Quantitative Aptitude PYQs

From the given data:

Total A on Monday and Thursday = 360 + 600 = 960

Total C on Monday and Thursday = 300 + Y

ATQ,

960 ÷ (300 + Y) = (8/5)

300 + Y = (960 × 5) ÷ 8

300 + Y = 600

Y = 300

Total B on Tuesday and Wednesday = 300 × 2 = 600

(Y − X) + 360 = 600

300 − X + 360 = 600

660 − X = 600

X = 60

Using X = 60 and Y = 300:

Printer D on Wednesday = X + Y = 60 + 300 = 360

Printer C on Wednesday = 360

Required Difference = 360 − 360 = 0

Ratio in 2017 = (7/10) :(5/6) ):(4/5) = 21:25:24

Let their salaries in 2017 be 21x, 25x, and 24x respectively.

In 2018: (21x + 7000) :(25x + 5000) :(24x + 8000) = 7:8:8

So, (21x + 7000) /(25x + 5000) = (7/8)

Or, 8 X (21x + 7000) = 7 X (25x + 5000)

Or, 168x + 56000 = 175x + 35000

Or, 7x = 21000

Or, x = 3000

Salary of Manish in 2017 = 24x = 24 × 3000 = 72000

From the given data:

Total A on Monday and Thursday = 360 + 600 = 960

Total C on Monday and Thursday = 300 + Y

ATQ,

960 ÷ (300 + Y) = (8/5)

300 + Y = (960 × 5) ÷ 8

300 + Y = 600

Y = 300

Total B on Tuesday and Wednesday = 300 × 2 = 600

(Y − X) + 360 = 600

300 − X + 360 = 600

660 − X = 600

X = 60

Using X = 60 and Y = 300:

Printer A on Tuesday = X + 40 = 60 + 40 = 100

Printer B on Tuesday = Y − X = 300 − 60 = 240

Printer C on Thursday = Y = 300

Calculation:

From the given data:

Number of articles printed by Printer C on Monday = 300

Number of articles printed by Printer A on Wednesday = 420

Required percent = (300/420) x 100 = 71.43%

From the given data:

Total A on Monday and Thursday = 360 + 600 = 960

Total C on Monday and Thursday = 300 + Y

ATQ,

960 ÷ (300 + Y) = (8/5)

300 + Y = (960 × 5) ÷ 8

300 + Y = 600

Y = 300

Using Y = 300:

Printer B on Thursday = 420

Printer C on Thursday = 300

Required ratio = 420: 300 = 7: 5

From the given data:

Number of articles printed by Printer A on Thursday = 600

Sum of the number of articles printed by Printer A on Thursday and Friday together = 1120

ATQ,

Thursday + Friday = 1120

600 + Friday = 1120

Friday = 1120 − 600

Friday = 520

From I:

Initial Milk = 7y, Initial Water = 5y

Final Milk = 7y + x, Final Water = 5y + 2x

(5y + 2x) – (7y + x) = 12

So, x – 2y = 12

Values cannot be determined from I alone.

From II:

Initial Milk - Initial Water = 8

7y – 5y = 8

2y = 8

So, y = 4

Value of x cannot be determined from II alone.

On combining statements I and II:

x – 2(4) = 12

so, x = 20

Final Milk = 7 x 4 + 20 = 48

Final Water = 5 x 4 + 2 x 20 = 60

Required ratio = 48:60 = 4:5

Hence, option E.

From I:

Speed while floating = Speed of stream (S)

Speed downstream = D

(80/S) = 6 x (40/D)

Or, (80/S) = (240/D)

Or, D = 3S

Or, V + S = 3S

Or, V = 2S

Upstream speed U = V - S = S

From II:

D = (240/3) = 80 km/h

On combining I and II:

3S = 80

Or, S = 80/3 km/h

So, U = 80/3 km/h

So, required distance = (80/3) x 3 = 80 km

Hence, option e.

Let total capacity of tank = LCM (6, 9, 18) = 18 units.

Efficiency of A = 3 units/hr

Efficiency of B = 2 units/hr

Efficiency of C = 1 unit/hr

Total efficiency = 3 + 2 + 1 = 6 units/hr

1/3^rd of the tank = 18 x 1/3 = 6 units

Time taken to fill 6 units by A, B and C = 6/6 = 1 hr

Remaining tank = 18 – 6 = 12 units

Time taken by A and B to fill remaining tank = 12 ÷ (3 + 2) = 12/5 = 2(2/5) hours

Total time taken = 1 + 2(2/5) = 3(2/5) hour

Let cost price be Rs. x

Selling price at 8% loss = 0.92x

Selling price at 4% profit = 1.04x

ATQ,

1.04x – 0.92x = 360

0.12x = 360

So, x = 360/0.12 = 3000

Profit share ratio of Ramesh to Mohit = (12000 × 18) : (16000 × 12)

= (12 × 18) : (16 × 12) = 18 : 16 = 9 : 8

Let the profits of Ramesh and Mohit be 9x and 8x, respectively.

