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Given:

The ratio of the present ages of three friends is 3 ∶ 5 ∶ 7.

The sum of their ages was 48 before four years.

Calculation:

Let the current age of three friends be 3x, 5x and 7x respectively.

Again, it is given that four years ago, the sum of their ages was 48.

(3x – 4) + (5x – 4) + (7x – 4) = 48

15x – 12 = 48

⇒ 15x = 60

⇒ x = 60/15 = 4

⇒ 3x = 3 × 4 = 12

⇒ 5x = 5 × 4 = 20

⇒ 7x = 7 × 4 = 28

∴ The present ages of three friends are 12 years, 20 years and 28 years respectively.

Given:

Total amount = 210

Ratio of the coins = 3 : 5 : 6

Concept used:

1 Rs. = 100 paise

Calculation:

Let's assume the number of one-rupee coins = 3a

The number of 50 paise coins = 5a

The number of 25 paise coins = 6a

⇒ (1 x 3a) + (0.5 x 5a) + (0.25 x 6a) = 210

⇒ 3a + 2.5a + 1.5a = 210

⇒ 7a = 210

⇒ a = 210/7

⇒ a = 30

The number of 25 paise coins = 6a

⇒ 6 x 30

⇒ 180

∴ The number of 25 Paise coins in the bag is 180.

Shortcut Trick

Net discount for two rates a and b = a + b − (a × b / 100).

For 12% and 15%: 12 + 15 − (12 × 15 / 100) = 27 − 1.8 = 25.2%.

For 25.2% and 18%: 25.2 + 18 − (25.2 × 18 / 100) = 43.2 − 4.536 = 38.664%.

∴ The correct answer is 38.664%.

Alternate Method

Given: Successive discounts = 12%, 15%, and 18%

Formula: Final Price = MP × (100 − d₁)/100 × (100 − d₂)/100 × (100 − d₃)/100

MP = 100 −12% −15% −18% Net SP = 61.336 Total Discount = 38.664%

⇒ Let Marked Price (MP) = 100 units ⇒ Price after 1^st discount = 100 × (88/100) = 88 units ⇒ Price after 2^nd discount = 88 × (85/100) = 74.8 units ⇒ Price after 3^rd discount = 74.8 × (82/100) = 61.336 units ⇒ Single equivalent discount = MP − Final Price = 100 − 61.336 = 38.664 units ⇒ Discount percentage = (38.664/100) × 100 = 38.664%

∴ The correct answer is 38.664%.

Additional Information

Successive Discount Property

The order in which successive discounts are applied does not change the final selling price. For example, 10% and 20% give the same net result as 20% and 10%.

Effective Discount Formula

For n discounts d₁, d₂, ... d_n, the effective discount is 1 − [(1 − d₁/100)(1 − d₂/100)...(1 − d_n/100)].

Relation between MP and SP

Selling Price (SP) = Marked Price (MP) − Discount. Always calculate discount percentage on the Marked Price (MP).

Given:

The average of 45 data is 150

46 is wrongly written as 91

Concept used:

Average = Sum of total observations/Total number of observations

Calculation:

The total sum of all 45 number = 150 × 45 = 6750

Now, 46 is wrongly written as 91

The correct sum of data = 6750 – (91 – 46) = 6705

Then, Correct average of the data = 6705/45 = 149

∴ The correct average is 149

Difference between wrong and actual numbers = 91 – 46 = 45

As the actual number is less than the wrong number

So the average decreased by 45/45 = 1

The correct average = 150 – 1 = 149

∴ The correct average is 149

Given:

Speed = 108 km/h

Time = 3 h

Formula:

Distance = Speed × Time

Solution:

The distance covered by the car is 108 × 3 = 324 km.

If the speed is reduced by 27 km/h, the new speed is 108 - 27 = 81 km/h.

The new time taken by the car to cover the same distance is 324/81 = 4 h.

Therefore, the time taken by the car to cover the same distance will be 4 h.

The answer is 4 h.

Given:

A = Rs. 1440, T = 4 years, R = 5%

Formula Used:

A = P + (P × R × T)/100

Calculation:

According to the question,

1440 = P + [(P × 5 × 4)/100]

⇒ 1440 = P + P/5

⇒ 6P/5 = 1440

⇒ P = 1440 × 5/6

⇒ P = 1200

Shortcut Trick

Let the sum be 100%

Simple interest for 4 years = 4 × 5 = 20%

⇒ 120% = 1440

⇒ 100% = 1200

Calculation:

Total population of town C = 8000

Number of people below poverty line = 20% of 8000 = (20 / 100) × 8000 = 1600

Number of people above poverty line = 8000 - 1600 = 6400

For people above the poverty line in town C, the ratio of males to females is 5:3.

The total parts representing the population above the poverty line = 6400

Since the ratio is 5 males : 3 females, we calculate the number of females as:

Number of parts for females = 3 × (Total people above poverty line / Total parts)

⇒ 3 × (6400 / 8) = 3 × 800 = 2400

Hence, the number of females above the poverty line in town C is 2400.

Given

Total marks are 1800.

Calculation

The marks in social science = 72°

⇒ 360° → 1800

⇒ 72° → (1800 × 72)/360

⇒ 72° → 360

The marks in social science is 360.

Concept used:

Range = Maximum value - Minimum value 

Average = sum of observations/Number of observations

Calculation:

According to the question

The range of temperatures of the five cities = Maximum value - Minimum value 

⇒ (41 - 30) = 11

Now, the average of temperatures of the five cities = (30 + 34 + 40 + 41 + 35)/5

⇒ (180/5) = 36

Now, the difference between the range of temperatures of the five cities and the average of temperatures of the five cities

⇒ (36 - 11) = 25 degree Celsius

∴ The required difference is 25 degree Celsius.

The logic follows here is:

In 202 - 40

⇒ 20 × 2 

⇒ 40

In 305 - 150

⇒ 30 × 5

⇒ 150

In 120 - 0

⇒ 12 × 0 

⇒ 0

Now, check the options one by one,

1. In 132 - 26

⇒ 13 × 2

⇒ 26

2) In 152 - 31

⇒ 15 × 2

⇒ 30 

3. In 241 - 24

⇒ 24 × 1

⇒ 24

4. In 223 - 66

⇒ 22 × 3

⇒ 66

Hence, the correct answer is 152 - 31.