Aptitude - True Discount - Discussion

Discussion :: True Discount - General Questions (Q.No.3)


A trader owes a merchant Rs. 10,028 due 1 year hence. The trader wants to settle the account after 3 months. If the rate of interest 12% per annum, how much cash should he pay?

[A]. Rs. 9025.20
[B]. Rs. 9200
[C]. Rs. 9600
[D]. Rs. 9560

Answer: Option B


Required money = P.W. of Rs. 10028 due 9 months hence
= Rs. 10028 x 100
100 + 12 x 9
= Rs. 9200.

Shashi Mishra said: (Mar 1, 2011)  
Why 100 is added in denominator?

Gnana said: (Mar 13, 2011)  
How answer comes 9200? I have tried in my calculator but it show me 3963. 63, How could this possible, please can any one post here.

Sundar said: (Mar 14, 2011)  

It is simple yar.

1. 10028 x 100 = 1002800

2. 100 + (12 x 9/12) ; here 12 will get cancelled, So 100+9 = 109

3. 1002800/109 = 9200 thats all.

Naveen said: (Apr 1, 2011)  
You have done a good job. Superb and thanks.

Vidu said: (May 11, 2011)  
How it s 9 months, please can anyone explain me ?

Mohan said: (Jun 8, 2011)  
Trader wants to pay after 3 months. But Trader owes a merchant 1 year hence for Rs. 10028/-. Since trader wants to pay after 3 months he has minus the 9 months interest (i.e., 12-3 months) from 10028. So 9 will comes into the picture here... I hope u will understand now...

Anuj Ojha said: (Jun 17, 2011)  
Thanks for the explanation.

Nikhil said: (Sep 9, 2011)  
Can anyone explain me meaning of this problem, I couldn't understand it properly?

Nitin Anuj said: (Sep 14, 2011)  
I think its the wrong answer..

Actually we can't use the formula like that.

Using 9/12 we means that the interest is on the value 3 months hence. But according to the question value 10028 is due 1 yr hence .

So first P.W.=(100 x 10028)/(100+(12x1))

Then, Amount=(100+(12x3/12))/100

and that would be the answer which is not 9200.

Please comment.

Devanshu Chourasiya said: (Sep 14, 2011)  
Trader wants to pay after 3 months. But Trader owes a merchant 1 year hence for Rs. 10028/-. Since trader wants to pay after 3 months he has minus the 9 months interest (i.e., 12-3 months) from 10028. So 9 will comes into the picture here. Good one.

Madhu said: (Sep 27, 2011)  
Rs. 10028/- has to be paid after 1 year including interest 12% P.A.
Present worth = 10028*100/112=8953.57
But he wants to pay after 3 months with interest 12% P.A
Interest = 8953.57*(12/100*(3/12)
= 268.60
Total Amount to be paid after 3 months = Present worth + 3 Months Interest.
i.e. 8953.57+268.60
= 9222.17

I got this Ans. Pls any body can help me on this.

David said: (Nov 18, 2011)  
What Madhu said makes sense to me? Please elaborate.

Rajee said: (Dec 8, 2011)  
Question must be like this he settle before 3 month...so we have calcutate 9 month intrest....
10028=intrest +pw( one year)......(1)

10028=9pw/100+pw from 1
so pw=9200

Garima said: (Aug 11, 2012)  
What is PW?

Prash said: (Aug 20, 2012)  
I've also calculated same as Madhu..

Prashant said: (Sep 1, 2012)  
In this question if we are taking money.that mean u have to pay for whole period and in this question he paid s.i. monthly.so he want to settle after 3 months....remaining month is 9.it means he will pay for 9 month completely.
the value of x=9200
am i correct?

Sankar said: (Feb 23, 2013)  
What @Rajee has said absolutely correct, the question the trader wants to settle the account after 3 months means he retained the amount with him for 3 months and then settled so he should pay 3 months interest not 9 months. So after must replace with before if we take 9 months into consideration.

Pooja said: (May 25, 2013)  
9/12 is in terms of years whereas 12 is in terms of months then why in the solution multiplication is performed between values with different units? how is it possible?

It is (9*12) or (1*9/12).

Jayadeep said: (Jul 5, 2013)  
A trader owes a merchant Rs. 10,028 due 1 year hence. Can anyone explain me the meaning?

