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Given:

Percentage values: 25%, 66.67%, 75%, 80%

Solution:

Let "x" be the unknown number.

25% of 66.67% of 75% of 80% of x = 6347

⇒ [(25/100) × (66.67/100) × (75/100) × (80/100)] × x = 6347

⇒ [(1/4) × (2/3) × (3/4) × (4/5] × x = 6347

⇒ 1/10 × x = 6347

⇒ x = 63470

40% of the number x = (40/100) × 63470

⇒ 2/5 × 63470

⇒ 25388

Therefore, 40% of the unknown number is 25388.

Shortcut Trick

Total Distance = 15 + 20 = 35 km

Total Time = 3 + 2 = 5 hours

Average Speed = Total Distance ÷ Total Time = 35 ÷ 5 = 7 km/h

∴ The correct answer is 7 km/h.

Alternate Method

Given:

Distance covered in 1^st part = 15 km

Time taken for 1^st part = 3 hours

Distance covered in 2^nd part = 20 km

Time taken for 2^nd part = 2 hours

Total Distance = 35 km

15 km 20 km

3 hours 2 hours

Total Time = 5 hours

Formula Used:

Average Speed = Total Distance ÷ Total Time

Calculations:

⇒ Total Distance = 15 km + 20 km = 35 km

⇒ Total Time = 3 hours + 2 hours = 5 hours

⇒ Average Speed = 35 ÷ 5 = 7 km/h

∴ The correct answer is 7 km/h.

Additional Information

Average Speed for Equal Distances

If two equal distances are covered at speeds x and y, Average Speed = 2xy ÷ (x + y).

Average Speed for Equal Time

If a journey is covered at speeds x and y for equal time intervals, Average Speed = (x + y) ÷ 2.

Relative Speed

When moving in the same direction, relative speed = (x − y). When moving in opposite directions, relative speed = (x + y).

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

33 of 6 - 39 + 12 ÷ 6

= 198 - 39 + 12 ÷ 6

= 198 - 39 + 2

= 200 - 39

= 161

∴ The value of ? is 161.

Given:

Ratio of incomes of A and B = 3 : 4

Ratio of expenditure of A and B = 9 : 5

The income of A = 3 × The expenditure of B

Formula used:

Savings = Income – Expenditure

Income = Savings + Expenditure

Expenditure = Income – Savings

Calculation:

Let the income of A and B be 3x and 4x respectively

And the expenses of A and B be 9y and 5y respectively

The income of A = 3 × The expenditure of B

⇒ 3x = 3 × (5y)

⇒ 3x = 15y

⇒ x = 5y

The income of A = 3x = (3 × 5y) = 15y

The income of B = 4x = (4 × 5y) = 20y

Savings of A = (15y – 9y)

⇒ 6y

Savings of B = (20y – 5y)

⇒ 15y

The ratio of savings of A and B = (6y : 15y)

⇒ 2 : 5

∴ Required ratio is 2 : 5

Given:

2145 : x :: 3003 : 42

Formula:

If a : b :: c : d ,then

a/b = c/d

Calculation:

2145 : x :: 3003 : 42

⇒ 2145/x = 3003/42

⇒ x = 2145 × (42/3003)

∴ x = 30

Now,

x : 2508 :: y : 11704

⇒ 30 : 2508 :: y : 11704

⇒ 30/2508 = y/11704

⇒ y = (30/2508) × 11704

∴ y = 140

Total no. of teachers = 300

Percentage of teachers between 30 – 60 = 28 + 24 + 15 = 67%

No. of teachers between 30 – 60 = 67% of 300 = 201

∴ Average no. of teachers in 3 age groups = 201/3 = 67

Total no. of teachers = 300

No. of teachers below 30 = 21% of 300 = 63

Male to female ratio of teachers below 30 = 5 ∶ 4

Sum of ratios = 5 + 4 = 9

∴ No. of female teachers below 30 = (4/9) × 63 = 28

Total no. of teachers = 300

No. of teachers belonging to age group 51 – 60 = 15% of 300 = 45

Percentage of male teachers in age group 51 – 60 = 100 – 40 = 60%

∴ No. of male teachers belonging to age group 51 – 60 = 60% of 45 = 27

Percentage of teachers between 30 – 40 = 28%

Percentage of teachers between 41 – 50 = 24%

After one year, the no. of teachers in the two groups will be equal,

⇒ New percentage = (28 + 24)/2 = 26%

∵ After one year, the teachers with current age of 40 years will leave the group 30 – 40 and be grouped in the age group 41 – 50,

Hence, percentage of teachers with current age of 40 years = 28 – 26 = 2%

Total no. of teachers = 300

∴ No. of teachers with current age of 40 years = 2% of 300 = 6

Given:

Length of two train = 275 m and 175 m

Faster train overtake slower train in 54 sec

Speed of the slower train = 40 km/h

Formula used:

Speed = Distance/Time

When two objects moves in same direction

Relative speed = a - b

Where a and b are speed of the objects, a > b

To convert m/s into km/h multiply by 18/5

Calculation:

Total length = 275 + 175 = 450

Let the speed of the faster train be x km/h

Relative speed = x - 40

⇒\(\dfrac{450}{54}\) = x - 40

⇒ \(\dfrac{450}{54} \times \dfrac{18}{5}\) = x - 40

⇒ 30 = x - 40

⇒ x = 70 km/h

∴ The speed of the faster train is 70 km/h