Quantitative Aptitude PYQs

General solution:

Number of persons who participated in only swimming and only fencing are in the ratio 4x: 3x

Number of persons who participated in only skating is 2 less than the number of persons who participated in only fencing = (3x - 2)

Number of persons who participated in all the three = 5

Number of persons who participated in both swimming and fencing but not skating =  (5 + 5) = 10

Number of persons who participated in both fencing and swimming but not skating and the number of persons who participated in swimming and skating but not fencing are in the ratio 2 : 3

Number of persons who participated in swimming and skating but not fencing = 10/2 ×  3 = 15

Number of person who participated in both fencing and skating but not swimming is 80% of the number of persons who participated in swimming and skating but not fencing.

Number of person who participated in both fencing and skating but not swimming  =15 ×  (80/100) = 12

Total number of persons who participated in only swimming , only fencing and only skating is 98.

(4x + 3x + 3x - 2) = 98

10x = 100

x = 10

Number of persons who likes swimming only = 40

Number of persons who likes fencing only = 30

Number of persons who likes skating = (30 - 2) = 28

Solution:

Number of males to females who participated only skating = 28

Number of males participated  only skating = 28/7 × 4 = 16

Number of females participated only in skating = (28 - 16) = 12

Number of females participated only swimming = 22 - 12 = 10

Number of males participated only swimming = (40 - 10) = 30

Required difference = (30 - 16) = 14

General solution:

Number of persons who participated in only swimming and only fencing are in the ratio 4x: 3x

Number of persons who participated in only skating is 2 less than the number of persons who participated in only fencing = (3x - 2)

Number of persons who participated in all the three = 5

Number of persons who participated in both swimming and fencing but not skating =  (5 + 5) = 10

Number of persons who participated in both fencing and swimming but not skating and the number of persons who participated in swimming and skating but not fencing are in the ratio 2 : 3

Number of persons who participated in swimming and skating but not fencing = 10/2 ×  3 = 15

Number of person who participated in both fencing and skating but not swimming is 80% of the number of persons who participated in swimming and skating but not fencing.

Number of person who participated in both fencing and skating but not swimming  =15 ×  (80/100) = 12

Total number of persons who participated in only swimming , only fencing and only skating is 98.

(4x + 3x + 3x - 2) = 98

10x = 100

x = 10

Number of persons who likes swimming only = 40

Number of persons who likes fencing only = 30

Number of persons who likes skating = (30 - 2) = 28

Solution:

Number of persons who participated in skating and fencing but not swimming = 12

Number of persons who participated in only swimming = 40

Required percentage = 12/40 ×  100 = 30%

General solution:

Number of persons who participated in only swimming and only fencing are in the ratio 4x: 3x

Number of persons who participated in only skating is 2 less than the number of persons who participated in only fencing = (3x - 2)

Number of persons who participated in all the three = 5

Number of persons who participated in both swimming and fencing but not skating =  (5 + 5) = 10

Number of persons who participated in both fencing and swimming but not skating and the number of persons who participated in swimming and skating but not fencing are in the ratio 2 : 3

Number of persons who participated in swimming and skating but not fencing = 10/2 ×  3 = 15

Number of person who participated in both fencing and skating but not swimming is 80% of the number of persons who participated in swimming and skating but not fencing.

Number of person who participated in both fencing and skating but not swimming  =15 ×  (80/100) = 12

Total number of persons who participated in only swimming , only fencing and only skating is 98.

(4x + 3x + 3x - 2) = 98

10x = 100

x = 10

Number of persons who likes swimming only = 40

Number of persons who likes fencing only = 30

Number of persons who likes skating = (30 - 2) = 28

Solution:

Number of persons who participated in swimming = (40 + 15 + 5+ 10) = 70

Number of persons who participated in fencing = (30 + 10 + 5 + 12) = 57

Required difference  = (70 - 57) = 13

Shortcut Trick

Let Total Income be 100%.

Planned Donation = 25% of Income.