Rucha said: (Jul 7, 2013)  
In short it means he has taken some money on loan for which he has to pay Rs. 10028 after 1 year.

Kanika said: (Jul 9, 2013)  
Which formula is used in this case? kindly tell me. Is there any alternative solution of this problem?

Sai said: (Aug 6, 2013)  
It did not understand this question can anyone explain in detail with right solution?

Ruthvik said: (Aug 16, 2013)  
What is PW? Somebody explain and elaborate.

Sandip said: (Aug 24, 2013)  
Why 9/12? what is the actual formula can anybody explain me it in deeply?

Krish said: (Sep 13, 2013)  
The trader is to pay 10028 to the merchant after an year as total sum(amount taken + interest). Instead he chooses to pay it back within 3 months i.e now he would have had to pay an interest for only 3 months on the amount taken instead of for 1 year. Logically calculate amount taken(8953) and calculate 3 months interest and so answer should be 9222.

Shivam Sadh said: (Oct 18, 2013)  
Yeah @Madhu @krish @david.

What you all said make sense to me too.

And even I am getting the same answer which is 9222.17.

Can anyone here please explain the answer given by our own Indiabix.

Thank you.

M.Raheel.Sultan said: (Jan 11, 2014)  

As the trader is settling the account after 3 months, that means he will going to recognize the amount (INT + down pay) for 3 months.

Opinion: In this forum I've analyzed 2 ways of treating the question, both methods are like a integer line (negative to positive)

1 Method: (Positive one):

10028*100/(109) = 9200.

IN THIS METHOD, Since, 10028 includes (3%+9%+down payment) people is making 10028*100 is equal to cost and then 1002800/109, which automatically lead us to the amount 9200 which includes (3% interest + down payment).

Finally:10028*(100/109) = 9200.

2 Method: (Negative one):

IN THIS METHOD, people are finding the down payment first by doing 10028*(100/112), then finding the interest for 3 months
8953.57*(12%)*(3/12) and adding them.

Finally:10028*(100/112)*(103/100) = 9222.17

IN 2nd method the whole interest is taken out first then it applied for three month as 8953.57*(12%)*(3/12) = 8953.57*1.03.

Conclusion: Both the methods are right at their own places, but 1 method is much better as it do not have double effect and no by dividing 10028/109, we make appropriately, but this figure is approximately calculated as both of 109 and 103 figs has gotten disturbed 8953.57*1.03.

RULE: Only! The total amount is divided by unnecessary Figure to get to the required figure.

Nandha said: (Aug 12, 2014)  
Hi Guys,

Always the P.W is calculated with due "n" year hence.

To Understand further, Normally first we would calculate P.W for this Rs.10068 with 1 year due hence.

But in this case the trader wants to settle 3 months later, which means we need to find the P.W 3 months later.

That is why 9 months is taken to calculate P.W after 3 months.

Hope this helped... :).

Ashish said: (Aug 31, 2014)  
PW = Present worth.

Dhanjit said: (Dec 9, 2014)  
Guys, where I will be able to get the full concept on this chapter please help. I too calculated PW as 8953.57 first. Please suggest a book or any other link. Thank you.

Shivangi said: (Jul 14, 2015)  
In previous formula what amount should be considered as amount specified in it? amount adding true discount or present worth.

It is not about this example specifically in general for all problems. Can anyone help me?

Neha said: (Jul 21, 2015)  
I didn't understand the formula for P.W. Please help.

Vishwajeet said: (Aug 3, 2015)  
10028 = p+prt/100 = p+12p/100 = 112p/100.

=> p = 10028*100/112 = 8953.57.

Now for 3 months.

Amount = p+prt/100 = p+3p/100 = 103p/100.

Therefore, amount = 103*8953.57/100 = 9222.17.

Only solution!

B>is Round Off.

Shibam Gupta said: (Nov 7, 2015)  
I got the answer as 9222 and I think if you go conceptually then it is right. Because if you pay interest, then you pay it on the actual principal and not from the amount where interest is already included.

Gopikrishna said: (Dec 16, 2015)  
1. P.W = 10028*100.

2. Due have payed in 3 months = 9/12.

3. Interest = 12%.

4. Rs = (10028*100)/100+(12*9/12).

5. 9200.

