Aptitude - True Discount - Discussion

Hi guys I want explain the answer of this question.

For this you must have to understand the concept of true discount. Now I will give you an example from which its deliberately easy for you all.

Now suppose a person has to pay Rs. 200 after 5 years and rate of interest is Rs. 20% per annum. Clearly this statement will make sense cause initially that person must have Rs. 100. So after 5 years at 20% per annum he would be able to pay that Rs. 200 amount. So we can say that.

Initial worth = Rs. 100.

Interest= 20% per annum for 5 year.

Sum due = Rs. 200 due 5 years hence;

True Discount (T.D.) = Rs. (200 - 100) = Rs. 100= (Sum due) - (Initial worth).

We define: T. D = Interest on initial worth cause both will be the same;

And Amount = (Initial.W.) + (T. D.).

Now I hope this concept will be clear to you.

In this question it will be easy to calculate Simple interest.

i.e P*R*T/100 = S. I.

To calculate True discount equation will be:

i.e (P - T.D.)*R*T/100 = T.D.

On solving these two equation we will get a relation i.e 4.

P = (S.I * T. D.)/(S.I - T.D)

From equation on putting the value of P = Rs. 2400 R = 5% and T = 4 years we will get.

S.I = Rs. 480.

Now substituting the value of P and S.I in equation 3 you may be able to calculate the value of T.D (True discount).

2400 = (480*T.D.)/(480 - T.D.)

On solving you will get:

T.D. = Rs. 400.

Now in order to calculate the difference.

S.I. - T.D = Rs. 480 - Rs. 400 = Rs. 80.

Guys I am explaining the above formula. How it came,

Let us assume x be the year, y be the interest rate and z be the sum.
z is our answer.

For simple interest:
(x*y*z)/100=85 -------- (1)

For true discount
(x*y*(z-80))/100=80 -------- (2)

Solving 1 & 2 i.e replace x*y from equation 1 into 2
We will get
z=85*80/(85-80).

True discount is simply the discount so we will pay 80 rs less. But why we are paying less? because this 80 rs will be paid as interest to shopkeeper on z-80(after discounting) & what will be value the interest ? this 80 rs. That means.

True discount is different from simple interest.
In simple interest, we are taking the principle value -1360 add after interest we are getting 1360+85. So total value after is 1445.

But in true discount, initial amount is (1360-80)1280 and after interest it is 1360.

So final value is sum in true discount.
But initial value is sum in simple interest.

In true discount this discount will be interest and interest is applied on the discounted money(sum- discount).

To solve this question, we have to proper definitions of terms and relationship among the terms.

P. W=present worth.
P. A=Payable amount =sum.

T. D=true discount =P. W*R*t/100=80(given in the question) --------------> (1)
S.I=simple interest =P. A*R*t/100=85(as per question) --------------> (2)
After solving equ 1 & equ 2, we will get the relationship between P. W and P. A.
P. W/P. A=16/17.

That means, when P. W=16, the P. A will be 17.
Then T. D will be =17-16=1.

Means,
When T. D=1, P. A=17.
Then when T. D=85 then P. A will be 17*85=1360.
So, the Answer will be option C(1360).

If the derivation of this equation is available, that would have been very useful. Memorizing the equations may not productive always.

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