Non- routine questions

Jeff took 8 hours to travel from Town A to Town B.
Nick took 12 hours to travel from Town B to Town A
Both Jeff and Nick started at 0930.
At what time would they pass each other on the way?

Actually, this is a relatively simple question... If you know how to do it, it is very easy.


The solution is below.

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METHOD 1:


Let the distance between Town A and Town B be 24km.

Speed of Jeff : Dist/Time = 24km/8h = 3km/h
Speed of Nick : Dist/Time = 24km/12h = 2km/h
Time taken to meet = Dist/Total speed
= 24/ 3+2
= 24/5
= 4.8h = 4h 48 min

0930 --4h 48 min ------ 1418--> ANSWER!

Simple???


METHOD 2 :

Jeff : 8h --> 1 journey
1h --> 1/8 journey

Nick : 12h --> 1 journey
1h --> 1/12 journey

1/8 + 1/12 = 3/24 + 2/24 = 5/24

5/24 journey = 1h
24/24 journey = 24/5 h = 4.8h = 4h 48min

Applying the concept of simple and compound interest on practical situations

You may ask, Why do I even need to learn simple/compound interest? All I have to do is not borrow and not lend money! Well, that thinking is very childish! GROW UP! In our life, I bet that we will borrow or lend money, and simple interest is for, well, simple amounts. For example, in primary school you may come across people saying"You lend me $1 I return you $2 tomorrow" This is a perfect and simple example of simple interest. You borrow money at a 100% interest.(Which is very stupid)
Now, compound interest. Its pretty much the same as simple interest, and you can think of compound interest as a series of back-to-back simple interest contracts. The interest earned in each period is added to the principal of the previous period to become the principal for the next period. For example, you borrow $10,000 for three years at 5% annual interest compounded annually:

p = principal (original amount borrowed or loaned)
i = interest rate for one period
n = number of periods

interest year 1 = p x i x n = 10,000 x .05 x 1 = 500(i1)
interest year 2 = (p2 = p1 + i1) x i x n = (10,000 + 500) x .05 x 1 = 525(i2)
interest year 3 = (p3 = p2 + i2) x i x n = (10,500 + 525) x.05 x 1 = 551.25

Total interest earned over the three years = 500 + 525 + 551.25 = 1,576.25. Compare this to 1,500 earned over the same number of years using simple interest. You will find that you earned A LOT of money as compared to charging simple interest.
So there you have it for those aspiring entrepreneurs, charge compound interest for any amount you lend, and you will be rolling in the green stuff if the lender is a procrastinator and takes ages to pay back. Ditto loan sharks
=)


Source: http://www.getobjects.com/Components/Finance/TVM/iy.html

Non-routine Mathematics Questions

Here are some non-routine maths questions for you to have some fun with.

Q1. 3 men go on a business trip and pay $30 altogether at a hotel. The manager of the hotel discovers that he has overcharged them and refunds them $5. The 3 men decide to accept $1 each and give the $2 to a bellboy. So, each man has spent $9 so they have an expenditure of $27. Including the tip, that's $29. So where is the missing $1?( Remember, they paid $30)

Answer: Actually, there is no missing $1. The men do pay a total of $9.00 each (total of $27.00) for the room, but only after you add in the amount they tipped the bellboy($2). They paid $25 for the room and they gave the bellboy $2 as a tip. ($25 + 2 = $27.00). Including the $3 the men received as a refund, you will get the full $30( $27+$3=$30).

Q2. A road is 300km long. Car A is at the very start of the road and Car B is at the very end of the road. They start driving at exactly the same time towards each other. A bird is on the roof of Car A. As soon as both cars start moving, the bird travels at a speed of 150km/h towards Car B. When it reaches Car B, it turns around and returns to Car A, then Car B, so on and so forth, until both cars reach the mid-point of the road. How far has the bird flown if Car A and Car B travel at 60km/h and 90km/h respectively?

<-------------------------------------------300km------------------------------------------->

Car A>------------------------------------>ROAD<--------------------------------------Car B

Answer: This question is really quite simple. It can be solved in just 2 steps. However, you must know the formula for calculating Distance, Time and Speed first. For your info, it is Distance= Time * Speed. Thus, before we find out the distance the bird has flown("How far has the bird flown") , we must find out its speed and time. We already know its speed( 150km/h). So, how do we know its time?

We know the road is 300km long and Car A and Car B travel at a total speed of 150km/h( 60km/h + 90km/h). Hence, we can work out easily that they will take 2 hours to meet. That is the time given to the bird to travel.

So, since Distance= Speed * Time, Distance flown= Bird's Speed* Bird's time to travel=150km/h * 2h= 300km.( Answer)