Aptitude - True Discount - Discussion

Discussion :: True Discount - General Questions (Q.No.8)

8. 

A man buys a watch for Rs. 1950 in cash and sells it for Rs. 2200 at a credit of 1 year. If the rate of interest is 10% per annum, the man:

[A]. gains Rs. 55
[B]. gains Rs. 50
[C]. loses Rs. 30
[D]. gains Rs. 30

Answer: Option B

Explanation:

S.P. = P.W. of Rs. 2200 due 1 year hence
= Rs. 2200 x 100
100 + (10 x 1)
= Rs. 2000.

Gain = Rs. (2000 - 1950) = Rs. 50.


Vidya said: (Oct 4, 2010)  
What is P.W. here? I can't understand that formula used.

Sundar said: (Oct 4, 2010)  
@Vidya:

P.W. - Present Worth

S.P - Selling Price

C.P. - Cost Price

T.D - True Discount

Kindly go through the Basic formulas for True Discount.

Sai said: (Jan 3, 2011)  
Using the formula sol u got is correct but logically its wrong.
let me explain
for 10% intrest 1950 will be 195 p.a
1950+195=2145
2200-2145=55

So 55 must be correct.

Pulkit said: (Jan 29, 2011)  
Totally agreed with mr sai. I have also used the same trick!

Sana said: (Feb 4, 2011)  
I think 10% should be calculated on present worth.

10% 0f 2000=200.

1950+200=2150.

2200-2150=50.

Because the rate mentioned is for present worth.

Arun Kumar said: (Feb 5, 2011)  
I also agree with sai.

I too followed the same logic.

If it is wrong could some one xplain tat?.

Ramesh said: (Mar 4, 2011)  
Here one man(lets assume some chiru) sold his watch at Rs 2200 it means some one(lets assume pavan) took that and gave 2200Rs to chiru at the interest of 10% p.a... meaning pavan gave 2200 to chiru so that he should be take interst on 2200 but not 1950 so 10% on 2200=220 but chiru buy 1950 and sold 2200 meaning he got 250 but he paid 220 interst so finally he got Rs30 gain.

So frends I think it is right.

Sumana said: (Mar 5, 2011)  
I m agree with Ramesh also.

Sachin said: (Mar 22, 2011)  
Ref: http://www.indiabix.com/aptitude/true-discount/formulas

He got 2200 after 1 year. It also include interest at 10%.

That means the watch was sold at actual price of rs.2000
200 was interest, with cant be taken as profit.

So there was a gain of Rs. 50.

Rits said: (Apr 17, 2011)  
Thanks ramesh.

Krishna said: (Apr 30, 2011)  
I am also agree with sai I also used same trick.

Abhishek said: (May 13, 2011)  
Thanks Sachin....

Pawan said: (Jun 4, 2011)  
I am also agree with sai. I also used same trick.

Aditya said: (Jun 7, 2011)  
Ya Sai is right. I have also use the same trick !

Tapan said: (Sep 11, 2011)  
Thanks ramesh.

Sayed Hamid said: (Sep 16, 2011)  
2200 is mark price and interest is 10% then
if selling price is x
then x*1.1=2200
so x=2000

Sayed Hamid Husain said: (Sep 16, 2011)  
2200 is M.P.
n if x is S.P.
then x*1.1=2200
x=2000

Mahesh said: (Sep 16, 2011)  
Thanks ramesh.

Anurag Singh said: (Oct 4, 2011)  
CP=1950. sp(after 1 yr )=2200.

Let present sp=p.
then use
SP(after 1 yr )=p+(p*r*t/100)
=> 2200=p+(p*10*1/100)
=> p=2000.

We are dealing with present values
present cp=1950
present sp=2000
=> Gain=2000-1950=50.

Sairam said: (Oct 25, 2011)  
Thanks sachin...

Faraz said: (Oct 29, 2011)  
Present value= (future value x 100) which is divide by 1 + interest rate (10)
but here you change formula
future value x 100 divided by 100 + (interest rate x 1)

Sharad Goyal said: (Nov 5, 2011)  
I agree with anurag singh.

Himani said: (Nov 16, 2011)  
Should we calcuate the value of 1950 at 10% per annum?

Kindly clear my doubt.

