Aptitude - True Discount - Discussion

Dear guys:

Don't think so much about the formula of personal wealth and discount. Moreover its conceptual question.

If someone returning money in 4 month he will get discount of INR 122 over the amount.

So instead of paying 2562 he is only paying = 2440 before 4 month otherwise he will pay 2562 after 4 month.

So 2562-2440 = 122 is interest which we getting at the end of 4 month.
So simple interest is = 122.

Formula for s.i = p*r*t/100.

So r = s.i*100/p*t(time should be in year so we use 1/3 year).

r = 122*100/2440*1/3 = 15%.

Answer explanation:

PW= 100*amount/R*T.

Therefore from the above formula , we need to find R. Hence formula becomes,

R= 100*amount/P*T ------(1).

Here amount = Rs.122 is the discount amount for 4 years.

P = 2562-122 = 2418 is the original amount after applying discount.
T= 4 out of 12 months i.e = 4/12 = 1/3.

Substitute the values in (1), you will get the answer

Friends,

SI = interest on principal amount,

in the same way,

TD = interest on present worth,so v take PW instead of principal.

In question they gave TD with principal,so we first calculate the PW from principal & TD using the formula PW= principal-TD and then we calculate rate using the formula which is similar to the SI.

@Ankush.

Amount = present worth + true discount.
pw = amt - td.

2562 - 122.

pw = 2440.

TIME = 4 MONTHS / 12 =1/3.

SI = PTR / 100.

PTR = SI * 100.

R = (SI * 100) /PT.

R = (122 * 100) /2440 * 1/3.

You have finally get the answer for the rate of present value, below.

R = 15%.

2562 is sum of the money borrowed and true discount for 4 months.

So 2562 = The money borrowed+122.

The money borrowed = 2562-122 = 2440.

Then,

4 months (1/3 year) ===> 122.
12 months (1 year) ===> 366.

And,

Rs. 2440 ===> 366.
Rs. 100 ===> (100*366)/2440 = 15 %

How come 15% I can't understand since 122 is the interest for 4 months then for each month it is 30.5,

Then it should be 12.5%,

Since 10% 24.4 and 2.5 % is 6.1 so the should be 12.5%.

I guess can you explain it please.

In the question there must not mention that true discount amount is inclusive or exclusive on Rs. 2562/-.

How anyone could assumed to be that?

Answer should be 14% if it is exclusive or 15% if it is inclusive.

The true discount is always reckoned on the amount.
It is given in the previous formula page;
So the given value is taken as amount,
Now, P.W. =amount - T.D.

Hope you all understood.

P.W = Amount - T.D.

So P.W = 2440.

T.D = (P.W)*R*T.

100 they ask rate percent.

So R = (100*T. D)/(P.W*T) %.

R = (100*122)/(2440*1/3).

= (100*122*3)/(2440*1).

Answer: 15%.

amt=present worth + true discount

pw=amt-td
2562-122
pw=2440

TIME=4MONTHS/12=1/3

SI=PTR/100

PTR=SI*100

R=(SI*100)/PT

R=(122*100)/2440*1/3
R=15%