Actual Donation = 85% of 25% = 21.25% of Income.

21.25% → ₹4250

100% → (4250 ÷ 21.25) × 100 = 200 × 100 = ₹20,000.

∴ The correct answer is ₹20,000.

Alternate Method

Given:

Actual donation = ₹4250

Actual donation = 85% of Planned donation

Planned donation = 25% of Monthly Income

Calculations:

⇒ 85% of Planned donation = ₹4250

⇒ Planned donation = (4250 × 100) ÷ 85

⇒ Planned donation = 50 × 100 = ₹5000

⇒ Now, 25% of Monthly Income = ₹5000

⇒ Monthly Income = (5000 × 100) ÷ 25

⇒ Monthly Income = ₹20,000

∴ The correct answer is ₹20,000.

Additional Information

Percentage Change

To find the original value from a percentage part, use: Original = (Given Value ÷ Percentage) × 100.

Successive Percentages

If a value is changed by a% and then b%, the effective percentage of the original is (a × b) ÷ 100.

Income and Savings

Total Income is always treated as the base (100%) when calculating components like expenditure, savings, or donations.

Shortcut Trick

In the final mixture, the milk and water ratio is 5 : 3.

Total volume remains constant at 280 liters because x liters are removed and x liters are added.

Total units in final mixture = 5 + 3 = 8 units.

8 units = 280 liters ⇒ 1 unit = 35 liters.

Water in final mixture = 3 units = 3 × 35 liters = 105 liters.

∴ The correct answer is 105 liters.

Alternate Method

Given: Initial volume = 280 liters, Initial Ratio (M:W) = 5:2, Final Ratio (M:W) = 5:3.

Formula: Ratio × constant = Actual Value.

⇒ When x liters of mixture is removed, the ratio of milk and water remains 5:2.

⇒ When x liters of water is added, the ratio becomes 5:3.

⇒ Since only water is added, the milk quantity stays constant (5 units in both cases).

⇒ Total volume of final mixture = Initial volume = 280 liters.

⇒ Final ratio sum = 5 + 3 = 8 units.

⇒ 8 units = 280 liters.

⇒ 1 unit = 280 ÷ 8 = 35 liters.

⇒ Water in final mixture = 3 units = 3 × 35 = 105 liters.

∴ The correct answer is 105 liters.

Additional Information

Mixture Removal Property

When a part of a mixture is removed, the ratio of components in the remaining mixture stays the same as the original ratio.

Replacement Concept

If x liters are removed and x liters of a single component are added, the total volume of the mixture remains unchanged.

Ratio Balancing

To solve replacement problems, keep the component that was not added constant in the ratio calculations.

Shortcut Trick

Total interest % in first case = 10% × 7 = 70% of x.

Total interest % in second case = 15% × 8 = 120% of (x + 10,100).

Difference: 120% of (x + 10,100) − 70% of x = 34,620.

⇒ 1.2x + 12,120 − 0.7x = 34,620 ⇒ 0.5x = 22,500.

⇒ x = 45,000.

∴ The correct answer is ₹45,000.

Alternate Method

Given: Rate₁ = 10%, Time₁ = 7 yrs, Principal₁ = x. Rate₂ = 15%, Time₂ = 8 yrs, Principal₂ = x + 10,100.

Formula Used: Simple Interest (SI) = (P × R × T) ÷ 100

⇒ SI₁ = (x × 10 × 7) ÷ 100 = 0.7x

⇒ SI₂ = [(x + 10,100) × 15 × 8] ÷ 100 = 1.2 × (x + 10,100)

⇒ SI₂ − SI₁ = 34,620

⇒ 1.2x + 12,120 − 0.7x = 34,620

⇒ 0.5x = 34,620 − 12,120

⇒ 0.5x = 22,500

⇒ x = 22,500 ÷ 0.5 = 45,000

∴ The correct answer is ₹45,000.

