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Given:

Visitors at Shop A = 22

Visitors at Shop B = 26

Calculation:

Increase = 26 − 22 = 4

Percentage increase = (Increase ÷ Original) × 100 = (4 ÷ 22) × 100

Percentage increase = 400 ÷ 22 = 200 ÷ 11 ≈ 18.18%

Thus, the number of visitors increased by approximately 18.18% from Shop A to Shop B.

Given:

Required ratio = Visitors at C : Visitors at E = 28 : 34 ⇒ 14 : 17

Hence, the correct answer is 14 : 17.

Given:

Total visitors = 22 + 26 + 28 + 30 + 34 = 140

Number of shops = 5

Average = Total visitors ÷ Number of shops = 140 ÷ 5 = 28

Thus, the average number of visitors per shop on Sunday = 28

Given:

Change:

Shop D visitors reduced by 20%.

New D = 30 × (1 − 0.20) = 30 × 0.80 = 24

Visitors at B = 26

Difference = |B − New D| = |26 − 24| = 2

Thus, the difference would be 2 visitors (Shop B has 2 more than Shop D).

Shortcut Trick

Total pens = 6 Blue + 4 Black = 10 pens.

Alternate colors with replacement: (Blue × Black) + (Black × Blue).

P(Alternate) = (6/10 × 4/10) + (4/10 × 6/10) = 24/100 + 24/100 = 48/100.

Simplifying 48/100 → 12/25.

∴ The correct answer is 12/25.

Alternate Method

Given:

Number of Blue pens = 6

Number of Black pens = 4

Total pens = 10

Formula Used:

Probability P(E) = (Number of favorable outcomes) ÷ (Total number of outcomes)

For with replacement, the total outcomes remain constant for each draw.

Calculations:

⇒ Case 1: First pen is Blue and second is Black.

⇒ P(Blue) × P(Black) = (6/10) × (4/10) = 24/100

⇒ Case 2: First pen is Black and second is Blue.

⇒ P(Black) × P(Blue) = (4/10) × (6/10) = 24/100

⇒ Total Probability = 24/100 + 24/100 = 48/100

⇒ Reducing the fraction: 48/100 = 12/25

∴ The correct answer is 12/25.

Additional Information

With Replacement vs Without Replacement

In with replacement, the sample space remains constant (10 × 10). In without replacement, the sample space reduces (10 × 9).

Independent Events

Drawing with replacement makes the events independent, meaning the outcome of the first draw does not affect the second.

Sum of Probabilities

The sum of all possible mutually exclusive outcomes in an experiment is always 1.

Shortcut Trick

Efficiency ratio of Pipe A to Pipe B = 1 : 4 (since A is 4 times slower).

Time ratio is the inverse of efficiency = 4 : 1.

Difference in time ratio parts = 4 − 1 = 3 units.

Given 3 units = 18 minutes ⇒ 1 unit = 6 minutes.

Time taken by Pipe A = 4 units = 4 × 6 = 24 minutes.

∴ The correct answer is 24 minutes.

Alternate Method

Given:

Efficiency of Pipe B = 4 × Efficiency of Pipe A

Let the time taken by Pipe B be T minutes.

Then the time taken by Pipe A = T + 18 minutes.

Formula Used:

Efficiency × Time = Constant (Total Work)

Calculations:

⇒ Efficiency_A × Time_A = Efficiency_B × Time_B

⇒ 1 × (T + 18) = 4 × T

⇒ T + 18 = 4T

⇒ 3T = 18

⇒ T = 6 minutes

⇒ Time taken by Pipe A = T + 18 = 6 + 18 = 24 minutes.

∴ The correct answer is 24 minutes.

Additional Information

Efficiency and Time Relationship

Efficiency is inversely proportional to time. If Pipe A is 'n' times as fast as Pipe B, then Pipe A takes (1/n) of the time taken by B.

Pipes and Cisterns Concept

Total capacity = LCM of time taken by individual pipes or Efficiency × Time taken.

Shortcut Trick

Ratio of ages of Ram, Shyam, and Neel = 4 : 5 : 7

Given, Neel's age (7 units) = 49 years ⇒ 1 unit = 7 years

Total units for present age = 4 + 5 + 7 = 16 units

Total present age = 16 × 7 = 112 years

Total age after 2 years = 112 + (3 × 2) = 118 years

∴ The correct answer is 118 years.

Alternate Method

Given: Ratio of ages = 4 : 5 : 7, Neel's age = 49 years.

Calculations:

⇒ Let the ages be 4x, 5x, and 7x.

⇒ 7x = 49

⇒ x = 49 ÷ 7 = 7

⇒ Ram's age = 4 × 7 = 28 years

⇒ Shyam's age = 5 × 7 = 35 years

⇒ Sum of present ages = 28 + 35 + 49 = 112 years

⇒ Sum of ages after 2 years = 112 + (2 + 2 + 2) = 118 years

∴ The correct answer is 118 years.

Additional Information

Ratio and Proportion

If quantities are in ratio a:b:c, then actual values can be taken as ax, bx, and cx where x is a common multiplier.

Age Problems Rule

When calculating the sum of ages after 'n' years for 'k' people, add (n × k) to the current total sum.

Total score of B = 155 + 92 + 98 = 345

Number of games = 3

Average score of B = Total score ÷ Number of games = 345 ÷ 3 = 115

Hence, the correct answer is 115.

Score of B in Football = 92

Score of A in Cricket = 120

Step 2: Ratio = B's Football : A's Cricket = 92 : 120

Simplify ratio → divide both by 4 → 23 : 30

Hence, the correct answer is 23 : 30.

Sportsperson A's scores:

Football = 85

Hockey = 105

Percentage Increase = ((New Value − Old Value) ÷ Old Value) × 100

Substitute values:

= ((105 − 85) ÷ 85) × 100

= (20 ÷ 85) × 100

= 23.53% (approx)

Hence, the correct answer is 23.53%.