Aptitude - True Discount - Discussion

Yes, I too get the answer as 55.

Thanks a lot @Jatin.

If we take interest on Rs 2200 how can he ever face a loss cuz he is selling at Rs 2000 that means he is already selling at a profit on which he is gaining the interest profit as well. If you take in that way the profit will become 250. 50 Rs on selling the difference between buying and Selling cost and the Rate of Interest money as well.

Instead the questions wants to see that he sold that Rs 2200 at a credit of 1 year and the general annual interest rate is 10% so did he make a loss or profit by selling it rather than gaining interest on it. Hence the 10% should be calculate at 1950 and then check with 2200 if he made a profit or loss.

Hence 55 comes as the correct answer.

Why 55 is wrong?

Because according to the people who are that's not true. We cannot predict the original price of the watch in future. Maybe it can be a loss!. But definitely, we can comment on present profit. So giving a profit after 1 year implicitly invalid whether it's 50, 55 or 30 until and unless there is not mention of a rate with which original price would have increased.

I think option A) 55 is the correct answer.

Suppose Present Worth of Rs. 2200 is A.

2200 = (A x 110)/100.

A = (2200 x 100)/110.

A = 2000.

Gain = 2000-1950 = 50.

I = PTR/100.

= 1950*1*10/100 = 195.

Therefore A = P+I.

= 1950+195 = 2145.

GAIN = 2200-2145 = 55.

So, the man gained Rs. 55.

And correct answer is "A".

Ok let me make this clear to all.

The man bought it at Rs. 1950 now.

The question literally means that at the end of 1 year, the man got Rs. 2200.

So Rs. 2200 is the amount.

Amount = P+SI.

2200 = P + P*R*T/100.

2200 = P + P*10*1/100.

2200 = P + 0.1 P.

Deducing from here comes P (The sum of money which the man could have got in terms of cash 1 year ago) = Rs. 2000 which is Rs. 50 (2000-1950) more than the cost price of the product (Rs. 1950).

Here's my take on this:

1) By default:

Begin Year 1, he bought a watch for 1950.

End Year 1, he sold it for 2200.

2) If he deposited in a bank, he got a 10% interest:

Begin Year 1, he deposited 1950.

End Year 1, he withdrawn all out and got 1950*1.1 = 2145.

=> So at the end of year 0, he gained 2200-2145 = 55.

I don't think the author of the question intend for it as a Present Value type. The 4 answers clearly said "gains/loses", it is simple present tense, which means he only "gains" the money at the end of year 1.

He cannot gain any money when we calculate PV at the Begin of year 1, because he has not bought the watch or deposited the money yet!

Where is 100 come from?