Aptitude - True Discount - Discussion

Discussion :: True Discount - General Questions (Q.No.1)


A man purchased a cow for Rs. 3000 and sold it the same day for Rs. 3600, allowing the buyer a credit of 2 years. If the rate of interest be 10% per annum, then the man has a gain of:

[A]. 0%
[B]. 5%
[C]. 7.5%
[D]. 10%

Answer: Option A


C.P. = Rs. 3000.

S.P. = Rs. 3600 x 100 = Rs. 3000.
100 + (10 x 2)

Gain = 0%.

Angel16 said: (Jul 7, 2010)  
Did not get why SP is calculatd by the given formula. Please elaborate.

Jayaprakash said: (Aug 11, 2010)  
What is the formula?

Hafiz said: (Aug 20, 2010)  
Link fo the formula:


Nagarajan said: (Nov 16, 2010)  
Buyer purchase for Rs.3000 on credit basis so he is liable to pay Rs.600 as interest for 2 years. i.e. 3000*2*10/100=600. On the other hand, he sold on that day for Rs. 3600 which bouht for Rs.3000 so he got Rs.600 as profit.

Now, see he got Rs. 600 as profit on the purchasing day but he pays Rs.600 as interest after 2 years. so, no profit for him.

Urvi Chheda said: (Nov 20, 2010)  
wht is the formula? & how it is calculated.

Dhirendra said: (Dec 4, 2010)  
What is cp & sp?

Harsha said: (Jan 30, 2011)  
elaborate the sp formula

Asama said: (Feb 8, 2011)  
cp=cost price
sp=selling price

Dinesh said: (Feb 19, 2011)  
How did you calculated the selling price?

Madhu said: (Mar 25, 2011)  
What is the formula ?

Bessie said: (Mar 30, 2011)  
Hmmmmm interesting!!!!
Cost Price (C.P) = 3000
Sellin Price (S.P) = 3600 receivable in 2yrs

Now, to calculate the present value (P.V) of 3600, we use the following formula:

P.V = F.V/(1+i) where F.V is future value (3600)

therefore, P.V. = 3600/(1+20%)
20% because we are talking of 2yrs

P.V. = 3000 approximately

Now Gain = Present value of selling price - cost price
= 3000 - 3000

Priti said: (Jun 30, 2011)  
Bessie, thanx for explaining,

Nisha said: (Aug 22, 2011)  
What do you mean by a credit of 2 years?

Anu said: (Sep 8, 2011)  

There are two buyers. In question its not mentioned that which buyer brought it for credit whether the buyer who brought for 3000 or 3600?

Lechisagadisa said: (Sep 16, 2011)  
Credit terms for first purchaser have not mentioned.

Sangeetha said: (Sep 18, 2011)  
Here it's not specified that the first man bought it for credit.

Sirisha said: (Sep 30, 2011)  
Why don't we think that the second man bought it for credit ?

Arpan said: (Oct 16, 2011)  
The seller made a profit of Rs.600 on the selling day, but he did that on credit of 2 years with an interest rate of 10%.

i.e 3000*10/100=300 for 1 year
for 2 years it will be 300*2=600

So, in gross he got nothing as interest as it was its future amount = 3600 after 2 years.

Arun Edathara said: (Nov 3, 2011)  
There is Easy way to understand that is 3000*10/100*2=600.

So there is no profit.

Arvind said: (Nov 13, 2011)  
As you buy anything (cow in above quest.) today you used the from not kept as it is thats why 600 may be considered as profit is it or not?

Sagar said: (Dec 16, 2011)  

Thanks a lot, your explanation helped me alot :-)

Simranjeet Singh said: (Feb 22, 2012)  

Its the correct Exlanation

Satya said: (May 11, 2012)  
Present value=future value/ (1+r/100) ^n.
With this it is coming 2974 for present value of 3600?

Aurum said: (Jul 30, 2012)  
Thanks for help

Vignesh Jagan said: (Aug 5, 2013)  
100 x Amount/100 + (R x T).

Dhruv Mahajan said: (Oct 4, 2013)  
On what basis did we decide that we need to calculate Simple Interest and not Compound Interest?

Pat* said: (Dec 6, 2013)  
Am lost help me out. How do you come up with 0%. Use a simple elaboration please.

