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Given:

**(**3/4)th distance is travelled with speed 30 km/h.

Formula used:

Speed = Distance/Time

Calculation:

Let the total distance be x km.

According to question

30 × 2 = 3x/4

⇒ x = 80 km 

∴ The total distance travelled by Mr. A is 80 km.

Calculation:

Value of 360° = 100%

So Q is (75/110) × 100 = 68.18 percent of candidates in S

∴ The correct option is 3

Given:

The ratio of the father's age to the son’s age is 3 ∶ 1

The product of their ages is 147.

Calculation:

Let the age of father is = 3x

The age of son is = x

According to question, 

3x × x = 147

3x² = 147

x² = 147/3 = 49

x = √49

x = 7

So, father's age is = 3 × 7 = 21 years

Son's age = 7 years

The age of father after 5 years = 21 + 5 = 26 years

The age of son after 5 years = 7 + 5 = 12 years

Ratio = 26 ∶ 12 = 13 ∶ 6

Hence, the correct answer is "13 : 6".

Shortcut TrickThe average weight of n members of a family is w kg, If one family member whose weight is W kg leaves the group,

then the new average weight of remaining family members = y

So,

W = {n × (w - y)} + y

According to the question,

⇒ 40 = 6 × (25 - y) + y

⇒ 40 = 150 - 6y + y

⇒ 40 = 150 - 5y

⇒ 5y = 150 - 40

⇒ 5y = 110

⇒ y = 22 kg

Therefore, '22 kg' is the required answer.

Alternate Method

Given:

The average weight of 6 members of a family is 25 kg,

If one family member whose weight is 40 kg leaves the group,

Formula used:

Sum of n numbers = (Average of n numbers) × n

Calculation:

The average weight of 6 members of a family = 25 kg

The total weight of all 6 members = 25 × 6 = 150 kg

The weight of the member who leaves the group = 40 kg

The remaining weight of remaining 5 members = 150 - 40 = 110 kg

The new average = \(\frac{110}{5}\) = 22 kg

Therefore, '22 kg' is the required answer.

Given:

Average age of 14 friends = 14 years

Calculation:

The average age of 14 friends is 14 years.

The sum of the ages of all 14 friends = 14 ×  14 = 196 years.

Now, if the age of the 15^th friend is added, the average remains the same. 

Let's denote the age of the 15^th friend as "x" years.

The sum of ages of all 15 friends (including the 15^th friend) would be 196 years + x years.

According to the given condition, the average remains the same. The new average is still 14 years.

We can set up an equation using the concept of averages:

(196 + x) / 15 = 14

Simplifying the equation:

196 + x = 14 ×  15

196 + x = 210

x = 210 - 196

x = 14

Therefore, the age of the 15^th friend is 14 years.

∴ Option 3 is the correct answer.

Calculation

The demand for company B = 600

The demand for company C = 2500

= 600/2500 × 100

= 24%

The demand for company B is 24% of the demand for Company C

Given:

The ratio in the coins of 20 P, 25 P and 50P = 7 : 6 : 5

Total amount = Rs. 297

Calculation

As we know that, 20 P = 1/5 Rs. , 25 P = 1/4 Rs. and 50 P = 1/2 Rs.

Bag contains 20 P, so total amount by 20 P coin = (1 ÷ 5) × 7x = 1.40x

Similarly, total amount by 25 P coin = (1 ÷ 4) × 6x = 1.50 x

And, total amount by 50 P coin = (1 ÷ 2) × 5x = 2.50x

According to question,

1.40x + 1.50x + 2.50x = 297

⇒ 5.40x = 297

Then, x = 55

∴ Number of coins of 25 P = 6x

55 × 6 = 330

Given:

Cost price of 12 pens is equal to the selling price of 8 pens.

Formula used:

Profit = selling price - cost price

Profit% = profit/cost price × 100

Calculation:

Let cost price of 1 pen = Rs 1

Cost price of 12 pens = Selling price of 8 pens = Rs 12

Cost price of 8 pens = Rs 8

Profit = Rs (12 - 8) = Rs 4

Profit% = 4/8 × 100

⇒ profit% = 50%

∴ profit% is 50%

Given:

X, Y and Z invested in the ratio 5 ∶ 7 ∶ 8. They invested for 14 months, 8 months and 7 months respectively.

Concept Used:

Share of profit divided in the ratio of investment

Calculation:

Let, investment of X = 5a

Investment of Y = 7a

Investment of Z = 8a

Weighted ratio of investment of X, Y and Z

⇒ 5a × 14 ∶ 7a × 8 ∶ 8a × 7

⇒ 70a ∶ 56a ∶ 56a

⇒ 5 ∶ 4 ∶ 4 

∴ Ratio of share of profit will be 5 : 4 : 4

The logic followed here is:

1^st word is "the item" and 2^nd word is "collection of those items".

According to the given information:

Cup ∶ Crockery → Cup is a type of Crockery.

Similarly

​Sharpener ∶ Stationery → Sharpener is a type of Stationery.

Hence, the correct answer is "​Sharpener ∶ Stationery".