Additional Information

Simple Interest Concept

Simple interest is calculated only on the principal amount. SI = P×R×T/100, where P is Principal, R is Rate per annum, and T is Time in years.

Amount Calculation

The total Amount (A) after T years is the sum of Principal and Interest: A = P + SI = P(1 + RT/100).

Effective Rate of Interest

For simple interest, the effective rate for the entire duration is simply (R × T)%. This allows for direct percentage-based comparisons between different investment scenarios.

General solution:

 

Total number of trousers and shirts sold in all the shops = 6950

(1200 + 50x + 40x + 50 + (2x + 10)/100 ×  2000 + 1600) = 6950

(1200 + 200 + 50 + 1600 + 130x ) = 6950

130x = 3900

x = 30

 

Shop A:

Total number of shirts and trousers sold = 1200

Number of trousers sold = 1200 ×  (70 - 30)/100 = 480

Number of shirts sold = (1200 - 480) = 720

 

Shop B:

Total number of shirts and trousers sold = 50 ×  30 = 1500

Number of trousers sold = 1500 ×  (30 + 30)/100 = 900

Number of shirts sold = (1500 - 900) = 600

 

Shop C:

Total number of shirts and trousers sold = (40 ×  30 + 50) = 1250

Number of trousers sold = 1250 ×  (2 ×  30 + 20)/100 = 1000

Number of shirts sold = (1250 - 1000) = 250

 

Shop D:

Total number of shirts and trousers sold = (2x + 10)% of 2000 = (2 ×  30 + 10) % of 2000 = 1400

Number of trousers sold = 1400 ×  (71.42/100) = 1000 (approx)

Number of shirts sold = (1400 - 1000) = 400

 

Shop E:

Total number of shirts and trousers sold = 1600

Number of trousers sold = 1600 ×  30/100 = 480

Number of shirts sold = (1600 - 480) = 1120

 

 

Solution:

Number of trousers sold in shop D = 1000

Number of trousers sold in shop E = 480

Total shirts sold in all the shops A, B, C, D and E = (720 + 600 + 250 + 400 + 1120) = 3090

Required percentage = (1480)/3090 ×  100 = 47.89% ~ 48%

General solution:

 

Total number of trousers and shirts sold in all the shops = 6950

(1200 + 50x + 40x + 50 + (2x + 10)/100 ×  2000 + 1600) = 6950

(1200 + 200 + 50 + 1600 + 130x ) = 6950

130x = 3900

x = 30

 

Shop A:

Total number of shirts and trousers sold = 1200

Number of trousers sold = 1200 ×  (70 - 30)/100 = 480

Number of shirts sold = (1200 - 480) = 720

 

Shop B:

Total number of shirts and trousers sold = 50 ×  30 = 1500

Number of trousers sold = 1500 ×  (30 + 30)/100 = 900

Number of shirts sold = (1500 - 900) = 600

 

Shop C:

Total number of shirts and trousers sold = (40 ×  30 + 50) = 1250

Number of trousers sold = 1250 ×  (2 ×  30 + 20)/100 = 1000

Number of shirts sold = (1250 - 1000) = 250

 

Shop D:

Total number of shirts and trousers sold = (2x + 10)% of 2000 = (2 ×  30 + 10) % of 2000 = 1400

Number of trousers sold = 1400 ×  (71.42/100) = 1000

Number of shirts sold = (1400 - 1000) = 400

 

Shop E:

Total number of shirts and trousers sold = 1600

Number of trousers sold = 1600 ×  30/100 = 480

Number of shirts sold = (1600 - 480) = 1120

 

 

Solution:

Number of cotton trousers sold in shop C =  1000 ×  (20/100) = 200

Number of cotton trousers sold in shop D =  1000 ×  (30/100) = 300

Number of fabric shirts sold in the shop C = 250 ×  (60/100) = 150

Number of fabric shirts sold in the shop D = 400 ×  (70/100) = 280

Required sum = (200 + 300 + 150 + 280) = 930

General solution:

 

