Given:

A thief is spotted by a policeman from a distance of 210 m.

When the policeman starts the chase, the thief also starts running.

The speed of the thief is 25 km/h and that of the policeman is 32 km/h

Concept used:

Distance = speed × time

Calculation:

Relative speed is (32 -25) × 5/18 = 35/18 m/s

Time taken to catch the thief 210 × 18/35 = 108 sec

Distance covered in that time by the thief is,

25 × 5/18 × 108 = 750 m

∴ The correct option is 4

Given:

CP = ₹4,500

Overhead Expenses = 4% of CP

Formula used:

1. Total CP = CP + Overhead Expenses

2. SP = CP × (100 + Profit)/100

Calculation:

Total CP = 4500 + 4% × 4500 = Rs 4680

To get 15% profit

⇒ SP = 4680 × (100 + 15)/100

⇒ SP = 4680 × (115/100)

⇒ SP = 5382

∴ To earn 15% profit SP of vegetables should be ₹5382.

Given:

Anita can do 1/3 of a work in 5 days

Vinita can do 2/5 of work in 10 days

Concept:

In these type of questions, we find the work done in 1 day by each individual and then calculate the total work done in 1 day.

We then divide 1 (total work) by the fraction of work done in 1 day by both.

Calculation:

Anita's 5 days work = 1/3 part

Anita's 1 day work = 1/15 part

Vinita's 10 days work = 2/5 part

Vinita's 1 day work = 1/25 part

Total work done in 1 day by Anita and Vinita = 1/15 + 1/25

= 16/150

= 8/75

∴ Time to complete whole work = 1/(8/75)

= 75/8 days

Now, substitute the value of the respective variable in the required expression.

⇒ (x - 17)²

⇒ (17 - 6√8 - 17)²

⇒ (- 6√8)²

⇒ (36 × 8) = 288

∴ The value of the required expression is 288.

Additional Information

Given data:

Average cost of an apple, orange, and mango = Rs. 36

Average cost of an apple and orange = Rs. 28

Average cost of an orange and mango = Rs. 32

Concept: The average cost of an item is the sum of costs divided by the number of items.

Solution:

⇒ Cost of an apple + orange + mango = 36 x 3 = Rs. 108

⇒ Cost of an apple + orange = 28 x 2 = Rs. 56

⇒ Cost of an orange + mango = 32 x 2 = Rs. 64

⇒ Cost of an orange = (Rs. 56 + Rs. 64 - Rs. 108) = Rs. 12

Hence, the cost of an orange is Rs. 12. The correct answer is 4) Rs. 12.

Given:

A discount of 20%, there is still a gain of 10%.

Formula used:

MP/CP = (100 + profit%)/(100 - discount%)

Calculation:

MP/CP = (100 + profit%)/(100 - discount%)

MP/CP = (110)/(80)

MP/CP = (11)/(8)

According to the question:

11 - 8 = 3

3/8 × 100 = 37.5%

∴ Option 2 is the correct answer.

Given:

P can complete a task in 20 days,

Q in 30 days,

R in 60 days,

P is helped by Q and R every third day.

Concept:

Work done is reciprocal of the time taken. Use the concept of man-days.

Solution:

Total work = LCM(20, 30, 60) = 60 units

Efficiency of P = 60/20 = 3

Efficiency of Q = 60/30 = 2

Efficiency of R = 60/60 = 1

Work done by P in two days = 2 days × 3 = 6 units.

On third day, all three work together, their combined work = 3 + 2 + 1 = 6 units.

Therefore, in every cycle of three days, work done = 6 + 6 = 12 units.

To finish 60 unit of work, days required = 3 × 5 = 15 days.

Hence, it will take 15 days to finish the work.

Given:

Longest diagonal of cube = 11√3 cm

Concept:

For a cube, the longest diagonal is √3 * side. The volume of a cube is given by side³.

Solution:

⇒ Side of cube = Longest diagonal / √3 = (11√3)/√3 = 11 cm

⇒ Volume of cube = Side³ = 11³ = 1331 cm³

Therefore, the volume of the cube is 1331 cm³.

Alternate Method

Formula used: 

(x³ + y³) = (x + y)³ - 3xy(x + y)

Calculation:

1/x + 1/y = 20/9

⇒ (y + x)/xy = 20/9 

⇒ 5/xy = 20/9 

⇒ xy = 9/4              ......(1) 

Now,

(x³ + y³) = 5³ - 3 × (9/4) × 5 (From eq 1 and formula)

⇒ 125 - 135/4

⇒ (500 - 135)/4 = 365/4

∴ The required value is 365/4.