Amit said: (Jan 4, 2012)  
Okay let me try.

We know man buy watch for rs 1950/-
and he sell it 2200 for a credit of 1 year.

Let us assume the current price of watch is X.
So X + (X*10*1)/100 = 2200 (after one year with interest)
X= 2000rs(after calculation)

So man see watch at Rs 2000/- so he gains 2000-1950 = Rs.50 .

Soni said: (Jan 7, 2012)  
Please explain this clearly.

Madhur Goel said: (Feb 5, 2012)  
The que actually is that the man buy the watch in Rs 1950 and sells it in 2200 in one yr.

But actually the rate of interest applies that time is 10%p.a. So if calculate the interest gain by guy due to dis rate, it will come out to be

c.p*r*t/100 =1950*10*1/100=195rs.

So actually the value of watch will be 1950+195=2095rs after one yr and the man sells it in rs.2200 .so clearly he gains a profit of RS 55 in 1 year.

I think this is correct according to the concept of the prob. without any formula.

Abhinav said: (Mar 21, 2012)  
He paid 1950 ...which will turn out to be 1950+195 =2145 after 1 year....

Now according to the question he gets 2200 after 1 year so the present value stands out to be 2000....

Therefore the answer has to be 55 (2200-2145) as this will be the final result of the deal....

Karimkhan said: (Apr 9, 2012)  
55 answer is right if we think logically, and in fact 10% of 1950 is 195, that a man paid as a interest, so his cost prize become 1950+195= 2145, and then he sold at 2200.

So clear profit is - 2200-2145=55.

Shawisk said: (Jun 16, 2012)  
@all.

After reading the all above comments.
Dear all interest paid by customer not by man who sale.
So the interest is 200 for 2000.
And 2000-1950=50.

Gain 50.

Anushk said: (Oct 6, 2012)  
I agree with karimkhan. The seller gets 2200 at the end of the year. If the seller had not bought the watch, he would have an additional rs 195 at the end of the year. Logically he has only made a profit of rs 55.

Khan said: (Dec 7, 2012)  
CP=1950. SP(after 1 yr )=2200.

Let present SP=p.
Then use

SP(after 1 yr )=p+(p*r*t/100)
=> 2200=p+(p*10*1/100)
=> p=2000.

We are dealing with present values
Present cp=1950
Present sp=2000

=> Gain=2000-1950=50.
This ans is correct.

Thilak said: (Jan 28, 2013)  
The scenario is.
Let ram buys a watch for Rs1950 and sells it to Rahim for credit.
Rahim pays ram Rs 2200 at the end of one year @ 10% s.i.

i.e x amounts to 2200 @ 10% s.i.
=> x =2000 ( present value of 2200).
i.e He sells it for a present worth of 2000rs.
Therefore rams profit is 50Rs @ present worth.

Dpk said: (Mar 31, 2013)  
p+(p*10/100) = 2200.

p(1+(1*10)/100) = 2200.

p((100+1*10)/100) = 2200.

p = (2200*100)/(100+1*10) = 2000.

=>gain = 2000-1950 = 50.

Rohan Mishra said: (Aug 2, 2013)  
Correct Answer Is Rs 55. Simple Logic Says Total Cost = Rs 1950 Rate Of Interest = 10 %, Time = 1 Yrs. If This Money Is Invested It Will Yield = Rs. 1950 + 195 = Rs 2145. Hence Profit Will Be Rs 2200 - 2145 = Profit Rs 55.

Akshat said: (Aug 13, 2013)  
Yup! correct answer is Rs 55 as the amount of money for which he is losing interest income is Rs 1950 only and not Rs 2200.

Abhinandan said: (Aug 27, 2013)  
"time value of money" is its logic to solve. time value of money means, after some interval of time the value of money changes(decreases mostly).

Ex: The value of 100 Rs 10 years ago was more valuable than the present value of Rs 100.

Thus, the discussions made in the favour of gain = 50 is totally correct (because PW is used here).

Partho said: (Dec 2, 2013)  
I think philosophical debate can be done on this question. Cos logic regarding both answers are attractive.

For Rs. 50 gain : Time value of Rs. 2200 at 10% discount rate spanning over 1 year is 2000 (NPV=FV(1+i/100)). So its a gain of Rs. 50.

