Aptitude - True Discount - Discussion

CONCEPT OF THE QUESTION:

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.

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.

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.

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.

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.

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... :).

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.

@All.

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.

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.

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.