + 1/40) + C = 1/30

⇒ 2C + 1/40 = 1/30

⇒ 2C = 1/30 - 1/40

To subtract the fractions, find the common denominator:

1/30 - 1/40 = (4 - 3) / 120 = 1/120

⇒ 2C = 1/120

⇒ C = 1/240

Now that we know C's efficiency, we can find the efficiencies of A, B, D, and E:

A = C + 1/40 = 1/240 + 1/40 = 1/240 + 6/240 = 7/240

B = (1/20 - A) = 1/20 - 7/240 = 12/240 - 7/240 = 5/240 = 1/48

D = 2 × C = 2 × 1/240 = 1/120

E = 2 × B = 2 × 1/48 = 1/24

Quantity I: Find the total time taken by C and E together to complete the work:

Efficiency of C + Efficiency of E = 1/240 + 1/24 = 1/240 + 10/240 = 11/240

Time taken by C and E together = 1 / (11/240) = 240/11 ≈ 21.82 days

Quantity II: Find the total time taken by A and D together to complete the work:

Efficiency of A + Efficiency of D = 7/240 + 1/120 = 7/240 + 2/240 = 9/240 = 3/80

Time taken by A and D together = 1 / (3/80) = 80/3 ≈ 26.67 days

Conclusion:

Quantity I = 240/11 ≈ 21.82 days

Quantity II = 80/3 ≈ 26.67 days

The relation between the magnitudes of Quantity I and Quantity II is that Quantity I is less than Quantity II.

Common Calculation

For shop A,

Number of copper items sold in shop A is 24.

Number of bronze items sold in shop A is 16.

So, total number of copper and bronze items sold in shop A is 24 + 16 = 40.

So, Ratio between total number of [ copper + bronze] items sold to number silver items sold.

So, Number of silver items sold in shop A is 40 × 4 /5 = 32

Similarly, we can calculate others values also, which is given in the table.

Calculation

In Shop D:

Copper = 36

→ Shop E = 36 × 1.25 = 45

Bronze = 24

→ Shop E = 24 × 1.125 = 27

Silver = 40

→ Shop E = 40 × 1.30 = 52

Total in Shop E = 45 + 27 + 52 = 124

Total in Shop C = 32 + 18 + 36 = 86

Difference = 124 – 86 = 38

Answer: 38

Common Calculation

For shop A,

Number of copper items sold in shop A is 24.

Number of bronze items sold in shop A is 16.

So, total number of copper and bronze items sold in shop A is 24 + 16 = 40.

So, Ratio between total number of [ copper + bronze] items sold to number silver items sold.

So, Number of silver items sold in shop A is 40 × 4 /5 = 32

Similarly, we can calculate others values also, which is given in the table.

Calculation

In Shop D:

Bronze = 24, Silver = 40 ⇒ Total = 64

Tin items = 25% more than 64 = 1.25 × 64 = 80

Now, tin = 80, copper = 36

Average = (80 + 36) ÷ 2 = 116 ÷ 2 = 58

Answer: 58

Common Calculation

For shop A,

Number of copper items sold in shop A is 24.

Number of bronze items sold in shop A is 16.

So, total number of copper and bronze items sold in shop A is 24 + 16 = 40.

So, Ratio between total number of [ copper + bronze] items sold to number silver items sold.

So, Number of silver items sold in shop A is 40 × 4 /5 = 32

Similarly, we can calculate others values also, which is given in the table.

Calculation

Copper in B + C = 30 + 32 = 62

Silver in B + C = 24 + 36 = 60

Difference = 62 – 60 = 2

Answer: 2

Common Calculation

For shop A,

Number of copper items sold in shop A is 24.

Number of bronze items sold in shop A is 16.

So, total number of copper and bronze items sold in shop A is 24 + 16 = 40.

So, Ratio between total number of [ copper + bronze] items sold to number silver items sold.

So, Number of silver items sold in shop A is 40 × 4 /5 = 32

Similarly, we can calculate others values also, which is given in the table.

