Aptitude - True Discount - Discussion

Just by basics:

Principle + 12%of principle for 1 year = 10028,
P{1+3/25}=10028,
28/25P=10028.
P = 8953.57.

Now we need to put interest for 3 months or 1/4th year.
8953.57 + (1/4)*(12/100) * 8953.57.
= 8953.57 + 268.60,
= 9222.17.

In this question, the time is given as 1 year so the amount to be paid is 10028.

Now, he wants to pay in 3 months. And question is, what is the amount he pays. so the pw of the money in the 3rd month should be calculated.
Now the amount 10028 is for 1 year and so if we use time as 1 year we get pw of 1 year before but what we need is the pw of the money after 3 months so the time reduces to 9 months from 1 year.

Present worth = not given.

p.w + t.d = 10028 given --> 1
td=p.w*n*r/100;

From above find p.w first
i.e, t.d=p.w*1*12/100 --> (2)
t.d=0.12p.w; put in (1).
p.w=8953.57.

Now from p.w find t.d for 3 months which is 268.605 --> formula given in(2))
Amount should pay = total=p.w+t.d for 3 month.
= 8953.571+268.805 = 9222.17.

Why 100 is added in the denominator?

It would be 10028/(1.12)^(9/12) = 9210.87.

I didn't understand this, please explain me.

In the first attempt, I also calculated the answer Rs. 9222.17 but this approach is wrong.

Because merchant makes a deal for one year and trader is paying before the due date so we have to subtract interset on that amount for 9 months.

The amount that trader has to pay after 1 year, he settles it after 3 months i.e. 9 months before the due date.

So PW of the amount now after 3 months i.e. 9 months before the actual payment as the deal is done can be calculated simply as given in the solution.

@gopikrishna. From where did you get PW? I'm sorry, I can't understand the question.

1. P.W = 10028*100.

2. Due have payed in 3 months = 9/12.

3. Interest = 12%.

4. Rs = (10028*100)/100+(12*9/12).

5. 9200.

I got the answer as 9222 and I think if you go conceptually then it is right. Because if you pay interest, then you pay it on the actual principal and not from the amount where interest is already included.