Total number of trousers and shirts sold in all the shops = 6950

(1200 + 50x + 40x + 50 + (2x + 10)/100 ×  2000 + 1600) = 6950

(1200 + 200 + 50 + 1600 + 130x ) = 6950

130x = 3900

x = 30

 

Shop A:

Total number of shirts and trousers sold = 1200

Number of trousers sold = 1200 ×  (70 - 30)/100 = 480

Number of shirts sold = (1200 - 480) = 720

 

Shop B:

Total number of shirts and trousers sold = 50 ×  30 = 1500

Number of trousers sold = 1500 ×  (30 + 30)/100 = 900

Number of shirts sold = (1500 - 900) = 600

 

Shop C:

Total number of shirts and trousers sold = (40 ×  30 + 50) = 1250

Number of trousers sold = 1250 ×  (2 ×  30 + 20)/100 = 1000

Number of shirts sold = (1250 - 1000) = 250

 

Shop D:

Total number of shirts and trousers sold = (2x + 10)% of 2000 = (2 ×  30 + 10) % of 2000 = 1400

Number of trousers sold = 1400 ×  (71.42/100) = 1000

Number of shirts sold = (1400 - 1000) = 400

 

Shop E:

Total number of shirts and trousers sold = 1600

Number of trousers sold = 1600 ×  30/100 = 480

Number of shirts sold = (1600 - 480) = 1120

 

 

Solution:

Number of trousers sold in shop D = 1000

Number of trousers sold in shop E = 480

Number of trouser sold after 20% increase in shop D = 1000 ×  120/100 = 1200

Number of trouser sold after 25% increase in shop E = 480 ×  125/100 = 600

Number of shirts sold in shop D = 400

Number of shirts sold in shop E = 1120

Number of trouser sold after 50% increase in shop D = 400 ×  (150/100) = 600

Number of trouser sold after 25% increase in shop E = 1120 ×  (125/100) = 1400

Required ratio = (1200 + 600): (600 + 1400) = 1800: 2000 = 9: 10

General solution:

 

Total number of trousers and shirts sold in all the shops = 6950

(1200 + 50x + 40x + 50 + (2x + 10)/100 ×  2000 + 1600) = 6950

(1200 + 200 + 50 + 1600 + 130x ) = 6950

130x = 3900

x = 30

 

Shop A:

Total number of shirts and trousers sold = 1200

Number of trousers sold = 1200 ×  (70 - 30)/100 = 480

Number of shirts sold = (1200 - 480) = 720

 

Shop B:

Total number of shirts and trousers sold = 50 ×  30 = 1500

Number of trousers sold = 1500 ×  (30 + 30)/100 = 900

Number of shirts sold = (1500 - 900) = 600

 

Shop C:

Total number of shirts and trousers sold = (40 ×  30 + 50) = 1250

Number of trousers sold = 1250 ×  (2 ×  30 + 20)/100 = 1000

Number of shirts sold = (1250 - 1000) = 250

 

Shop D:

Total number of shirts and trousers sold = (2x + 10)% of 2000 = (2 ×  30 + 10) % of 2000 = 1400

Number of trousers sold = 1400 ×  (71.42/100) = 1000

Number of shirts sold = (1400 - 1000) = 400

 

Shop E:

Total number of shirts and trousers sold = 1600

Number of trousers sold = 1600 ×  30/100 = 480

Number of shirts sold = (1600 - 480) = 1120

 

 

Solution:

Total number of trousers sold in shop B = 900

Total number of shirts sold in shop B = 600

a/100 ×  900 ×  120 + 2a/100 ×  600 ×  180 = 97200

1080a + 2160a = 97200

97200/3240 = a

a = 30

General solution:

 

Total number of trousers and shirts sold in all the shops = 6950

(1200 + 50x + 40x + 50 + (2x + 10)/100 ×  2000 + 1600) = 6950

(1200 + 200 + 50 + 1600 + 130x ) = 6950

130x = 3900

x = 30

 

Shop A:

