Aptitude - True Discount - Discussion

The answer is 55. I can explain this clearly see.

A person invested 1950 which is Principal amount.

Given Rate = 10% PA.
Time =1 year.

So, the amount he should get back at 10% after year is (110/100) * 1950 i.e 2145.
He sold it for 2200.
He got 2200 - 2145 = 55rs profit.

Yes, I too get the answer as 55.

Friends,

CP RS -1950.
After 1 year credit the amount in bank 2200,
So the sale present, so if he increase sale Rs 50 + 1950 = 2000 After 1 year the credit amount is 200.

2000, after 1-year interest is 20.

A = P + I.
2200 = P + P * 1 * 10/100.
2200 = P{100 + (1 * 10)}/100.
P = 2200 * 100/{100 + (1 * 10)}
P = 2000.

GAIN = 2000 - 1950 = 50.

Let's assume instead of purchasing the watch if he gives that money on interest then of for interest for one year will be I = 1950 * 10 * 1/100 = 195.

So after one year his total money will be 1950 + 195 = 2145.

But he sold the watch for 2200.

So there must be a gain of 55.

if we think what profit he has made now and work with current values, we get the answer as 50.

If we work with future value (after 1 year, we get the answer as Rs 55). When we go with the method where we find current value of 2200 and get the value to be 2000, we see a profit of Rs 50. Here we are comparing the values in present time.

When we go with the method of applying 10% interest to 195, we compare both the values after a year.

So the profit he has made as per the current value is 50, but as per future value, it's 55.
and this justified by the fact that present value of Rs.55 after an year is Rs 50 (50 X 1.1 = 55).

The question isn't clear whether we have to determine profit on the basis of present value or value after an yer, so we assume by default that we have to calculate profit based on present values, in which case the answer is 50.

So 200 was the interest and 50 was the profit but why isn't 200 considered profit? I mean profit is basically the difference b/w the money I sold the product and the money I bought the product for right?

We assume the worth to be 100 and hence sp * 100/100 + (10 * N) where N is the number of years for which the credit is offered.

Hence we get a profit of Rs. 50/-.

@Sachin.

You are absolutely right. Thanks.

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".