Harry said: (May 26, 2014)  
In my understanding, the man has purchase the cow for 3000 and sold it on the same day for 3600 which means a straight gain of 600 plus the interest of 10% per annum on 3600 which comes to 720 in 2 years.

Raga said: (Jun 23, 2014)  
I am too weak in maths so please explain in detail. I don't know why 600 is consider as profit. After 2 years I got 3600. But he bought the cow for 3000 only.

Amanda said: (Sep 11, 2014)  
I think it means:.

If I did not buy that cow, but I deposited it into the bank, then after 2 years I will be able to get 3600 dollar. (because of interest).

So now I decide not to put the money into the bank but instead buy the cow, which would also give me 3600 2 years later.

So profit is 0.

Anil said: (Sep 21, 2014)  

For the amount of 3000 per year 10% interest means = 300.

Then for 2 years = 2x300 = 600.
So buyer have to credit to him 3600.
As per the question he sold at 3600.
Therefore no gain for the seller.

Xyz said: (Sep 25, 2014)  
I think it means that the buyer is paying the man $3600 two years later,

So the present value of the $3600 is ($3600/(1+0.1*2)) = $3000.

SO when you consider the present value of $3600, the man actually has $0 gain.

Jok said: (Nov 2, 2014)  
The way I saw it, a buyer is buying on credit, not the man.

Plus is it clear if buyer is paying an interest rate of 10%, because you're only calculating an interest rate as seller's loss?

Lavender said: (Dec 15, 2014)  
Very confusing how this one is worded. It was not clear at all which man was buying on credit. If the first man paid in full the 3000 then in turn sold it to the other man for 3600, then he would have had a profit.

I think this one should be reworded to make it clear that BOTH men were buying on credit.

Buddhika said: (Dec 25, 2014)  
Please explain step by step easy English.

Naveen said: (May 2, 2015)  
Can anyone please tell me what does 'Credit of 2 years' means?

Komal said: (May 28, 2015)  
Present value of 3600 which is going to be received in future with interest is 3000. It means the value of money decreases as time pass on.

In other language future 3600 plus interest is equal to 3000 in present time because of that man has a gain of 0% and the present value of the future amount will be calculated by this formula: Present Value = Future Value/(1+r/100)^n.

Rubaiyat Fahim said: (Jul 21, 2015)  
3600 this will be got after two years. So if we want to know the gain/profit we have to calculate the present value of 3600.

The formula of Present value (if not compounding):

Pv = fv/(1+r*n).
= 3600/(1+0.10*2).
= 3000.

So gain 0.

Zaid said: (Nov 8, 2015)  
I would explain this one, here is concept of Future Value & present value, If the person sold on the same day then he would get 600 as profit but here is term of 10% per annum interest which is time value of money, after two year he will get 600 as interest not as profit. So no profit no loss.

If we calculate 10 per annum interest for 2 years then we will get 600 or you may cross verify by finding the present value of 3600. It means if we discount the future cash flows we will get today value which is Rs. 3000. In short, we have to differentiate today profit & discounted value of future cash flows wink emoticon.

Gaurav said: (Jan 11, 2016)  
Allowing the buyer a credit of 2 years? What's this mean?

Vishal said: (Mar 6, 2016)  
See this question is a tricky one in its language pattern. Here its written "A man purchased a cow for 3000 and sold it the same day for 3600 " now this very statement means that the man has sold the cow instantly for 3600 rupees while making a gain of net 600 rupees. And please Note the word "Purchased" because this is the key word. Purchase means buying any thing legaly like for some agreement of emi etc in which some money is given first and remaining later on. Whereas Buy means to buy things directly without any future payment to be done.

So now here as you can see that there is only one Man being talked about, so this man Purchased the cow for 3000 on an interest rate of 10% annum for a time period of 2 year hence the man has to pay an interest of 3000*2*10/100= 600 rupees, and as you know that Man had already made a gain of 600 rupees by selling the cow for 3600 rupees, which mean that no profit actually.

And one more thing, you can also interpret this question like this. To sell a product the word Selling is only used, whereas for taking that product there are two ways, either you buy it by paying full amount, or you can purchase that product with any kind of agreement that the shopkeeper is giving like discount, installment scheme etc.