Total number of shirts and trousers sold = 1200

Number of trousers sold = 1200 ×  (70 - 30)/100 = 480

Number of shirts sold = (1200 - 480) = 720

 

Shop B:

Total number of shirts and trousers sold = 50 ×  30 = 1500

Number of trousers sold = 1500 ×  (30 + 30)/100 = 900

Number of shirts sold = (1500 - 900) = 600

 

Shop C:

Total number of shirts and trousers sold = (40 ×  30 + 50) = 1250

Number of trousers sold = 1250 ×  (2 ×  30 + 20)/100 = 1000

Number of shirts sold = (1250 - 1000) = 250

 

Shop D:

Total number of shirts and trousers sold = (2x + 10)% of 2000 = (2 ×  30 + 10) % of 2000 = 1400

Number of trousers sold = 1400 ×  (71.42/100) = 1000

Number of shirts sold = (1400 - 1000) = 400

 

Shop E:

Total number of shirts and trousers sold = 1600

Number of trousers sold = 1600 ×  30/100 = 480

Number of shirts sold = (1600 - 480) = 1120

 

 

Solution:

Number of trousers sold in shop A = 480

Number of trousers sold in shop A at discount = 480/3 = 160

Number of trousers sold in shop A at marked price = (480 - 160) = 320

Number of branded trousers sold at marked price in shop A = 320/8 = 40

Number of shirts sold in shop A = 720

Number of shirts sold in shop A at discount = 720/4 = 180

Number of shirts sold in shop A at marked price = (720 - 180) = 540

Number of branded shirts sold at marked price in shop A = 540/3 = 180

Required total = (40 + 180) = 220

Shortcut Trick

For 2 years, Simple Interest (SI) = 2x% and Compound Interest (CI) = 2r + r²/100 where r = (x − 2).

Equating interest rates: 2x = 2(x − 2) + (x − 2)²/100 ⇒ 4 = (x − 2)²/100.

√400 = x − 2 ⇒ 20 = x − 2 ⇒ x = 22.

New rate = x − 7 = 15%. SI for 5 years = 15% × 5 = 75%.

Amount = Principal × (100 + 75)% = 3000 × 1.75 = ₹ 5250.

∴ The correct answer is ₹ 5250.

Alternate Method

Given: Principal (P) for both cases is same. Time (T) = 2 years. SI rate = x%. CI rate = (x − 2)%.

Formula Used: SI = (P × R × T)/100; CI = P[(1 + R/100)^T − 1]

⇒ Interest from SI = (P × x × 2) / 100 = 2Px / 100

⇒ Interest from CI = P[(1 + (x − 2)/100)² − 1]

⇒ 2x/100 = [1 + (x − 2)/100]² − 1

⇒ 2x/100 + 1 = 1 + 2(x − 2)/100 + ((x − 2)/100)²

⇒ 2x/100 = 2x/100 − 4/100 + (x − 2)²/10000

⇒ 4/100 = (x − 2)² / 10000 ⇒ (x − 2)² = 400

⇒ x − 2 = 20 ⇒ x = 22

⇒ New principal = ₹ 3000, New rate = 22 − 7 = 15%, Time = 5 years

⇒ SI = (3000 × 15 × 5) / 100 = ₹ 2250

⇒ Amount = 3000 + 2250 = ₹ 5250

∴ The correct answer is ₹ 5250.

Additional Information

Effective rate of Compound Interest

For 2 years, the effective CI rate is given by the formula R_eff = 2R + R²/100 %.

Simple Interest Amount

The final amount under SI is A = P(1 + RT/100), where R is the annual rate and T is time in years.

Difference between CI and SI

For a period of 2 years at the same rate R, the difference is CI − SI = P(R/100)².

Shortcut Trick

Profit Ratio = (Capital × Time) ratio.

Ratio of P : Q : R Capitals = 16000 : 20000 : 24000 = 4 : 5 : 6.

Ratio of Time = 12 : (12 − x) : (12 − x).

