[Download PDF] AP ICET 2015 Paper with Solutions

Instructions

For the following questions answer them individually

Question 81

By selling an item for ₹ 754, a trader gets 16% profit. Then the cost price of the item in rupees is

Video Solution

Solution

S.P=754

trader get 16 % profit

so 116 unit =754

1 unit=6.5

100 unit =650

So C.P is 650.

Question 82

A pipe can fill an empty tank in 15 hours. Due to a leak at the bottom, the tank is filled in 20 hours. If the tank is full, then in how much time (in hours) will the leak take to empty the tank ?

Video Solution

Solution

Pipe can fill in 15 hr

Pipe along with Leak hole take 20 hr

So lcm of both 60

hence efficiency of pipe is 60/15= 4

Efficiency of both is 60/20= 3

So efficiency of leak is 4-3=1 so the leak hole take 60/1 = 60 hr to leak out all water.

Question 83

Two pipes A and B can fill an empty tank independently in 3 hours and 4 hours, respectively. If the pipes A and B are opened in alternate hours starting with B, then the total time taken, in hours, to fill the tank is

Video Solution

Solution

A and B can fill the tank in 3 hours and 4 hours respectively.
Let the capacity of the tank be 12 units (LCM of 3 and 4)
Efficiency of A = $$\dfrac{12}{3} = 4$$ units/hour.

Efficiency of B = $$\dfrac{12}{4} = 3$$ units/hour.

If A and B are open every alternate hour starting with B, then in 2 hours, 7 units of the tank is filled.
Remaining capacity = 12-7 = 5 units.
3 units will be filled by B in 1 hour.
Remaining 2 units will be filled by A in $$\dfrac{1}{2}$$ hour.

Therefore, Total tank is filled in $$2+1+\dfrac{1}{2} = 3\dfrac{1}{2}$$ hours.

Question 84

Two cars A and B start at the same time ad move in opposite directions between the places x and y. The time taken by Car A and Car B to reach their destinations after they meet each other on their way is 4 hours and 9 hours respectively. Then the ratio of the speeds of cars A and B is

Video Solution

Solution

Question 85

A car travels at $$\frac{8}{7}$$ times its usual speed and reaches the destination 15 minutes early. Then the time taken by the car in hours to reach its destination with its usual speed is

Video Solution

Solution

New Speed of car is 8/7 of old speed

So new time is 7/8 of old time

8-7=1 unit =15 min early

So original time is 8×15=120 min or 2 hr

Question 86

A can turnout twice the amount of work that B can do. If B alone can complete that work in 12 days, then in how many days can A and B complete that work together ?

Video Solution

Solution

A is twice efficient than B

So A =2

B=1

Total efficiency of A & B=3

B can complete the work in 12 days

So total work is 12×1=12

A & B complete the work in together is =12/3=4 days

Question 87

2 men and 3 women can do a particular work in 10 days, whereas 4 men can do that work in 10 days. Then in how many days can 3 men and 3 women complete the same work ?

Video Solution

Solution

2 men+3 women complete the work in 10 days.

2 men +3 women =10 days

4 men = 10 days

So equate both equation

2 men + 3 women =4 men

3 women = 2 men

men/women=3/2

Total work is= (2 m+3 w) ×10 days =(2×3+3×2)×10=12×10=120

So 3 men + 3 women=3×3+3×2=15

So 120/15=8 days.

Question 88

The sides of a rectangle of perimeter 52 meter are in the ratio 4 : 9. Then the area in square meters of that rectangle is

Video Solution

Solution

Breadth to Length ratio is 4:9

So let Breadth is 4x & Length is 9x

We know perimeter of rectangle is 2(L+B)

2(4x+9x)=52

26x=52

X=2

so Length is=9x=9×2=18

Breadth=4x=4×2=8

So area of rectangle is L×B

18×8=144 meter square.

Question 89

The radius of the base of a right circular cylinder is r and the radius of a sphere is $$\frac{r}{2}$$. If the volumes of that cylinder and the sphere are equal, then the height of the circular cylinder in proper units is

Video Solution

Solution

Volume of Cylinder =V=$$\pi r^2 h$$

Volume of sphere V=$$\frac{4}{3}\times \pi (r/2)^3$$

Cylinder Volume = Sphere Volume

So $$\pi \times r^2 \times h = \frac{4}{3} \times \pi \times (r/2)^3$$

$$h=r/6$$

Question 90

The volume of a cube (in cubic feet) whose total surface area is 384 square feet is

Video Solution

Solution

Total surface area of cube 6a^2=384

So a=8 feet

Where a = side of cube

So volume of cube is a^3=(8)^3=512 cube feet

CAT Content

AP ICET 2015

By selling an item for ₹ 754, a trader gets 16% profit. Then the cost price of the item in rupees is

A pipe can fill an empty tank in 15 hours. Due to a leak at the bottom, the tank is filled in 20 hours. If the tank is full, then in how much time (in hours) will the leak take to empty the tank ?

Two pipes A and B can fill an empty tank independently in 3 hours and 4 hours, respectively. If the pipes A and B are opened in alternate hours starting with B, then the total time taken, in hours, to fill the tank is

Two cars A and B start at the same time ad move in opposite directions between the places x and y. The time taken by Car A and Car B to reach their destinations after they meet each other on their way is 4 hours and 9 hours respectively. Then the ratio of the speeds of cars A and B is

A car travels at $$\frac{8}{7}$$ times its usual speed and reaches the destination 15 minutes early. Then the time taken by the car in hours to reach its destination with its usual speed is

A can turnout twice the amount of work that B can do. If B alone can complete that work in 12 days, then in how many days can A and B complete that work together ?

2 men and 3 women can do a particular work in 10 days, whereas 4 men can do that work in 10 days. Then in how many days can 3 men and 3 women complete the same work ?

The sides of a rectangle of perimeter 52 meter are in the ratio 4 : 9. Then the area in square meters of that rectangle is

The radius of the base of a right circular cylinder is r and the radius of a sphere is $$\frac{r}{2}$$. If the volumes of that cylinder and the sphere are equal, then the height of the circular cylinder in proper units is

The volume of a cube (in cubic feet) whose total surface area is 384 square feet is

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