Quantitative Aptitude PYQs

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

Common Calculation

Let number of items manufactured on Monday is 5x and number of items manufactured on Tuesday is 2x in company A.

So, ATQ, 5x – 2x = 45

Or, 3x = 45

Or, x = 45/3 = 15

So, Number of items manufactured on Monday is 5 × 15 = 75

And number of items manufactured on Tuesday is 2 × 15 = 30

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

 

Calculation

Items manufactured Monday = 105

Items manufactured Tuesday = 135

→ Average = [105 + 135] /2 = 240/2 = 120

Common Calculation

Let number of items manufactured on Monday is 5x and number of items manufactured on Tuesday is 2x in company A.

So, ATQ, 5x – 2x = 45

Or, 3x = 45

Or, x = 45/3 = 15

So, Number of items manufactured on Monday is 5 × 15 = 75

And number of items manufactured on Tuesday is 2 × 15 = 30

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

 

Calculation

Monday: 40% items sold

→ Items Unsold = 60% of 120 = 0.6 × 120 = 72

Tuesday: 60% items sold

→ Unsold = 40% of 150 = 0.4 × 150 = 60

Total items unsold = 72 + 60 = 132

Common Calculation

Let number of items manufactured on Monday is 5x and number of items manufactured on Tuesday is 2x in company A.

So, ATQ, 5x – 2x = 45

Or, 3x = 45

Or, x = 45/3 = 15

So, Number of items manufactured on Monday is 5 × 15 = 75

And number of items manufactured on Tuesday is 2 × 15 = 30

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

 

Calculation

Company F:

Number of items manufactured on Monday by E = 240

→ Number of items manufactured on Monday by F

= 240 + [0.3 × 240] = 240 + 72 = 312

Number of items manufactured on Tuesday by F

= Monday + 68 = 312 + 68 = 380

Common Calculation

Let number of items manufactured on Monday is 5x and number of items manufactured on Tuesday is 2x in company A.

So, ATQ, 5x – 2x = 45

Or, 3x = 45

Or, x = 45/3 = 15

So, Number of items manufactured on Monday is 5 × 15 = 75

And number of items manufactured on Tuesday is 2 × 15 = 30

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

 

Calculation

Monday total:

B = 105, C = 75

→ Total = 105 + 75 = 180

Tuesday total:

B = 135, C = 50

→ Total = 135 + 50 = 185

So, ratio = 180 : 185

Simplify: divide by 5 → 36:37

So, x = 36, y = 37:

So, 7x + 8y = [7 × 36] + [8 × 37] = 252 + 296 = 548

Common Calculation

Let number of items manufactured on Monday is 5x and number of items manufactured on Tuesday is 2x in company A.

So, ATQ, 5x – 2x = 45

Or, 3x = 45

Or, x = 45/3 = 15

So, Number of items manufactured on Monday is 5 × 15 = 75

And number of items manufactured on Tuesday is 2 × 15 = 30

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

 

Calculation

Total number of items manufactured on Monday = 75

→ 20% defective = 0.2 × 75 = 15

→ Non-defective = 75 – 15 = 60

Now, non-defective on Tuesday = 40% of 60 = 24

Total number of items manufactured on Tuesday = 30

→ Defective = 30 – 24 = 6