Profit Ratio = (4 × 12) : 5(12 − x) : 6(12 − x) = 48 : 5(12 − x) : 6(12 − x).

Given Profit Ratio = 48 : 35 : 42.

Comparing Q's share: 5(12 − x) = 35 ⇒ 12 − x = 7 ⇒ x = 5.

∴ The correct answer is 5.

Alternate Method

Given: P's investment = Rs. 16,000 for 12 months; Q's investment = Rs. 20,000 for (12 − x) months; R's investment = Rs. 24,000 for (12 − x) months.
Formula: Profit Share = Investment × Time Period

⇒ Profit of P = 16,000 × 12 = 192,000.
⇒ Profit of Q = 20,000 × (12 − x).
⇒ Ratio P : Q = 192,000 : 20,000(12 − x) = 48 : 35.
⇒ 192,000 / [20,000(12 − x)] = 48 / 35.
⇒ 192 / [20(12 − x)] = 48 / 35.
⇒ 4 / (12 − x) = 4 / 7 (after dividing 192 by 48).
⇒ 12 − x = 7.
⇒ x = 12 − 7 = 5.

∴ The correct answer is 5.

Additional Information

Partnership Basics

In a partnership, the profit is distributed in the ratio of the product of Investment and Time Period.

Ratio Conversion

If Profit Ratio and Investment Ratio are given, Time Ratio = (Profit Ratio ÷ Investment Ratio).

Shortcut Trick

Speed of Steamer (u) = 24 km ÷ (50/60) h = 28.8 km/h.

Using Difference in Time formula: [D × (2v)] ÷ (u² − v²) = ΔT.

[22.5 × 2v] ÷ (28.8² − v²) = 25/60.

By testing Option (2): v = 7.2 km/h ⇒ (45 × 7.2) ÷ (829.44 − 51.84) = 324 ÷ 777.6 = 5/12 h = 25 minutes.

∴ The correct answer is 7.2 km/h.

Alternate Method

Given:

Distance (D) = 22.5 km

Speed of steamer in still water (u) = 24 ÷ (50/60) = 24 × 6/5 = 28.8 km/h

Time difference (ΔT) = 25/60 = 5/12 hours

Formula Used:

Time = Distance ÷ Speed

Upstream Speed = u − v | Downstream Speed = u + v

Calculations:

⇒ [22.5 / (28.8 − v)] − [22.5 / (28.8 + v)] = 5/12

⇒ 22.5 × [(28.8 + v − 28.8 + v) / (28.8² − v²)] = 5/12

⇒ 22.5 × [2v / (829.44 − v²)] = 5/12

⇒ 45v / (829.44 − v²) = 5/12

⇒ 9v × 12 = 829.44 − v²

⇒ v² + 108v − 829.44 = 0

⇒ Solving quadratic equation or verification by options:

⇒ If v = 7.2, then 7.2² + 108(7.2) = 51.84 + 777.6 = 829.44

∴ The correct answer is 7.2 km/h.

Additional Information

Relative Speed in Water

Downstream speed is the sum (u + v) and Upstream speed is the difference (u − v) where u is boat speed and v is stream speed.

Average Speed for Round Trip

The average speed for a round trip in a river is [(u² − v²) / u] which is always less than the speed in still water.

Time Difference Formula

Difference between Upstream and Downstream time ΔT = [2 × Distance × Stream Speed] ÷ [u² − v²].

Shortcut Trick

Efficiency A : B = 2 : 1 → Days A : B = 1 : 2. Let days be x and 2x.

Days C : D = 2 : 3. Combined efficiency (1/x + 1/2x) = (1/2y + 1/3y) where C = 2y, D = 3y.

3/2x = 5/6y ⇒ 18y = 10x ⇒ y = 5x/9.

Given B − C = 16 ⇒ 2x − 2y = 16 ⇒ 2x − 10x/9 = 16 ⇒ 8x/9 = 16 ⇒ x = 18.

∴ The correct answer is 18 days.

