Aptitude - True Discount - Discussion

Hi Saurabh/everybody,

This is what I also did earlier, But then, What you are wrong is considering 10% interest on the cost price which is wrong, Since he is not investing 1950 for 1 year but his current selling price 2000, Which is agreed over a period of 1 year.

He gains 10% on this current sp, which accumulate to 2200 over 1 year. So current selling price is 2000(with a simple interest calculations you can arrive at this figure). And hence he gains 50 rs from his current cost price of 1950.

Answer is wrong because,

(1950*1*10)/100 = 195.
1950+195 = 2145.
2200-2145 = 55 Rs. Gain.

I think sai is correct because how to know whether it is think logically or do formula based.

I think philosophical debate can be done on this question. Cos logic regarding both answers are attractive.

For Rs. 50 gain : Time value of Rs. 2200 at 10% discount rate spanning over 1 year is 2000 (NPV=FV(1+i/100)). So its a gain of Rs. 50.

For Rs. 55 gain : The seller has invested Rs 1950 for one year at a rate of interest of 10% over 1 year span. So he is supposed to gain Rs. 195 at the end, but he would gain Rs. 250 so extra gain of Rs. 55.

Now we have to keep in mind that both calculations are virtual and depends on viewpoint of individual. Now think this problem another way - suppose the buyer (who is to pay Rs. 2200 after 1 year ) thinks to keep the money aside for future ease and engages somewhere at 10% interest rate for 1 year would have to bear Rs. 1980 out of his pocket and so he gets the same watch after 1 year with only Rs 30 extra cost but he has to sacrifice liquidity of Rs 2200 for one year.

Finally time value of money is always associated with investment. Here the tangible investment is Rs 1950 only and it will yield Rs. 2145 after 1 year at 10% rate and will make a gain of Rs. 55 to the "SELLER". And in pro-rate basis Rs 2200 is as good as Rs 2000 w.r.t "BUYER".

So what say?

"time value of money" is its logic to solve. time value of money means, after some interval of time the value of money changes(decreases mostly).

Ex: The value of 100 Rs 10 years ago was more valuable than the present value of Rs 100.

Thus, the discussions made in the favour of gain = 50 is totally correct (because PW is used here).

Yup! correct answer is Rs 55 as the amount of money for which he is losing interest income is Rs 1950 only and not Rs 2200.

Correct Answer Is Rs 55. Simple Logic Says Total Cost = Rs 1950 Rate Of Interest = 10 %, Time = 1 Yrs. If This Money Is Invested It Will Yield = Rs. 1950 + 195 = Rs 2145. Hence Profit Will Be Rs 2200 - 2145 = Profit Rs 55.

What is P.W. here? I can't understand that formula used.

The scenario is.
Let ram buys a watch for Rs1950 and sells it to Rahim for credit.
Rahim pays ram Rs 2200 at the end of one year @ 10% s.i.

i.e x amounts to 2200 @ 10% s.i.
=> x =2000 ( present value of 2200).
i.e He sells it for a present worth of 2000rs.
Therefore rams profit is 50Rs @ present worth.

CP=1950. SP(after 1 yr )=2200.

Let present SP=p.
Then use

SP(after 1 yr )=p+(p*r*t/100)
=> 2200=p+(p*10*1/100)
=> p=2000.

We are dealing with present values
Present cp=1950
Present sp=2000

=> Gain=2000-1950=50.
This ans is correct.