So, 9x − 8x = 3000

Or, x = 3000

Total profit = 9x + 8x = 17x

So, required total profit = 17 × 3000 = Rs. 51,000

General Solution:

Let’s define the following sets:

• Only C (Coffee) = A
• Only M (Milk) = B
• Only T (Tea) = C
• C ∩ M only (not T) = D
• C ∩ T only (not M) = E
• M ∩ T only (not C) = F
• C ∩ M ∩ T (all three) = G

We are given:

1. Only Tea (C) = 10

⇒ C = 10
2. All three (G) = 16 3. Only Coffee (A) = 20% more than only Tea

⇒ A = 10 + 20% of 10 = 10 + 2 = 12
4. Only Milk (B) = C ∩ T only (not M) = E

⇒ B = E
5. M ∩ T only (F) = Half of C ∩ M only (D)

⇒ F = ½ × D

And D = 24

⇒ F = 12

So far we have:

• A = 12
• B = E (unknown)
• C = 10
• D = 24
• E = B
• F = 12
• G = 16

Now, total number of people = 100

Sum of all individual segments of the Venn diagram =

A + B + C + D + E + F + G

= 12 + B + 10 + 24 + B + 12 + 16

= (12 + 10 + 24 + 12 + 16) + 2B = 74 + 2B

Set that equal to total surveyed:

74 + 2B = 100

⇒ 2B = 26

⇒ B = 13

Then E = 13

Thus,

 

Calculations:

Only one = 12 + 13 + 10 = 35 people → ₹15 × 35 = ₹525

Exactly two = 24 + 13 + 12 = 49 people → ₹25 × 49 = ₹1225

All three = 16 people → ₹35 × 16 = ₹560

Total = 525 + 1225 + 560 = ₹2310

Hence, the correct answer is ₹2310.

General Solution:

Let’s define the following sets:

• Only C (Coffee) = A
• Only M (Milk) = B
• Only T (Tea) = C
• C ∩ M only (not T) = D
• C ∩ T only (not M) = E
• M ∩ T only (not C) = F
• C ∩ M ∩ T (all three) = G

We are given:

1. Only Tea (C) = 10

⇒ C = 10
2. All three (G) = 16 3. Only Coffee (A) = 20% more than only Tea

⇒ A = 10 + 20% of 10 = 10 + 2 = 12
4. Only Milk (B) = C ∩ T only (not M) = E

⇒ B = E
5. M ∩ T only (F) = Half of C ∩ M only (D)

⇒ F = ½ × D

And D = 24

⇒ F = 12

So far we have:

• A = 12
• B = E (unknown)
• C = 10
• D = 24
• E = B
• F = 12
• G = 16

Now, total number of people = 100

Sum of all individual segments of the Venn diagram =

A + B + C + D + E + F + G

= 12 + B + 10 + 24 + B + 12 + 16

= (12 + 10 + 24 + 12 + 16) + 2B = 74 + 2B

Set that equal to total surveyed:

74 + 2B = 100

⇒ 2B = 26

⇒ B = 13

Then E = 13

Thus,

 

Calculations:

People who like Tea =

Only Tea = 10

Tea & Coffee only = 13

Tea & Milk only = 12

All three = 16

Total = 10 + 13 + 12 + 16 = 51

Percentage = (51 / 100) × 100 = 51%

Hence, the correct answer is 51%.

General Solution:

Let’s define the following sets:

• Only C (Coffee) = A
• Only M (Milk) = B
• Only T (Tea) = C
• C ∩ M only (not T) = D
• C ∩ T only (not M) = E
• M ∩ T only (not C) = F
• C ∩ M ∩ T (all three) = G

We are given:

1. Only Tea (C) = 10

⇒ C = 10
2. All three (G) = 16 3. Only Coffee (A) = 20% more than only Tea

⇒ A = 10 + 20% of 10 = 10 + 2 = 12
4. Only Milk (B) = C ∩ T only (not M) = E

⇒ B = E
5. M ∩ T only (F) = Half of C ∩ M only (D)

⇒ F = ½ × D

And D = 24

⇒ F = 12

So far we have:

• A = 12
• B = E (unknown)
• C = 10
• D = 24
• E = B
• F = 12
• G = 16

Now, total number of people = 100

Sum of all individual segments of the Venn diagram =

A + B + C + D + E + F + G

= 12 + B + 10 + 24 + B + 12 + 16

= (12 + 10 + 24 + 12 + 16) + 2B = 74 + 2B

Set that equal to total surveyed:

74 + 2B = 100

⇒ 2B = 26

⇒ B = 13

Then E = 13

Thus,

 

Calculations:

Total respondents = 100

We are to find how many people like at most two beverages, i.e., not all three.

