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Direction : Study the following question carefully and choose the right answer.
1
A man starts from a place P and reaches the place Q in 7 hours. He travels 1/4 th of the distance at 10 km/hour and the remaining distance at 12 km/hour. The distance, in kilometer, between P and Q is:
» Explain it
C
Let one-fourth of the distance between P and Q be x km

then

Time taken for the first one-fourth distance =  x  km/hour
10

and

Time taken for the remaining distance =  3x  km/hour
12

Since  Total time taken is 7 hours.

⇒ 7 =  x  +  3x
10 12

On solving, x = 20

Total distance = 4x = 80 km.

Hence, option C is correct.

2
In the school, Mohan and Govind took a part in the race and the ratio between their speeds is 5 : 7. Mohan losses the race by 360m then what is the length of the track (in km)?
» Explain it
A
t =  D
S

According to the question,

Let Speed = 5x, 7x Distance = y m

y – 360  =  y
5x 7x

y – 360  =  y
5 7

7 (y – 360) = 5y

7y – 5y = 2520

2y = 2520

y = 1260

= 1.26 km.

Hence, option A is correct. 
3
The respective ratio between the speed of a car, a train, and a bus is 5 : 9 : 4.The average speed of the car , the bus and the train is 72 km/hr together. What is the average speed of the car and the train together?
» Explain it
C
Let speed of the car, the train, and the bus be 5a Km/hr , 9a Km/hr and 4a Km/hr respectively
 
Given   

total speed = (72 × 3) Km/hr  = 216 Km/hr
 
⇒    5a + 9a + 4a = 216
 
⇒    18a = 216
 
⇒    a = 12Km/hr 
 
⇒    speed of car = 5 × 12 = 60 Km/hr
 
And     

speed of train = 9 × 12 = 108 Km/hr
 
⇒ their average speed =  60 + 108  = 84 Km/hr
2

Hence, option (C) is correct.
4
Ranvir goes to his office from his house at a speed of 16 km/hr and returns to his home from his office at a speed of 20 km/hr and he takes 4 hour 30 minutes in all. If the distance of his friend's house from his office is 20% more than the distance of his house from his office, find the distance of his house to his friend's house.(assuming the office lies between Ranvir's house and his friend's house)
» Explain it
E
Let the distance of his house to his office = D km

T =  D
S

4 hour 30 minutes =  D  +  D  
16 20

9  =  5D + 4D
2 80

9  =  9D
2 80

D = 40

The distance from his house to his office = 40 km

The distance from his office to his friend's house = 40  km × 120% = 48 km

The distance from his house to his friend's house = 40 + 48 = 88 km

Hence, option E is correct.

5
Mohit and Anuj took a part in a race. Mohit runs 300m in 50 second and Anuj takes 1 minute to cover the same distance. By what distance will Mohit beat Anuj in 300 m race?
» Explain it
D
Mohit runs 300m in 50 sec.
 
Anuj runs 300m in 60 sec.

Now, In 1 sec Anuj runs 5m

Therefore, in 50 sec Anuj runs 50×5 = 250m
 
Mohit beats Anuj by 300 - 250 = 50m .

Hence, option D is correct.