Aptitude - True Discount - Discussion

It's very simple.

This kind of situations when we take credit from some bank.

For e.g., let's say I have taken an amount of X i.e. Present Worth(P.W.).

Now I have promised to bank that I am going to pay the amount in T years. So they will tell directly about the total amount I need to pay after T years and this is Total Amount. The Same situation also comes when we sell something to someone who is not able to pay now and instead ask him to pay the amount after some time but at some interest.

For eg. I am to sell my watch at Rs. 1000 to you and you don't have money now to pay so I will tell you to pay rs 1500 after 2 years. It means that PW is 1000 and True Discount is 500.

The rate of interest (R) can be calculated by using simple formula TD = PW * T * R.

P.S. Please go by basics only. Don't use the formulae blindly.

Thank You.

Guys, there is only a little difference between SI and True Discount(TD).
SI is always calculated on the principal amount while TD is always calculated on the PW.

For eg., If the amount g is given as 1000 the SI will be SI = 1000 * R * T.
But for TD, first we need to get PW = (1000 - TD).
Then, TD = (1000 - TD) * R * T.

Hope you guys find it helpful. Thank You.

First we have to find the value of (R*T) using the formula for PRESENT WORTH.
AMT = PRESENT WORTH + TRUE DISCOUNT.

Then calculate the value for (T/2) i.e., (R*T)/2, using this value and the same amount calculate the new PRESENT WORTH.

Case 1:

PW would be (260-20) = 240.

20 = 240xrxt.

rt = 1/12.

case 2:

Sum due = 260, let's take true discount be 'X'.

PW = 260-X.

t = t/2 => rt = 1/24.

X = (260-X) x 1/24

25X = 260

X = 10.4.

T.D = 10.4.

T.D = 20
Amount = 260
P.w = Amount - TD = 240.
S.I on p.w = 20.

By formula:
R * T = S.I * 100/p.w = 25/3.

Again by question:
Td = p.w * R * T/100.

Where the Time is half so R*T/2.
i.e 25/6.
We get TD = 10.49.

Here's the correct way,
Td=20,A=260,pw=240,
Td=pw * rt ÷ 100; rt=100/12.

ATQ, time is reduced to half so new time(rt2) will b 100/24.
Td=a * rt2/100+rt2;
Td=(260 * (100/24))÷ (100+100/24) = 10.4.

@Somesh Saurabh,
Your explanation really helped us, but could anyone correct me if im wrong:
that is why divide by 100 is Missing:
i.e, SI = P*R*T/100.
so, SI on TD = (Amount - TD *R*T)/100.

I am unable to understand such type of ques, SI & CI ques, I can solve but there occur many problems when I solve it, please tell me easy of understand such type of questions.

Thanks.

Please explain how this method is wrong
Amount is 260
PW would be (260-20)=240
20=240xrxt/100
rt=100/12

if t=t/2

TD=240 x r x t/2 x r/100
TD=240 x 100/2400
TD=10

How are you all calculate RT to be 1/12, by using TD=PW*(RT)?

Shouldn't the formula be TD=PW*(RT)/100? Which should give RT=100/12?