From the previous data:

People who like all three beverages = 16

So, people who like at most two beverages = 100 – 16 = 84

Required % = (84 / 100) × 100 = 84%

Hence, the correct answer is 84%.

General Solution:

Let’s define the following sets:

• Only C (Coffee) = A
• Only M (Milk) = B
• Only T (Tea) = C
• C ∩ M only (not T) = D
• C ∩ T only (not M) = E
• M ∩ T only (not C) = F
• C ∩ M ∩ T (all three) = G

We are given:

1. Only Tea (C) = 10

⇒ C = 10
2. All three (G) = 16 3. Only Coffee (A) = 20% more than only Tea

⇒ A = 10 + 20% of 10 = 10 + 2 = 12
4. Only Milk (B) = C ∩ T only (not M) = E

⇒ B = E
5. M ∩ T only (F) = Half of C ∩ M only (D)

⇒ F = ½ × D

And D = 24

⇒ F = 12

So far we have:

• A = 12
• B = E (unknown)
• C = 10
• D = 24
• E = B
• F = 12
• G = 16

Now, total number of people = 100

Sum of all individual segments of the Venn diagram =

A + B + C + D + E + F + G

= 12 + B + 10 + 24 + B + 12 + 16

= (12 + 10 + 24 + 12 + 16) + 2B = 74 + 2B

Set that equal to total surveyed:

74 + 2B = 100

⇒ 2B = 26

⇒ B = 13

Then E = 13

Thus,

 

Calculations:

We are given:

People who like only Coffee = 12

People who like only Milk = 13

People who like both Milk and Tea but not Coffee = 12

So,

Required Ratio = (Only Coffee + Only Milk) : (Milk ∩ Tea only)

= (12 + 13) : 12

= 25 : 12

Hence, the correct answer is 25:12.

General Solution:

Let’s define the following sets:

• Only C (Coffee) = A
• Only M (Milk) = B
• Only T (Tea) = C
• C ∩ M only (not T) = D
• C ∩ T only (not M) = E
• M ∩ T only (not C) = F
• C ∩ M ∩ T (all three) = G

We are given:

1. Only Tea (C) = 10

⇒ C = 10
2. All three (G) = 16 3. Only Coffee (A) = 20% more than only Tea

⇒ A = 10 + 20% of 10 = 10 + 2 = 12
4. Only Milk (B) = C ∩ T only (not M) = E

⇒ B = E
5. M ∩ T only (F) = Half of C ∩ M only (D)

⇒ F = ½ × D

And D = 24

⇒ F = 12

So far we have:

• A = 12
• B = E (unknown)
• C = 10
• D = 24
• E = B
• F = 12
• G = 16

Now, total number of people = 100

Sum of all individual segments of the Venn diagram =

A + B + C + D + E + F + G

= 12 + B + 10 + 24 + B + 12 + 16

= (12 + 10 + 24 + 12 + 16) + 2B = 74 + 2B

Set that equal to total surveyed:

74 + 2B = 100

⇒ 2B = 26

⇒ B = 13

Then E = 13

Thus,

 

Calculations:

Exactly two beverages = 24 (C∩M) + 13 (C∩T) + 12 (M∩T) = 49

Only one beverage = 12 (C) + 13 (M) + 10 (T) = 35

Difference = 49 – 35 = 14

Hence, the correct answer is 14.

Shortcut Trick

12% of Salary = ₹7,200

⇒ 1% of Salary = 7200 ÷ 12 = ₹600

Total expenditure (Education + Groceries) = 60% of Salary

⇒ 12% + x% = 60%

⇒ x% = 60% − 12% = 48%

∴ The correct answer is 48%.

Alternate Method

Given:

Education Expenditure = 12% of Salary = ₹7,200

Total Expenditure = 60% of Salary

Formula:

Total Expenditure = Education % + Groceries %

Calculations:

⇒ Let Total Salary be S.

⇒ (12/100) × S = 7200

⇒ S = (7200 × 100) ÷ 12

⇒ S = 600 × 100 = ₹60,000

⇒ Total Expenditure = 60% of 60,000 = 36,000

⇒ Groceries Expenditure = Total − Education

⇒ Groceries Expenditure = 36,000 − 7,200 = ₹28,800

⇒ x = (28,800 ÷ 60,000) × 100

⇒ x = 288 ÷ 6 = 48

∴ The correct answer is 48%.

Additional Information

Percentage Change

Percentage change = (Change / Original Value) × 100. Useful for finding growth in salary or expenses.

