SRCC GBO 2016

Speed of A = V

Speed of B = V + 2

Let the distance between points P and Q = D

Now, 

$$\frac{D}{V + (V + 2)} = \frac{72}{60} = 1.2$$

D = 1.2(2V + 2)

D = 2.4V + 2.4 .......... (1)

$$\frac{D}{(V + 2) - V} = 6$$

D = 12 ......... (2)

From (1) and (2):

12 = 2.4V + 2.4

V = 4

Speed of A = V = 4 km/h

Speed of B = V + 2 = 6 km/h

Distance between two stations = 240 km

Their meeting point is 160 km from one of the stations.

So, one train travels 160 km and other train travels 240 - 160 = 80 km.

Since, distance travelled by one train is double of the distance travelled by another train at the same time. 

Hence, the ratio of speed will be = 2: 1 or 1: 2

Let speed of train and car is 'x' and 'y' respectively. 

According to the quetsion: 

$$\frac{120}{x} + \frac{480}{y} = 8$$ .......... (1)

$$\frac{200}{x} + \frac{400}{y} = 8 + \frac{20}{60} = \frac{25}{3}$$ .......... (2)

From (1) and (2):

x = 60 and y = 80

Required ratio = x: y = 60: 80 = 3: 4

Remaining distance = $$\frac{6}{2}$$ = 3 km

Remaining time = $$45 * \frac{1}{3}$$ = 15 minutes

Required speed = $$\frac{3}{15} * 60$$ = 12 km/h

Let principle amount = 1000

SI for first 4 months = $$\frac{1000 * 12 * 1}{100 * 4}$$ = 30

SI for second 4 months = $$\frac{1030 * 12 * 1}{100 * 4}$$ = 30.9

SI for third 4 months = $$\frac{1060.9‬ * 12 * 1}{100 * 4}$$ = 31.827

SI for last 4 months = $$\frac{1092.727‬‬ * 12 * 1}{100 * 4}$$ = 32.78181‬

Total amount at the end of 1 year = 1092.727 + 32.78181‬‬ = 1125.50881‬

Effective interest = $$\frac{1125.50881 - 1000‬}{10}$$ = 12.55% = 12.5% (Approx)

Total amount of interest given by A to B = $$\frac{4800 * 9 * 3}{100}$$ = Rs.1296

Let extra amount added by A = X

Total amount of interest received by A to C = $$\frac{(4800 + X) * 12 * 3}{100}$$ = (1728 + 0.36X)

Now, 

(1728 + 0.36X) - 1296 = 720

0.36X = 288

X = 800

Hence, extra amount added = Rs.800

Total amount of interest at the end of 3 years = 8000 * 1.05 * 1.08 * 1.12 - 8000

= 10160.64 - 8000

= Rs.2160.64

Total amount left at the end of 1 year = $$5000 + \frac{5000 * 8 * 1}{100} - 1000$$ = Rs.4400

Total amount left at the end of 2 year = $$4400 + \frac{4400 * 8 * 1}{100} - 1000$$ = Rs.3752

Total amount left at the end of 3 year = $$3752 + \frac{3752 * 8 * 1}{100} - 1000$$ = Rs.3052.16

Let the height of cone = 'h' cm

Volume of cylinder = Volume of cone

$$\pi * 2^2 * 8 = \frac{1}{3} * \pi * 1.5^2 * h$$

3 * 4 * 8 = 1.5 * 1.5 * h

h = 42.67 m

Total character in 20 sheets of 55 lines each = 20 * 55 * 65

Let the number of sheets after reductio = N

According to the question: 

20 * 55 * 65 = N * 65 * 70

N = $$\frac{110}{7} = 15.7 pages = 16 pages$$

Reduction in number of sheets = 20 - 16 = 4 pages

Required percent = $$\frac{4}{20} * 100 = 20$$%