Aptitude - True Discount - Discussion

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.

p+(p*10/100) = 2200.

p(1+(1*10)/100) = 2200.

p((100+1*10)/100) = 2200.

p = (2200*100)/(100+1*10) = 2000.

=>gain = 2000-1950 = 50.

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.

I agree with karimkhan. The seller gets 2200 at the end of the year. If the seller had not bought the watch, he would have an additional rs 195 at the end of the year. Logically he has only made a profit of rs 55.

@all.

After reading the all above comments.
Dear all interest paid by customer not by man who sale.
So the interest is 200 for 2000.
And 2000-1950=50.

Gain 50.

55 answer is right if we think logically, and in fact 10% of 1950 is 195, that a man paid as a interest, so his cost prize become 1950+195= 2145, and then he sold at 2200.

So clear profit is - 2200-2145=55.