The correct answer is Option 1 i.e. 11.

[(12/5 + 13/40) × (500 - 20 × 5)] ÷ [(13/3 + 1/9 ÷ 12/27) ÷ (15 - 7/4)]  ÷ [(218 × 159)/121]

⇒ [(109/40) × (500 - 100)] ÷ [(13/3 + 1/4) ÷ (53/4)] ÷ [(218 × 159)/121]

⇒ [(109/40) × (400)] ÷ [(55/12) ÷ (53/4)] ÷ [(218 × 159)/121]

⇒ [1090] ÷ [55/159] ÷ [(218 × 159)/121]

⇒ [1090] × [159/55] × [121/(218 × 159)]

⇒ 121/11 = 11

The correct answer is Option 1 i.e. 50%.

The surface area of the sphere = 4πr² = 4π × 10²

Now

The total surface area of the half-sphere = 3πr² = 3π × 10²

Here, Ratio = The surface area of the sphere/(2 × The total area of the half-sphere)

= 4π × 10²/[2 × 3π × 10²] = 2 : 3

Difference = 3 - 2 = 1

Hence, Percentage change = 1/2 × 100 = 50%

The correct option is 2 i.e Rs 45

The correct option is 2 i.e 70%.

The correct answer is Option 3 i.e. Rs. 112.

A is 8 years older than B and 17 years older than C

So,

The age difference of A and B = 8 years

Age difference of B and C = 17 – 8 = 9 years

The difference in money received by A and B is 4 times of their age difference and difference of money received by B and C is twice of their age difference

Suppose Money received by A = Rs. X

So,

Money received by B = X – 4 × 8 = Rs. (X – 32)

And,

Money received by C = (X – 32) – 2 × 9 = Rs. (X – 50)

Total money = Rs. 350

So,

X + X – 32 + X – 50 = 350

⇒ 3X = 432

⇒ X = 144

Hence,

Money received by B = X – 32 = Rs. 112

The correct answer is Option 3 i.e. 190 meters

Speeds of trains P and Q are 90 km/h and 72 km/h respectively.

Converting them to m/s:

90 × 5/18 = 25 m/s

72 × 5/18 = 20 m/s

So, relative speed when running in opposite directions = 25 + 20 = 45 m/s

Suppose the lengths of trains P and Q are ‘2x’ and ‘x’ meters.

So,

⇒ (2x + x)/45 = 30

⇒ 3x = 1350

⇒ x = 450

Hence, length of train B = 450 m

Now, suppose length of bridge = a meter

So,

⇒ (450 + a)/20 = 32

⇒ 450 + a = 640

⇒ a = 190

Hence, length of bridge = 190 meters

The correct answer is option 4 i.e. 24

Time taken by two pipes alone to fill the tank = (1/15 + 1/20) - 1 = 60/7 minutes

But the time difference arises only for filling the 2/5th of the tank above the leak

Let the time taken by the leak to empty the portion above it be x minutes

Time taken by two pipes to fill 2/5th of the tank = 2/5 × 60/7 = 24/7 minutes

Time taken when also leak is opened

{1/(24/7) – 1/x} - 1 = Original time + 4/7

(7/24 – 1/x) - 1 = 24/7 + 4/7

24x/(7x – 24) = 4

24x = 28x – 96

96 = 4x

x = 24 minutes

The correct answer is option 2 i.e. 44/9 km/hr.

Average speed if various distances covered at different time = (distance covered in x hr + distance covered in y hr)/(x + y)

x + y is the total time

Distance = speed × time

A man travels for 5 hr at a speed of 4 km/hr

Next, he travels for 4 hr at a speed of 6 km/hr

The distance covered by him in 5 hr = (5 × 4) = 20 km

The distance covered by him in the next 4 hr = (6 × 4) = 24 km

The total distance covered = (20 + 24) = 44 km

Total time = (5 + 4) = 9 hr

The average speed = 44/9

The correct answer is option 3 i.e. Rs 4000.

Profit = (C.P × P%)/100

Let the CP of the book = x and the SP of the book = y, and Let the profit = P

Given, x + y = 5000

A/Q,

⇒ 10% of x + 12% of y = P........(I)

⇒ 12% of x + 10% of y = P + 60.......(II)

Subtract (I) from (II) we get

⇒ 2% of x - 2% of y = 60

⇒ x - y = 3000

⇒ x + y = 5000 (given)

⇒ x = 4000

So, the cost price of the book = Rs.4000

The correct answer is option 4 i.e. 9 : 28.

The ratio of money of Rakesh and Shyam = 4 : 7

The ratio of money of Vimal and Amit = 9 : 16

Ratio of product of money with Rakesh and Vimal to Shyam and Amit:

⇒ (4 × 9) : (7 × 16) = 9 : 28

Hence, the required ratio is 9 : 28