Sabari said: (Mar 2, 2016)  
@gopikrishna. From where did you get PW? I'm sorry, I can't understand the question.

Parul Mehta said: (Jun 24, 2016)  
In the first attempt, I also calculated the answer Rs. 9222.17 but this approach is wrong.

Because merchant makes a deal for one year and trader is paying before the due date so we have to subtract interset on that amount for 9 months.

The amount that trader has to pay after 1 year, he settles it after 3 months i.e. 9 months before the due date.

So PW of the amount now after 3 months i.e. 9 months before the actual payment as the deal is done can be calculated simply as given in the solution.

Ramesh said: (Jul 18, 2016)  
I didn't understand this, please explain me.

Abhinav said: (Sep 1, 2016)  
It would be 10028/(1.12)^(9/12) = 9210.87.

Yamini.R said: (Sep 9, 2016)  
Why 100 is added in the denominator?

Amit Ambadkar said: (Jun 13, 2017)  
Present worth = not given.

p.w + t.d = 10028 given --> 1

From above find p.w first
i.e, t.d=p.w*1*12/100 --> (2)
t.d=0.12p.w; put in (1).

Now from p.w find t.d for 3 months which is 268.605 --> formula given in(2))
Amount should pay = total=p.w+t.d for 3 month.
= 8953.571+268.805 = 9222.17.

Manjunath said: (Jul 5, 2017)  
In this question, the time is given as 1 year so the amount to be paid is 10028.

Now, he wants to pay in 3 months. And question is, what is the amount he pays. so the pw of the money in the 3rd month should be calculated.
Now the amount 10028 is for 1 year and so if we use time as 1 year we get pw of 1 year before but what we need is the pw of the money after 3 months so the time reduces to 9 months from 1 year.

Prabal Sinha said: (Sep 24, 2019)  
Just by basics:

Principle + 12%of principle for 1 year = 10028,
P = 8953.57.

Now we need to put interest for 3 months or 1/4th year.
8953.57 + (1/4)*(12/100) * 8953.57.
= 8953.57 + 268.60,
= 9222.17.

Anonymous said: (Oct 30, 2019)  
Please understand the basic concept, in question, they asked about the present worth.

So, and we know 10028 is the money after one year of something present worth so to calculate after 3 months which means. Whatever the present worth it should have to reach eqaul to 10028 after the 9 month.

Suppose if he asked after the 9 month then meaning of question will be, you have to calculate money which should have to reach 10288 after three months.

Plasi said: (Jun 21, 2020)  

We need to find out an amount of money(SAY, X) that will generate 10028 in 9 months (remember, originally 10028 was due in 12 months, now it is due in 9 months).

So basically,
10028 = X + (X*R*T)/100,
10028= X + (X* 12* 9/12)/100,
10028= X + (X*9)/100 as 12 gets cancelled,
10028= (100X+9X)/100,
10028*100 = 109x.
X= (10028 * 100)/109 = 9200.

Aishu said: (Jul 18, 2020)  

Your explanation is clear. Thank you so much.

Ayushi Garkoti said: (Aug 22, 2020)  
Just use a simple formula- SI= P*R*t/100 , ans easily solve the question.

Amount = 10028 i.e, P+S.I.
10028 = P+ S.I or S.I= 10028- P.
10028 - P = {P*12*(9/12)}/100,
1002800 = 109P,
P= 9200.

Vishnu Vardhan Reddy said: (Sep 3, 2020)  
@Ayushi Garkoti.

Why do you take a time period of 9 months? Please explain.

Charan said: (Nov 9, 2020)  
It is like this.

Actually, interest was put for whole 1 year (starting from January).
But he tells that, he will pay after 3 months (starting from April).

Meaning he is going to start to pay interest from 3rd month to 12th month, that means only 9 months.

Tanav said: (Jul 1, 2021)  
The trader buys something at a credit of 12008 Rupees which he has to pay after 1 year. But, he wants to pay the amount after 3 months rather than the whole year. So, we find the present worth of the money at the end of 3 months, on which 9 months of interest will be equal to the sum due, i.e., 12008 rupees.

Using the formula,
Sum due * 100/100+(R+T)
= 12008 * 100/100+(12 * 9/12)
= 9200 Rupees.

Correct me, if I am wrong.

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