Savings Calculation

Savings = Total Salary − Total Expenditure. In this case, savings would be 40% of the salary.

Base Change Rule

When multiple percentages are calculated on the same base (Total Salary), they can be added or subtracted directly.

Shortcut Trick

For two people A and B, combined time = (Product of times) ÷ (Sum of times).

2t = (5 × 5t) ÷ (5 + 5t)

2 = 25 ÷ (5 + 5t) ⇒ 10 + 10t = 25 ⇒ 10t = 15 ⇒ t = 1.5

Combined time = 2t = 2 × 1.5 = 3 days.

∴ The correct answer is 3 days.

Alternate Method

Given:

Time taken by A = 5 days

Time taken by B = 5t days

Time taken by A + B = 2t days

Formula Used:

1/T_total = 1/T_A + 1/T_B

Calculations:

⇒ 1/(2t) = 1/5 + 1/(5t)

⇒ 1/(2t) − 1/(5t) = 1/5

⇒ (5 − 2) / (10t) = 1/5

⇒ 3 / (10t) = 1/5

⇒ 10t = 15

⇒ t = 1.5

⇒ Time taken by A and B together = 2t = 2 × 1.5

⇒ Time taken = 3 days

∴ The correct answer is 3 days.

Additional Information

Efficiency and Time Relation

Efficiency is inversely proportional to the time taken to complete a work. Efficiency = Total Work ÷ Time.

Pipes and Cisterns

The same logic applies where filling pipes have positive efficiency and leakage/outlet pipes have negative efficiency.

Shortcut Trick

Ratio of Final Milk to Initial Milk after 2 operations = (√0.9604) = 0.98

Remaining fraction = (Total − Replaced) ÷ Total ⇒ 0.98 = (80 − x) ÷ 80

x = 80 × (1 − 0.98) = 80 × 0.02 = 1.6 litres

∴ The correct answer is 1.6 litres.

Alternate Method

Given: Initial quantity (C) = 80 litres, Number of operations (n) = 2, Final concentration = 96.04%.

Formula Used: Final Quantity = Initial Quantity × [1 − (x/C)]ⁿ

⇒ 0.9604 × 80 = 80 × [1 − (x/80)]²

⇒ 0.9604 = [1 − (x/80)]²

⇒ √0.9604 = 1 − (x/80)

⇒ 0.98 = 1 − (x/80)

⇒ x/80 = 1 − 0.98

⇒ x/80 = 0.02

⇒ x = 80 × 0.02 = 1.6 litres

∴ The correct answer is 1.6 litres.

Additional Information

Successive Replacement Formula

For n repeated operations of removing x units and replacing with water: Final Milk = Initial Milk × (1 − x/Total)ⁿ.

Alligation Rule

Used when two mixtures are mixed; for successive dilutions, the geometric ratio method (Shortcut Trick) is faster.

Percentage to Decimal

Always convert percentage concentrations to decimals for easy square root calculation: 96.04% = 0.9604.

Common Calculation –

According the question,

[ 8% + 12% + (2P + 5) % + P% + 15 %] = 100%

So, 2P + 5 + P = 100 – 15 – 12 – 8 = 65

Or, 3P = 60

Or, P = 60/3 = 20

So, Percentage distribution of number of items manufactured in factories A, B, C, D and E is 8%, 12%, [2 × 20 + 5] =45%, 20% and 15% respectively.

So, Item manufactured in factory A is 1200 × 8 /100 = 96

Similarly, we can calculate the number of items manufactured by others factory also, which is given in the table.

 

Calculation

Factory C = 540

→ 20% defective = 20% of 540 = 108

Factory D = 240

→ defective items = 25% less than 108

 ⇒ 108 – 25% of 108 = 108 – 27 = 81

Factory B = 144 → defective items = (2/9) of (108 + 81) = (1/4) of 189 = 42

Non-defective in:

C = 540 – 108 = 432

D = 240 – 81 = 159

B = 144 – 42 = 102

Total non- defective is = 432 + 159 + 102 = 693

Common Calculation –

According the question,

[ 8% + 12% + (2P + 5) % + P% + 15 %] = 100%

So, 2P + 5 + P = 100 – 15 – 12 – 8 = 65

Or, 3P = 60

Or, P = 60/3 = 20

So, Percentage distribution of number of items manufactured in factories A, B, C, D and E is 8%, 12%, [2 × 20 + 5] =45%, 20% and 15% respectively.

So, Item manufactured in factory A is 1200 × 8 /100 = 96

Similarly, we can calculate the number of items manufactured by others factory also, which is given in the table.

 

Calculation

Total in A and E = A + E = 96 + 180 = 276

Total in B and D = B + D = 144 + 240 = 384

Ratio = 276 : 384 =23 : 32