Hela said: (Mar 17, 2016)  
A = Pw+TD.
TD = Pw.R.N/100.
A = Pw +Pw.R.N/100.
A = Pw(1+R.N/1000.
Pw = A*100/100 +R.N.

Satyanarayana said: (Jul 12, 2016)  
Question is not clear, the rate of interest and due time are for cost price or selling price how we find out.

What I can understand C. P + S. I = S. P 3000 + (PTR/100) = 3000 + ( (300 * 2 * 10) /100) = 3600.
So C. P (3600) =S. P (3600) there is no gain.

Chaudhari said: (Jul 19, 2016)  
3000 's -> 10% = 300.

2year credit =300 * 2 = 600.
3600 - 600 = 3000(same to cost prize).
So, 0%profit.

Jiten said: (Aug 10, 2016)  
Guys, see no formula required for this question.

C.P = 3000, S.P = 3600.

Now if seller will deposit 3000 in bank, after 2 years his profit will be 600. Because interest is 10% per annum, so for 2 years it will be 20%. 20% of 3000 is 600. So value of 3000 in future will be same as value of 3600 in future.

Tamizharasi said: (Aug 15, 2016)  

Your explanation is very useful to understand the problem. Thank you, sir.

Shivam said: (Sep 30, 2016)  
Here the cp = 3000.
Now sp = p.w.
p.w = A - td = 3600 - p * 2 * 10/100 = 3000.
cp - pw = 0.

Thus 0 profit gain.

Abhi said: (Oct 6, 2016)  
A person purchased a watch for Rs. 3000 and sold at 3600 on credit for 9 years at the rate of interest 7. 5%. What is the gain or loss to him?

Abhi said: (Oct 6, 2016)  
A person buy a watch for Rs. 1950 in cash and sells it same day at Rs. 2200 on credit for 1 year, if the rate of interest is 10%. How much he gains?

Shalini Negi said: (May 6, 2017)  
What do you mean bu credit " allowing the buyer a credit of 2 years"? Please explain me.

Bharadwaz Bhuma said: (May 18, 2017)  
@ Shalini Negi. The buyer here is referred to the first person, the one who bought the cow for 3000. The buyer pays the money in installments. So the interest is also to be paid. Since nothing is mentioned we go with simple interest.

The buyer receives a profit of 600 (3600-3000) on the first day.

He pays the interest for 2 years which is equal to 3000*2*10% = Rs. 600.

Hence at the end of 2 years, he receives no profit i.e., 600-600 = Rs. 0.

Sem said: (Jul 23, 2017)  
Value of cow is Rs.3000

------------ =300

Now credit 2 years,
so, 300*2=600,
So 0 discount.

Riddhi said: (Jul 28, 2017)  
Why the amt is not taken to calculate gain?

Because actually, he is selling at 3600 (although at credit) but he is getting 600 as profit.

Drj said: (Nov 19, 2017)  
You are correct @Amanda.

Shra said: (Dec 18, 2017)  
What is mean by P.W?

Please, clear the concept briefly.

Abhilasha said: (May 5, 2018)  
The formula used is.

True discount = {Banker's discount x 100}/{100+ (rate x time)}.

Rahul Gupta said: (Aug 14, 2020)  
Let us assume,
(P. W) 2 = present worth in second case.
P. A = Payable amount
T. D = True Discount
P. A = (P. W) 2 + T. D.
3600 = (P.W)2 + 600.

=>(P. W)2 = 3600 - 600 = 3000
Gain = (P.W)2-PW = 3000 - 3000 = 0,
%gain= (0/3000) * 100 = 0%.
So, the Answer will be 0%.

Chandra Vardhan said: (Sep 30, 2020)  

Here let's assume that I am selling the cow to you.
So, here I purchased with 3000. So to get any profit I need to sold it to you more than 3000.

Here you agree to pay 10% interest rate per annum for 2 years.

So, When I calculate with that interest, after 2 years my cow will cost 3600. And you pay exactly 3600.

So profit is 0 for me.

Hope this is clear explanation.

Prakash Prajapat said: (Aug 25, 2021)  
As simple as that, Frist man buy and sell a cow on the same day. And he buys bow on credit 3000 for 2year on 10% interest.

So he has to pay after two years. (3000*2*10) /100=600 as interest. Total is 3600.
And he sold the cow the same day in 3600 rs.
So, at the end he did not get any profit. i.e Zero gain.

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