Alternate Method

Given: Efficiency of A is twice of B. Time taken by (A+B) = Time taken by (C+D). Ratio of days C : D = 2 : 3. B − C = 16 days.

⇒ Time taken by (A+B) = 2x ÷ 3.

⇒ For C and D, let days be 2y and 3y. Time taken by (C+D) = (2y × 3y) ÷ (2y + 3y) = 6y/5.

⇒ According to question: 2x/3 = 6y/5 ⇒ 10x = 18y ⇒ 5x = 9y ⇒ y = 5x/9.

⇒ Difference in days B − C = 16 ⇒ 2x − 2y = 16 ⇒ x − y = 8.

⇒ Substitute y: x − 5x/9 = 8 ⇒ 4x/9 = 8 ⇒ 4x = 72 ⇒ x = 18.

∴ The correct answer is 18 days.

Additional Information

Efficiency and Time Relationship

Efficiency is inversely proportional to the time taken to complete a work. If efficiency ratio is a : b, then time ratio is b : a.

Combined Work Formula

If two people take X and Y days respectively, they together take (X × Y) ÷ (X + Y) days to complete the work.

General solution:

 

Monday:

Number of (males + females) visiting park = 1500 ×  (18/100) = 270

Number of males visiting parks = 800 ×  (15/100) = 120

Number of females visiting parks = (270 - 120) = 150

 

Tuesday:

Number of (males + females) visiting park = 1500 ×  (22/100) = 330

Number of males visiting parks = 800 ×  (25/100) = 200

Number of females visiting parks = (330 - 200) = 130

 

Wednesday:

Number of (males + females) visiting park = 1500 ×  (24/100) = 360

Number of males visiting parks = 800 ×  (20/100) = 160

Number of females visiting parks = (360 - 160) = 200

 

Thursday:

Number of (males + females) visiting park = 1500 ×  (16/100) = 240

Number of males visiting parks = 800 ×  (17.5/100) = 140

Number of females visiting parks = (240 - 140) = 100

 

Friday:

Number of (males + females) visiting park = 1500 ×  (20/100) = 300

Number of males visiting parks = 800 ×  (22.5/100) = 180

Number of females visiting parks = (300 - 180) = 120

 

Solution:

Number of males visited park in FN on Monday = 120 ×  3/5 = 72

Number of males visited park in AN on Monday = 120 - 72 = 48

Number of males having four wheelers AN on Monday = 48/2 = 24

Total having two wheelers visiting on Monday = (72 + 24) = 96

General solution:

 

Monday:

Number of (males + females) visiting park = 1500 ×  (18/100) = 270

Number of males visiting parks = 800 ×  (15/100) = 120

Number of females visiting parks = (270 - 120) = 150

 

Tuesday:

Number of (males + females) visiting park = 1500 ×  (22/100) = 330

Number of males visiting parks = 800 ×  (25/100) = 200

Number of females visiting parks = (330 - 200) = 130

 

Wednesday:

Number of (males + females) visiting park = 1500 ×  (24/100) = 360

Number of males visiting parks = 800 ×  (20/100) = 160

Number of females visiting parks = (360 - 160) = 200

 

Thursday:

Number of (males + females) visiting park = 1500 ×  (16/100) = 240

Number of males visiting parks = 800 ×  (17.5/100) = 140

Number of females visiting parks = (240 - 140) = 100

 

Friday:

Number of (males + females) visiting park = 1500 ×  (20/100) = 300

Number of males visiting parks = 800 ×  (22.5/100) = 180

Number of females visiting parks = (300 - 180) = 120

 

Solution:

Number of females visited park on Monday = 150

Number of females visited park on Saturday = 150 ×  (120/100) = 180

Number of married females visiting park on saturday = 180 ×  (3/5) = 108

Number of unmarried females = (180 - 108) = 72

Required percentage = 72/(700) ×  100 = 10.28%

General solution:

 

Monday:

