Quantitative Aptitude - Arithmetic Ability Questions

Average speed = Total distance / Total time.

Total distance traveled by Joel = Distance covered in the first 3 hours + Distance covered in the next 5 hours.

Distance covered in the first 3 hours = 3 x 60 = 180 miles
Distance covered in the next 5 hours = 5 x 24 = 120 miles

Therefore, total distance traveled = 180 + 120 = 300 miles.

Total time taken = 3 + 5 = 8 hours.

Average speed = 300/8 = 37.5 mph.

we know that 1 mile = 1.6 kms

=> 37.5 miles = 37.5 x 1.6 = 60 kms

Average speed in Kmph = 60 kmph.

$$\begin{gathered} 2211 x 75 x 112 \\ => 222 x 75 x 112 \end{gathered}$$

 Total number of prime factors is (22+5+2) = 29

Let Mohan present age = p

ATQ,

5/6 x p = p - 5

p = 30

His wifes age = 30 - 3 = 27 yrs.

1. How to find Speed(s) if distance(d) & time(t) is given:

 Speed (S) = Distance (D)Time (T) 

Ex: Find speed if a person travels 4 kms in 2 hrs?

Speed = D/T = 4/2 = 2 kmph.

2.  Similarly, we can find distance (d)  if speed (s) & time (t) is given by

Distance (D) = Speed (S) x Time (T)

Ex : Find distance if a person with a speed of 2 kmph in 2 hrs?

Distance D = S X T = 2 x 2 = 4 kms. 

3.  Similarly, we can find time (t) if speed (s) &  distance (d) is given by

Time (T) = Distance (D)Speed (S)

Ex : Find in what time a person travels 4 kms with a speed of 2 kmph?

Time T = D/S = 4/2 = 2 hrs.

4. How to convert  km/hr into m/sec :

P km/hr = P x 518 m/sec

Ex : Convert 36 kmph into m/sec?

36 kmph = 36 x 5/18 = 10 m/sec 

5. How to convert  m/sec into km/hr :

P m/sec = P x 185 kmph.

Ex : Convert 10 m/sec into km/hr?

10 m/sec = 10 x 18/5 = 36 kmph.

6.  If the ratio of the speeds of A and B is a:b, then the ratio of the times taken by them to cover the same distance is b : a.

7.  Suppose a man covers a certain distance at x km/ hr and an equal distance at y km/hr . Then, the average speed during the whole journey is 2xyx+y km/hr.

We know that:

When one card is drawn from a pack of 52 cards

The numbers of possible outcomes n(s) = 52

We know that there are 26 red cards in the pack of 52 cards
⇒ The numbers of favorable outcomes n(E) = 26

Probability of occurrence of an event: P(E)=Number of favorable outcomes/Numeber of possible outcomes=n(E)/n(S)

∴ required probability = 26/52 = 1/2.