Aptitude - True Discount - Discussion

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 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.

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

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

Then you will get Rs.50 as the answer.

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.

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.

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.

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.