Aptitude - True Discount - Discussion

I think I agree with @Sai, we were asked to find the present value of the gain or loss in that case it would have been 50.

Hey.

It can be understand like this.

Cost to the buyer is 2200.

This cost also includes the interest too.

So the selling price by the owner would be.

SP = 2200*100/110 = 2000.

So profit = 50.

Suppose that he bought it for Rs 2000 then after 1 year its cost must be 2200.
But the man paid 1950 i.e 50 Rs less.

Actually here we have to calculate that what should be the initial price of the watch so that after 1 year with interest its price would become 2200.

Think from the seller's perspective and live at present.

Then you will get Rs.50 as the answer.

Okay So the when looking from the seller's perspective the answer is correct. Thanks all.

The question is bit ambiguous and so all these confusion. The question can either be what's the gain at present value or at end of one year. If it is at present value, we need to discount Rs. 2200 with 10% discounting rate to find out its present value - formula is PV = FV / (1+r)^n i.e., Present Value = 2200 (1+0.10)^1 = Rs. 2000 and so the gain would be Rs. 50.

If it is at the end of one year, Rs. 1950 + 10% would be Rs. 2145 and the gain would be Rs. 55 at the end of one year. Discounting Rs. 55 gain at the rate of 10%, you would get again Rs. 50 present value. So it depends on whether one would like to find out the gain at present value or the value at the end of one year.

It's better to frame the question like this without any ambiguity.

Here the CP = 1950.

Let the principal price is x over which a 10% of interest is credited in one year.

i.e {x+x(10/100)} = 2200.

= (100x+10x) /100 = 2200.
= 110x = 220000.

x = 220000/110.
x = 2000.

So principal price = 2000 & CP = 1950.

Then profit = 2000-1950 = 50 (Ans).

The fact is interest should be counted on 1950 as he would have invested it at the rate of 10% pa. So at current time he must be having 2145 if he would not have bought that watch, but he did and now he is selling it for 2200 and so he is gaining 2200-2145=55.

ANS: 55.

@Santosh:

I think we can not earn interest at the instance of time as it is matter of duration. So we can not consider here the interest on 2200 at the time of selling.

Correct answer should be 55 not the 50. As gain would be on the amount spent not on the 2200.

@Ramesh is wrong.

How could he take interest @2200, which is the last amount to be paid i.e. interest is already included, so the principal on which interest should be calculated must be lesser than 2200 which is 2000+200 (@10%P.A.) and then the actual gain of rs 50. Out of interest is valid.