For Rs. 55 gain : The seller has invested Rs 1950 for one year at a rate of interest of 10% over 1 year span. So he is supposed to gain Rs. 195 at the end, but he would gain Rs. 250 so extra gain of Rs. 55.

Now we have to keep in mind that both calculations are virtual and depends on viewpoint of individual. Now think this problem another way - suppose the buyer (who is to pay Rs. 2200 after 1 year ) thinks to keep the money aside for future ease and engages somewhere at 10% interest rate for 1 year would have to bear Rs. 1980 out of his pocket and so he gets the same watch after 1 year with only Rs 30 extra cost but he has to sacrifice liquidity of Rs 2200 for one year.

Finally time value of money is always associated with investment. Here the tangible investment is Rs 1950 only and it will yield Rs. 2145 after 1 year at 10% rate and will make a gain of Rs. 55 to the "SELLER". And in pro-rate basis Rs 2200 is as good as Rs 2000 w.r.t "BUYER".

So what say?

Raju said: (Jan 25, 2014)  
I think sai is correct because how to know whether it is think logically or do formula based.

Saurabh Jain said: (Jul 10, 2014)  
Answer is wrong because,

(1950*1*10)/100 = 195.
1950+195 = 2145.
2200-2145 = 55 Rs. Gain.

Biplab Sarkar said: (Jul 18, 2014)  
Hi Saurabh/everybody,

This is what I also did earlier, But then, What you are wrong is considering 10% interest on the cost price which is wrong, Since he is not investing 1950 for 1 year but his current selling price 2000, Which is agreed over a period of 1 year.

He gains 10% on this current sp, which accumulate to 2200 over 1 year. So current selling price is 2000(with a simple interest calculations you can arrive at this figure). And hence he gains 50 rs from his current cost price of 1950.

Mildred said: (Jul 20, 2014)  
I think I agree with @Sai, we were asked to find the present value of the gain or loss in that case it would have been 50.

Anshu said: (Aug 5, 2014)  
Hey.

It can be understand like this.

Cost to the buyer is 2200.

This cost also includes the interest too.

So the selling price by the owner would be.

SP = 2200*100/110 = 2000.

So profit = 50.

Ankit said: (Aug 10, 2014)  
Suppose that he bought it for Rs 2000 then after 1 year its cost must be 2200.
But the man paid 1950 i.e 50 Rs less.

Actually here we have to calculate that what should be the initial price of the watch so that after 1 year with interest its price would become 2200.

Logician said: (Aug 28, 2014)  
Think from the seller's perspective and live at present.

Then you will get Rs.50 as the answer.

Parvez said: (Sep 16, 2014)  
Okay So the when looking from the seller's perspective the answer is correct. Thanks all.

S. Ravichandran said: (Oct 7, 2014)  
The question is bit ambiguous and so all these confusion. The question can either be what's the gain at present value or at end of one year. If it is at present value, we need to discount Rs. 2200 with 10% discounting rate to find out its present value - formula is PV = FV / (1+r)^n i.e., Present Value = 2200 (1+0.10)^1 = Rs. 2000 and so the gain would be Rs. 50.

If it is at the end of one year, Rs. 1950 + 10% would be Rs. 2145 and the gain would be Rs. 55 at the end of one year. Discounting Rs. 55 gain at the rate of 10%, you would get again Rs. 50 present value. So it depends on whether one would like to find out the gain at present value or the value at the end of one year.

It's better to frame the question like this without any ambiguity.

Santosh said: (Dec 17, 2014)  
Here the CP = 1950.

Let the principal price is x over which a 10% of interest is credited in one year.

i.e {x+x(10/100)} = 2200.

= (100x+10x) /100 = 2200.
= 110x = 220000.

x = 220000/110.
x = 2000.

So principal price = 2000 & CP = 1950.

Then profit = 2000-1950 = 50 (Ans).

Chirag said: (Feb 19, 2015)  
The fact is interest should be counted on 1950 as he would have invested it at the rate of 10% pa. So at current time he must be having 2145 if he would not have bought that watch, but he did and now he is selling it for 2200 and so he is gaining 2200-2145=55.

ANS: 55.