Calculation

In Shop B:

Copper = 30 × 750 = 22,500

Bronze = 28 × 550 = 15,400

Silver = 24 × 1050 = 25,200

Total value = 22,500 + 15,400 + 25,200 = 63,100

Total items = 30 + 28 + 24 = 82

Average selling price = 63100 ÷ 82 = Rs. 769.51 (approx)

Answer: Rs. 770

Common Calculation

For shop A,

Number of copper items sold in shop A is 24.

Number of bronze items sold in shop A is 16.

So, total number of copper and bronze items sold in shop A is 24 + 16 = 40.

So, Ratio between total number of [ copper + bronze] items sold to number silver items sold.

So, Number of silver items sold in shop A is 40 × 4 /5 = 32

Similarly, we can calculate others values also, which is given in the table.

Calculation

In Shop A:

Total silver items = 32

Number of x-type silver items = 3m + 2

Number of y-type silver items = 2n + 6

So,

3m + 2 + 2n + 6 = 32

⇒ 3m + 2n = 24

Also, m + n = 10,

So, m = 4 and n = 6

⇒ Required ratio m : n

Answer: m : n = 4 : 6 = 2 : 3

Calculation

Initial mixture (60 litres in 3:1 ratio)

Milk = (3/4) × 60 = 45 litres

Water = (1/4) × 60 = 15 litres

8 litres of mixture removed

Ratio = 3:1 → in 8 litres:

Milk removed = (3/4) × 8 = 6 litres

Water removed = (1/4) × 8 = 2 litres

Remaining:

Milk = 45 - 6 = 39 litres

Water = 15 - 2 = 13 litres

Add p litres of milk and q litres of water

Final milk = 39 + p

Final water = 13 + q

New ratio = (39 + p) / (13 + q) = 9 / 5

So, 5(39 + p) = 9(13 + q)

So, 195 + 5p = 117 + 9q

=> 5p - 9q = -78 → [Equation 1]

Also, p + q = 11 → [Equation 2]

From Equation 2: p = 11 - q

Substitute into Equation 1:

5(11 - q) - 9q = -78

So, 55 - 5q - 9q = -78

So, 55 - 14q = -78

=> -14q = -133

=> q = 9.5

=> p = 11 - 9.5 = 1.5

Difference between p and q is 9.5 – 1.5 = 8

Considering the given series,

4, 12, 24, 96, 480, 2880, 20160

The logic of above series can be explained as,

4 × 2 ≠ 12 (should be 8)

8 × 3 = 24

24 × 4 = 96

96 × 5 = 480

480 × 6 = 2880

2880 × 7 = 20160

∴ Wrong number is 12

The pattern of the given series is:

⇒ 23

⇒ 23 + (2³ – 1) = 30

⇒ 30 + (3³ – 1) = 56

⇒ 56 + (4³ – 1) = 119

⇒ 119 + (5³ – 1) = 243

⇒ 243 + (6³ – 1) = 458

∴ The wrong term is 118.

Given:

110, 136, 164, 194, 226, 260, 306

Calculation:

The series follows the following pattern 

10² + 10 = 110

11² + 15 = 136

12² + 20 = 164

13² + 25 = 194

14² + 30 = 226

15² + 35 = 260

16² + 40 = 296 ≠ 306

∴ 306 is wrong and should be replaced by 296

Given:

The number series:

50, 25, 15, 6.25, 3.125, 1.5625

Concept Used:

Number series following a fixed pattern.

Calculation;

The given number series follows the pattern:

50 ÷ 2 = 25

25 ÷ 2 = 12.5

12.5 ÷ 2 = 6.25

6.25 ÷ 2 = 3.125

3.125 ÷ 2 = 1.5625

∴ The Wrong Number in the given number series is 15

The series follows the following pattern:

6 × 1.5 = 9

12 × 2.5 = 30

24 × 3.5 = 84

48 × 4.5 = 216

96 × 5.5 = 528

192 × 6.5 = 1248

∴ wrong number of the series is 86