AP ICET 2nd May 2018 Shift-1

Given, number of boys in the class = 36

Percentage of girls in the class = 55%

$$\Rightarrow$$  Percentage of boys in the class = 45%

Let total students in the class = x

$$\Rightarrow$$ 45% of x = 36

$$\Rightarrow$$ $$\frac{45}{100}$$x = 36

$$\Rightarrow$$  x = 80

$$\therefore\ $$Total number of students in the class = 80

SP1 = 240

CP1 = 240/1.2 =200 Rs

SP2=240

CP2 = 240/0.8 = 300

Total SP = 480 and total CP = 500

Loss % = 20/500 = 4%

Let CP = 100 Rs

According to the problem,

MP = $$\frac{150}{100}\times100$$ = Rs 150

Profit% = 20%

SP = $$\frac{120}{100}\times100$$ = Rs 120

Discount = 150 - 120 = Rs 30

Discount% = $$\frac{30}{150}\times100$$ = 20%

Hence, the correct answer is Option A

Let the capitals of A, B, C are a, b, c respectively

According to the problem, 3a = 4b = 5c

Let 3a = 4b = 5c = t

$$\Rightarrow$$ a = $$\frac{t}{3}$$, b = $$\frac{t}{4}$$, c = $$\frac{t}{5}$$

$$\therefore\ $$Ratio of their capitals = a : b : c

= $$\frac{t}{3}$$ : $$\frac{t}{4}$$ : $$\frac{t}{5}$$

= $$\frac{1}{3}$$ : $$\frac{1}{4}$$ : $$\frac{1}{5}$$

= $$\frac{60}{3}$$ : $$\frac{60}{4}$$ : $$\frac{60}{5}$$

= 20 : 15 : 12

Let the capacity of tank = 60litres

Speek of A = 60/20 = 3litres/min

Speed of B = 60/30 = 2 litres/min

In 4 min, A will fill 12l and B will fill 8 l. Total 20 litres

Left = 40 litres

Time required by B to fill remaining = 40/2 = 20 min

Total time = 24min

Time and speed are inversely proportional

hence ratio of times = $$\frac{1}{3}:\frac{1}{4}:\frac{1}{5\ }$$

Multiply by 60, we get 20:15:12

Let length of the tunnel  = x

Length of the train = 600 m

Speed of the train = 72 km/h = 72 x $$\frac{1000}{3600}$$ m/sec = 20 m/sec

Time = 1 min = 60 sec

Speed = $$\frac{\text{distance}}{\text{time}}$$

$$\Rightarrow$$  20 = $$\frac{600+\text{x}}{60}$$

$$\Rightarrow$$  x + 600 = 1200

$$\Rightarrow$$  x = 600 m

$$\therefore\ $$Length of the tunnel = 600 m