The correct answer is Option 2 i.e. 23.07 km/hr.

Average Speed = Total Distance/Total Time

Distance covered at the speed of 35 km/hr in 30 minutes

Distance = 30 × 35/60 = 17.5 km

Distance covered at the speed of 12 km/hr in 25 minutes

Distance = 12 × 25/60 = 5 km

Distance covered at the speed of 15 km/hr in 10 minutes

Distance = 15 × 10/60 = 2.5 km

Total distance = 17.5 + 5 + 2.5 = 25 km

Total Time (in hours) = (30 + 25 + 10)/60 = 65/60 hours

Average Speed = 25/(65/60) = 25 × 60/65 = 23.076 km/hr

The correct answer is option 3 i.e. 44 years

Suppose the present ages of Tushar, Garima and Saurav are 5x, 7x and 4x respectively.

Given: sum of their ages after 9 years will be 139 years

So,

(5x + 7x + 4x) + 9 × 3 = 139

⇒ 16x = 139 – 27

⇒ 16x = 112

⇒ x = 7

Hence, age of Garima 5 years ago = 7 × 7 – 5 = 44 years

The correct answer is option 4 i.e. 21.

Average = Sum of all weights/Total number of people

⇒ Sum of all weights = 55 × 7

⇒ 385kg

When X is removed from the group the total weight becomes,

⇒ 385 - X

When Y is added,

⇒ 385 - X + Y

New average = 58 × 7

⇒ 406

⇒ 385 - X + Y = 406

⇒ X - Y = -21

Or |-21| = 21

The correct answer is Option 3 i.e. Rs.48600.

The difference between the amounts of Ajay and Vijay is Rs.4950

⇒ 40x - 29x = 4950

⇒ 11x = 4950

⇒ x = 450

The total amount of money is to be distributed among three of his friends.

A certain amount of money is to be distributed among three friends Ajay, Vijay, and Anuj in the ratio 40 : 29 : 39 = 40x + 29x + 39x = 108x

⇒ 108 × 450 = Rs.48600

Total amount = Rs.48600

The correct answer is Option 3 i.e. 6%.

Since, the amount of simple interest earned remains the same for every year.

So, interest earned in one year = Rs. 5400

Then, the principal amount deposited, P = 111600 – 4 × 5400

P = Rs. 90000

So, the required rate of interest, R = (5400 × 100)/90000

R = 6%

The correct answer is option 2 i.e. 36%.

The number of students in class 10th = 200a

The number of students in class 12th = 272a

Required percentage = [(students in class 10th - students in class 120th)/students in class 10th] × 100

= (272a - 200a)/200a × 100

= 36%

The correct answer is option 4 i.e. Rs.142.75.

Total fund collected from Russia = 4%

⇒ 4% = 4/100 × 28550 lakhs = Rs.1142 lakhs

If the total fund collected from Russia gets doubled = (2 × 1142) = Rs.2284 lakhs

Now,

Total fund collected from India = 15%

⇒ 15% = 15/100 × 28550 lakhs = Rs.4282.5 lakhs

If the total fund collected from India gets halved = 4282.5/2 = Rs.2141.25 lakhs

Difference = (2284 - 2141.25) = Rs.142.75 lakhs

The correct answer is Option 3 i.e. 3136 m², 176 m.

The area of the circle is 2464 m²

Area of the circle = πr²

πr² = 2464

22/7 × r × r = 2464

r × r = 2464 × 7/22

=112 × 7

= 784

r² = 784

r = 28m

Circumference of the circle = 2πr

= 2 × 22/7 × 28

= 2 × 4 × 22

= 176m

Diameter of the circle = side of the square

Side of the square= 2 × 28 = 56 m

Area of the square = a²

= 56 × 56

= 3136 m²

The correct answer is option 3 i.e. 24 m.

Let, the depth of the tank (h) = h meters

Given,

The diameter of the base = 14 m

The volume of the cylinder = 3696 m³ 

Formula:

The volume of the cylinder = πr²h    [where r = 14/2 = 7 m]

According to the question:-

⇒ πr²h = 3696

⇒ h = 3696/πr² = (3696 × 7)/(22 × 7 × 7)

⇒ h = 3696/(22 × 7) = 24 m

Alternative method:

The volume of cylinder = Capacity of cylinder

⇒ h = (3696)/(π × 49)

⇒ h = 24 m

The correct answer is Option 3 i.e. 1.

We know that,

⇒ cosec (90 - A)° = sec A

⇒ cosec 48° = cosec (90 - 48)° = sec 42°

⇒ 1/sin A = cosec A

Now putting these values,

(sec 42° × cosec 48° - 1) × [(1/sin²42°) - 1]

⇒ (sec² 42° - 1) (cosec² 42° - 1) [We know that 1 + tan²A = sec²A and 1 + cot²A = cosec²A]

So,

⇒ (sec² 42° - 1) (cosec² 42° - 1) = tan² 42° × cot² 42° = 1