Aptitude - True Discount - Discussion

Discussion :: True Discount - General Questions (Q.No.6)

6. 

Goods were bought for Rs. 600 and sold the same for Rs. 688.50 at a credit of 9 months and thus gaining 2% The rate of interest per annum is:

[A].
16 2 %
3
[B].
14 1 %
2
[C].
13 1 %
3
[D]. 15%

Answer: Option A

Explanation:

S.P. = 102% of Rs. 600 = 102 x 600 = Rs. 612.
100

Now, P.W. = Rs. 612 and sum = Rs. 688.50.

T.D. = Rs. (688.50 - 612) = Rs. 76.50.

Thus, S.I. on Rs. 612 for 9 months is Rs. 76.50.

Rate = 100 x 76.50 % = 16%
612 x 3
4


Aravind said: (Dec 9, 2010)  
SP = 102 % of 600 cannot be rs. 612
Hence the answer is wrong
please correct the error
Regards
Aravind

Omer said: (Jul 14, 2011)  
How to put 9.375 in fraction in easy method to get 16*2/3

Kindly help me out

Abbin said: (Aug 9, 2011)  
On reading the Q, I had a confusion that the 2% is for Rs.600 or Rs.688.50. I think that also should be mentioned in the question.

Sirisha said: (Sep 30, 2011)  
As the gain is 2% then gain in Rupees is calculated as
gain=(2/100)*cost price
=(2/100)*600
=12

So the selling price that is the PW value becomes 600+12=612

Then TD=amount-PW=688.50-612=76.50
from this we claculate R using the formula
P.W=(100*T.D)/(R*T)

Mukesh Vyas said: (Apr 18, 2012)  
Please resolve value 102%.

Jyothi said: (Apr 3, 2013)  
Purchase price = 600 consider it 100%.

Gain 2% on purchase price.

Present value of selling price = 100% + 2% = 102%.

Anjali Singh said: (Oct 15, 2013)  
Unable to understand how we get 102%of 600 = 612. What is the formula behind it?

Likhitha said: (Jun 20, 2014)  
@Anjali.

(102/100)*600 = 612.

But I can't understand why?

P.W = (amount*100)/(R*T) this formula was used as real one is
P.W = (amount*100)/(100+(R*T).

Vignesh said: (Sep 25, 2014)  
What is pw ?

Aparna said: (Jul 8, 2015)  
Shall I know what is the formula for are how that 76.5 came here in the formula of rate?

Md. Kamrujjaman said: (May 9, 2016)  
Here gaining 2% means the gain in purchase price not 2% interest for 9 months.

So the purchase price + gain (profit) = sale price.
= 600 + 600 * 2% = 612.

Now discount 688.50 for 9 months taking 612 as P. W. (present worth).

For example:

612 = (688.50 * 100)/[100 + (x * 9/12)].
X = 50/3=>rate of interest per annum.

Venkatesh said: (May 19, 2016)  
I'm little confused. Is there any easy methods to solve and understand this problem?

Srk said: (Jun 21, 2016)  
2% profit,

hence,

600*2/100 = 12

Total = 612

So, net price 688.50 - 612 = 76.50

And the formula is for rate is used.

Deepa A J said: (Jan 11, 2017)  
Why 3/4 is taken in the problem?

Anchal said: (Feb 1, 2017)  
@Kamrujjaman.

9/12 =3/4.

Sushmita said: (Mar 30, 2017)  
Cost price= 600.

He sold the goods at a credit of 9 months, it means that the buyer will pay him after 9 months rupees 688.50. It's also given in the question that the seller has 2% profit.

So the Present value (PV) of 688.50 should be equal to 102/100 * 600 = 612.
It means SI on 612 for 9 months = 688.50 - 612 = 76.50.
612*R*9/100 * 12 = 76.50

Solving we get R = 16.666% = option A.

Hope it's clear enough.

Vijay said: (Jun 21, 2018)  
Well, it's simple.

Goods were bought for 600.
Sold for 688.50 at the credit of 9 months.
Gain = 2%,
Rate = x%.

P.W = C.P + Gain.
= 600 + 2% of 600,
= 600 + 12 = 612.

Simple Interest = 688.50 - 612 = 76.50,
By formula, P.W * R * T /100 = S.I.
R = S.I * 100 / (P.W * T).
R = 76.50 * 100 / (612 * 9/12).
R = 16.66%.

Kiran Roy said: (Oct 8, 2018)  
Why it is 9/12 instead of 12/9?

Sowmya said: (Dec 21, 2018)  
What is the formula for rate of interest?

Dulle said: (May 3, 2020)  
@Sowmya

The formula of Interest = PRT/100.

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