Number of (males + females) visiting park = 1500 ×  (18/100) = 270

Number of males visiting parks = 800 ×  (15/100) = 120

Number of females visiting parks = (270 - 120) = 150

 

Tuesday:

Number of (males + females) visiting park = 1500 ×  (22/100) = 330

Number of males visiting parks = 800 ×  (25/100) = 200

Number of females visiting parks = (330 - 200) = 130

 

Wednesday:

Number of (males + females) visiting park = 1500 ×  (24/100) = 360

Number of males visiting parks = 800 ×  (20/100) = 160

Number of females visiting parks = (360 - 160) = 200

 

Thursday:

Number of (males + females) visiting park = 1500 ×  (16/100) = 240

Number of males visiting parks = 800 ×  (17.5/100) = 140

Number of females visiting parks = (240 - 140) = 100

 

Friday:

Number of (males + females) visiting park = 1500 ×  (20/100) = 300

Number of males visiting parks = 800 ×  (22.5/100) = 180

Number of females visiting parks = (300 - 180) = 120

 

 

Solution:

Number of males visited park on Tuesday = 200

Number of males visited park on Thursday = 140

Number of females visited park on Monday = 150

Number of females visited park on Wednesday = 200

Required difference = (350 - 340) = 10

General solution:

 

Monday:

Number of (males + females) visiting park = 1500 ×  (18/100) = 270

Number of males visiting parks = 800 ×  (15/100) = 120

Number of females visiting parks = (270 - 120) = 150

 

Tuesday:

Number of (males + females) visiting park = 1500 ×  (22/100) = 330

Number of males visiting parks = 800 ×  (25/100) = 200

Number of females visiting parks = (330 - 200) = 130

 

Wednesday:

Number of (males + females) visiting park = 1500 ×  (24/100) = 360

Number of males visiting parks = 800 ×  (20/100) = 160

Number of females visiting parks = (360 - 160) = 200

 

Thursday:

Number of (males + females) visiting park = 1500 ×  (16/100) = 240

Number of males visiting parks = 800 ×  (17.5/100) = 140

Number of females visiting parks = (240 - 140) = 100

 

Friday:

Number of (males + females) visiting park = 1500 ×  (20/100) = 300

Number of males visiting parks = 800 ×  (22.5/100) = 180

Number of females visiting parks = (300 - 180) = 120

 

Solution:

Number of males visiting park below 30 = 120/3 = 40

Number of males visiting park above 30 = (120 - 40) = 80

Number of males visiting park below 30 = 180 ×  2/3 = 120 

Number of males visiting park above 30 = (180 - 120) = 60

Number of females visiting above = (250 - 140) = 110

solution:

 

Monday:

Number of (males + females) visiting park = 1500 ×  (18/100) = 270

Number of males visiting parks = 800 ×  (15/100) = 120

Number of females visiting parks = (270 - 120) = 150

 

Tuesday:

Number of (males + females) visiting park = 1500 ×  (22/100) = 330

Number of males visiting parks = 800 ×  (25/100) = 200

Number of females visiting parks = (330 - 200) = 130

 

Wednesday:

Number of (males + females) visiting park = 1500 ×  (24/100) = 360

Number of males visiting parks = 800 ×  (20/100) = 160

Number of females visiting parks = (360 - 160) = 200

 

Thursday:

Number of (males + females) visiting park = 1500 ×  (16/100) = 240

Number of males visiting parks = 800 ×  (17.5/100) = 140

Number of females visiting parks = (240 - 140) = 100

 

Friday:

Number of (males + females) visiting park = 1500 ×  (20/100) = 300

Number of males visiting parks = 800 ×  (22.5/100) = 180

Number of females visiting parks = (300 - 180) = 120

 

Solution:

Number of males visiting park on Tuesday = 200

Number of males visiting park on Wednesday = 160

Number of females visiting park on Thursday = 100

Number of females visiting park on Friday = 120

Required ratio = (200 + 160): (100 + 120) = 360: 220 = 18: 11