@Santosh:

I think we can not earn interest at the instance of time as it is matter of duration. So we can not consider here the interest on 2200 at the time of selling.

Raman Malik said: (Mar 10, 2015)  
Correct answer should be 55 not the 50. As gain would be on the amount spent not on the 2200.

Abhishek Kumar said: (Mar 22, 2015)  
@Ramesh is wrong.

How could he take interest @2200, which is the last amount to be paid i.e. interest is already included, so the principal on which interest should be calculated must be lesser than 2200 which is 2000+200 (@10%P.A.) and then the actual gain of rs 50. Out of interest is valid.

Lokendra Rajak said: (Jun 18, 2015)  
Suppose Present Worth of Rs. 2200 is A.

2200 = (A x 110)/100.

A = (2200 x 100)/110.

A = 2000.

Gain = 2000-1950 = 50.

Maninder said: (Jul 15, 2015)  
If someone has sell the thing on credit then I should get interest. So profit should increase.

Sethupathi said: (Aug 5, 2015)  
2200 is the credit for after 1 year. So (2200/110)*100 = 2000.

So the amount might be 2000. So his gain must be 50.

Mike said: (Aug 23, 2015)  
Where is 100 come from?

Nouman Rana said: (Sep 3, 2015)  
Where is 100 come from?

Viet said: (Oct 10, 2015)  
Here's my take on this:

1) By default:

Begin Year 1, he bought a watch for 1950.

End Year 1, he sold it for 2200.

2) If he deposited in a bank, he got a 10% interest:

Begin Year 1, he deposited 1950.

End Year 1, he withdrawn all out and got 1950*1.1 = 2145.

=> So at the end of year 0, he gained 2200-2145 = 55.

I don't think the author of the question intend for it as a Present Value type. The 4 answers clearly said "gains/loses", it is simple present tense, which means he only "gains" the money at the end of year 1.

He cannot gain any money when we calculate PV at the Begin of year 1, because he has not bought the watch or deposited the money yet!

Happy said: (Jan 17, 2016)  
Ok let me make this clear to all.

The man bought it at Rs. 1950 now.

The question literally means that at the end of 1 year, the man got Rs. 2200.

So Rs. 2200 is the amount.

Amount = P+SI.

2200 = P + P*R*T/100.

2200 = P + P*10*1/100.

2200 = P + 0.1 P.

Deducing from here comes P (The sum of money which the man could have got in terms of cash 1 year ago) = Rs. 2000 which is Rs. 50 (2000-1950) more than the cost price of the product (Rs. 1950).

Khadyoth said: (Feb 5, 2016)  
I = PTR/100.

= 1950*1*10/100 = 195.

Therefore A = P+I.

= 1950+195 = 2145.

GAIN = 2200-2145 = 55.

So, the man gained Rs. 55.

And correct answer is "A".

Pramod Kumar Jangir said: (May 18, 2016)  
@Sachin.

You are absolutely right. Thanks.

Cholan said: (Jul 28, 2016)  
We assume the worth to be 100 and hence sp * 100/100 + (10 * N) where N is the number of years for which the credit is offered.

Hence we get a profit of Rs. 50/-.

Sindhu said: (Aug 2, 2016)  
So 200 was the interest and 50 was the profit but why isn't 200 considered profit? I mean profit is basically the difference b/w the money I sold the product and the money I bought the product for right?

Sanchit Kukreja said: (Aug 3, 2016)  
if we think what profit he has made now and work with current values, we get the answer as 50.

If we work with future value (after 1 year, we get the answer as Rs 55). When we go with the method where we find current value of 2200 and get the value to be 2000, we see a profit of Rs 50. Here we are comparing the values in present time.

When we go with the method of applying 10% interest to 195, we compare both the values after a year.

So the profit he has made as per the current value is 50, but as per future value, it's 55.
and this justified by the fact that present value of Rs.55 after an year is Rs 50 (50 X 1.1 = 55).

The question isn't clear whether we have to determine profit on the basis of present value or value after an yer, so we assume by default that we have to calculate profit based on present values, in which case the answer is 50.

Arjun Chouhan said: (Aug 10, 2016)  
Let's assume instead of purchasing the watch if he gives that money on interest then of for interest for one year will be I = 1950 * 10 * 1/100 = 195.

