**Find solutions for all the questions at the end of each set:**

### Set A

1.A train of 320 m cross a platform in 24 seconds at the speed of 120 km/h. while a man cross same platform in 4 minute. What is the speed of man in m/s?

(a) 2.4

(b) 1.5

(c) 1.6

(d) 2.0

2.A car travel 1st 39 km distance in 45 km minute while nest 25 km distance in 35 minutes. What is its average speed?

(a) 45 Km/h

(b) 35 Km/h

(c) 48 Km/h

(d) 90 Km/h

3.A car starts with the speed of 70 km/h with its speed increasing every two hours by 10 km/h. In how many hours will it cover 345 km?

(a) 9/4 hours

(b) 4 hours 5 minute

(c) 9/2 hours

(d) Cannot be determined

4. Aditya rides a cycle at the speed of 15 km/h but stops for 10 minute to take rest every 20 kms. How much time will he take to cover a distance of 150 kms?

(a) 11 hours 10 minutes

(b) 11 hours

(c) 12 hours 30 minutes

(d) 15 hours

5.A train 120 m in length passes a pole in 4 second and another train of length 225 m travelling in the same direction in 15 second. Find the speed of second train?

(a) 8 m/s

(b) 7 m/s

(c) 12 m/s

(d) 22 m/s

6.The ratio between the speed of bike and train is 15 : 27 respectively. Also a bus cover a distance of 720 km in 9 hours. The speed of the bike is 3/4th the speed of bus how much distance will the train cover in 7 hours?

(a) 756 km

(b) 760 km

(c) 740 km

(d) Cannot be determined

7.A 280 m long train moving with an average speed of 108 km/h cross a platform in 12 second. A boy crosses the same platform in 10 second. What is the speed of boy in m/s?

(a) 5 m/s

(b) 8 m/s

(c) 10 m/s

(d) Cannot be determined

8.A car covers a distance of 210 km in a certain amount of time at the speed of 35 km/h. What is the average speed of a truck that travel distance of 18 km less than the car in the same time?

(a) 64 km/h

(b) 66 km/h

(c) 65 km/h

(d) None of these

9.A truck cover 224 km in 4 hours the average speed of a bike is 1/4th the average speed of the truck how much distance will the bike cover in seven hour?

(a) 96 km

(b) 98 km

(c) 95 km

(d) 92 km

10.A bus started its journey from Bettiah and reached Motihari in 44 minute with its average speed 50 km/h if the average speed of bus is increased by 5 km/h. If the average speed of bus is increased by 5 km/h how much time will it take to cover the same distance?

(a) 31 min

(b) 36 min

(c) 38 min

(d) 40 min

Answers and Solution:

1.(d) Speed of train = 120*5/18=100/3 m/s

(320 + x) = 24 x 100/3

320 + x = 800

∴x = 480

So platform length = 480

So, speed of man = 480/(4*60 = 2 m/s

2.(c)Total distance = 39 + 25 = 64 km

Time taken = 45 + 35 = 80 minutes = 4/3 hours

So, average speed = 64/(4/3) = 48 km/h

3.(c)1st 2 hours =70 x 2 = 140

Next 2 hours = 80 x 2 = 160

After 4 hour total distance cover = 300

So next 45 km with speed of 90 km/h is 45/90=1/2 hour

So, total time taken = 4 1/2 hour

4.(a) For 150 km he take 150/15 = 10 hour

For 150 km he stop = 150/20=(7×10) = 70 minute

So total time taken = 11 hours 10 minutes

5.(b)Speed of train = 120/4 = 30 m/s

Total distance = 225 + 120 = 345 m

Relative speed = 345/15 = 23 m/s

But the speed of 1st train is 30 m/s.

So, speed of 2nd train = 30 – 23 = 7 m/s

6.(a)Speed of bike = 720/9*3/4 = 60 km/h

Speed of train = 60/15*27 = 108 km/h

So, train cover = 108 x 7 = 756 km

7.(b)Speed = 108 x 5/18 = 30 m/s

Length of platform = 30 x 12 – 280 = 80 m

Speed of boy = 80/10 = 8 m/s

8.(d)Time = 210/35 = 6 hours

Speed of truck = (210-18)/6 = 32 km/h

9.(b) 224/4*1/4*7 = 98 km

10.(d) (44*50)/(50+5)= 40 min.

**Find solutions for all the questions at the end of each set:**

### Set B

1.The sum of five consecutive even numbers is equal to 170. What is the sum of the second largest number and the square of the smallest number amongst them together?

(a) 940

(b) 932

(c) 936

(d) 934

2.If 50% of (x – y) = 20% of (x + y), then what percent of x is y?

(a) 250/7 %

(b) 300/7 %

(c) 150/7 %

(d) 42%

3.In a stream running at 2 kmph, a motorboat goes 6 km upstream and back again to the starting point in 33 minutes. Find the speed of the motorboat in still water.

(a) 22 km/hr

(b) 20 km/hr

(c) 25 km/hr

(d) 18 km/hr

4.In a school 70% of the students are girls. The number of boys are 510. Then the total number of students in the school is:

(a) 850

(b) 1700

(c) 1830

(d) 2000

5.A shopkeeper mixed two verities of rice at Rs. 20/kg and Rs. 30/kg in the ratio 2 : 3 and sell the mixture at 10% profit. Find the price per kg at which he sold the mixture?

(a) Rs. 26

(b) Rs. 28.8

(c) Rs. 28

(d) Rs. 28.6

6.A tap can fill a tank in 6 hours. After half these tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?

(a) 3 hours 15 min

(b) 3 hours 45 min

(c) 3 hours 40 min

(d) 3 hours 50 min

7.A merchant has 1000 kg of sugar part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The Quantity sold at 18% profit is

(a) 400

(b) 300

(c) 600

(d) 250

8.An order was placed for supply of carpet of breadth 3 meters, and the length of the carpet was 1.44 times of the breadth. Subsequently the breadth and the length were increased by 25 and 40 per cent respectively. At the rate of Rs 45 per square metre, what would be the increase in the cost of the carpet?

(a) Rs 1020.60

(b) Rs 398.80

(c) Rs 437.40

(d) Rs 583.20

9.Rs.460 was divided among 41, boys and girls such that each boy Rs.12 and each girl got Rs.8. What is the number of boys?

(a) 33

(b) 30

(c) 36

(d) 28

10.What will be the compound interest accrued on an amount of Rs 10,000 @20p.c.p.a. in two years if the interest is compounded half-yearly?

(a) Rs 4,400

(b) Rs 4,600

(c) Rs 4,641

(d) Rs 4,680

ANSWER KEY:

1.(c)

2.(b)

3.(a)

4.(b)

5.(d)

6.(b)

7.(c)

8.(c)

9.(a)

10.(c)