5 Dec 2015

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Basics of Discounts

WHAT IS  DISCOUNT?

In the garment stores, you’ve come across this sign many times: “HURRY! 20% OFF!!
That 20% is called discount.
Suppose a Music CD has price tag of Rs.100 and the shopkeeper is offering 20% discount.
That means 20% less on the price tag.
The price you’ve to pay
=Rs.100 minus 20% of 100
=100-(20×100/100)
=100-20
=Rs. 80 you’ve to pay, to buy that music CD.
But in exam, we don’t have no time to do such lengthy calculations.
So just think in your head:
20 percent discount means you’ve to pay 100 percent minus 20 percent=80 percent of the price tag.
% means one upon hundred (1/100)
So 80% means (80/100=0.8)
So you’ve to pay 0.8 times the original price.
=0.8 x 100
=Rs. 80

Now let is learn about Successive Discounts.

SUCCESSIVE DISCOUNTS -

Successive discounts means discount on discount.
Let us take an example for better understanding.

OFFERING 10% discount on MRP then OFFERING another 10% Discount.
When we go for shopping we generally find that a number of shops are have banners with statement "50% +50% Discount" This statement seems to be ambiguous. whether the discount is 100% or something else. It should be clear that this is not 100% because these types of statements are with T&C. Let us take a problem

Q.The original price of a music CD is Rs.200. A shopkeeper offers 10% discount on this music CD and then again offers 20% discount on the new price. How much will you have to pay, finally?

A. Cost Price =Rs. 200/-
Initial discount = 10%
so the selling price after discount is 180.
Then in second part we have to find the 20% of this 180 Rs
That is 36 Rs So the amount paid by the customer will be 144Rs.

If we go by the concepts the question becomes complex and tedious. So let us learn a formula, A panacea for all Problems based on Discounts.

FORMULA :

A = B + C + (BxC)/100.

A= Result Hike .
B= Initial Hike .
C= Second Hike .This formula is a sign convention DEPENDENT
Hike  is taken + ve whereas Discount is taken as -ve.

let us solve the above problem with this formula.
In the question we were having INITIAL DISCOUNT i.e B=10 and FINAL DISCOUNT i.e C=20
putting the values in the formula

A= -10 -20 +(200/100)         { Because (-A x-B)= +A.B}
A= -28.

Let us take other Problem in which there is a hike in Price than Discount-
Q.  A shopkeeper increase the Marked Price by 20% of its Cost Price and then allows a discount of  10% on it Find the Profit of shopkeeper?
A.   In this case initial hike in price is 20% and there is a discount of 10%.So in this question B= +20 and C= -10.
putting values in the formula,
result percentage hike = +20 -10 -(200)/100.
"                "           "    = 8%.
we can verify it by conventional method
let us take C.P = Rs.100
Price after hike of 20% = 120.
Then discount of 10% on this price = 0.9 x 120= 108.
so, In this case the profit percentage is 8%.

With this formula we can solve a number of problems.

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