So after one year his total money will be 1950 + 195 = 2145.

But he sold the watch for 2200.

So there must be a gain of 55.

Nayeem said: (Sep 9, 2016)  
A = P + I.
2200 = P + P * 1 * 10/100.
2200 = P{100 + (1 * 10)}/100.
P = 2200 * 100/{100 + (1 * 10)}
P = 2000.

GAIN = 2000 - 1950 = 50.

Murugesan said: (Sep 19, 2016)  
Friends,

CP RS -1950.
After 1 year credit the amount in bank 2200,
So the sale present, so if he increase sale Rs 50 + 1950 = 2000 After 1 year the credit amount is 200.

2000, after 1-year interest is 20.

Ajay said: (Sep 23, 2016)  
Yes, I too get the answer as 55.

Sumanth said: (Sep 25, 2016)  
The answer is 55. I can explain this clearly see.

A person invested 1950 which is Principal amount.

Given Rate = 10% PA.
Time =1 year.

So, the amount he should get back at 10% after year is (110/100) * 1950 i.e 2145.
He sold it for 2200.
He got 2200 - 2145 = 55rs profit.

Aniket said: (Nov 6, 2016)  
Please explain the answer more clearly. I couldn't get it.

Arijit said: (Dec 9, 2016)  
Let's clear it up. Say the seller is S and buyer is B.

So S bought the watch for Rs.1950. Now B said he wanted to buy the watch. S gave the selling price as Rs.2200. B bought the watch from S at Rs.2000 and asked S to keep those Rs.2000 at a bank for 1 year at 10% interest. That way after 1 year, S will get his Rs. 2200.

So, at present S made a profit of only Rs.50 although after 1 year the overall profit will stand out to be Rs.250.

This seems correct.

Please correct me if I'm wrong.

Sneha said: (Jan 28, 2017)  
I agree with you @Arijit.

Jatin said: (Feb 1, 2017)  
Guys we'll se present value of 2200.
Present value of 2200 = 2200 ÷ 1.1 = 2000,
(Let us assume present value of 2200 be x.
So x+10%of x = 2200,
1.1x = 2200,
X=2000.
Profit = 2000 - 1950 = 50.

Shubham Singh said: (Feb 15, 2017)  
If P = 100 on 10% rate of interest he have to pay I = 110.
So, 100 -> 110.
x -> 2200.
By Solving x = 2000.
So, profit is 2000 - 1950 = 50.

Rohit said: (Feb 17, 2017)  
Thanks a lot @Jatin.

Yogesh Meena said: (Apr 1, 2017)  
2200 =interest + actual selling prize.
S.p. = x
2200 = x10/100 + x,
x = 2000.

So, that 2000-1950 = 50.

Shubham Modi said: (Aug 15, 2017)  
If we take interest on Rs 2200 how can he ever face a loss cuz he is selling at Rs 2000 that means he is already selling at a profit on which he is gaining the interest profit as well. If you take in that way the profit will become 250. 50 Rs on selling the difference between buying and Selling cost and the Rate of Interest money as well.

Instead the questions wants to see that he sold that Rs 2200 at a credit of 1 year and the general annual interest rate is 10% so did he make a loss or profit by selling it rather than gaining interest on it. Hence the 10% should be calculate at 1950 and then check with 2200 if he made a profit or loss.

Hence 55 comes as the correct answer.

Rahul said: (Aug 17, 2017)  
According to me, 55 is the correct answer.

Suhail Abdul Rehman Chougule said: (Jan 23, 2018)  
The answer given here 50 is wrong it should be 55, Because Seller in Investing 1950 as to incur the cost at 10%(i.e. 195) and the buyer is paying 2200 after a year.

So, the sellers cost is 1950+195 =2145 and hence his gain in the transactions is 2200-2145 =55.

Austim said: (Jan 28, 2018)  
Why 55 is wrong?

Because according to the people who are that's not true. We cannot predict the original price of the watch in future. Maybe it can be a loss!. But definitely, we can comment on present profit. So giving a profit after 1 year implicitly invalid whether it's 50, 55 or 30 until and unless there is not mention of a rate with which original price would have increased.

Akshay Thakur said: (Jul 4, 2018)  
I also agree @Ankit.

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