Question

If 3 dupattas are offered free on purchase of 6 dupattas priced Rs.1200 each, what is the effective discount on each dupatta?
(a) 25%
(b) 20%
(c) 12.5%
(d) 33.33%

Answer 1

Hint: To solve this question we will first of all determine the actual and effective cost of one dupatta using the unitary method. We will take 6 dupattas for actual cost and 6+3=9 for effective cost calculation. Then we will calculate the discount and discount percentage using the formula.
Discount = actual cost – effective cost.
Discount % = (Discount / actual cost) \[\times 100\]

Complete step-by-step answer:
Given that 3 dupattas are offered free on purchase of 6 dupattas priced Rs.1200 each. The effective price on each dupatta is to be determined.
We know that the price of 6 dupattas is Rs.1200.
Then using the unitary method, we get that the price of 1 dupatta will be = \[\dfrac{1200}{6}=200\].
So the cost of 1 dupatta is Rs.200.
Now 3 dupattas are given free.
So, basically we are paying Rs.1200 for 6 + 3 = 9 dupattas.
Using the unitary method, we can get the effective cost of each dupatta is = \[\dfrac{1200}{9}\].
\[\Rightarrow \] The effective cost of 1 dupatta is = \[\dfrac{400}{3}\].
So, this \[\dfrac{400}{3}\] is the effective cost of 1 dupatta and 200 is the actual price of 1 dupatta.
Discount = actual price – effective price
Discount = 200 - \[\dfrac{400}{3}\]
Discount = \[\dfrac{200\times 3-400}{3}\]
Discount = \[\dfrac{200}{3}\]
Now we have to calculate the discount percentage.
Discount % = (Discount / Actual cost) \[\times 100\]
Substituting all the values we get;
Discount % = \[\dfrac{\dfrac{200}{3}}{200}\times 100\]
Discount % = \[\dfrac{100}{3}=33.33\%\]
So, the correct answer is “Option D”.

Note: Here we have to determine the discount on each dupatta. The possibility of error in this question can be calculating the discount on all of the 9 dupattas which would be wrong. Also while applying the discount percentage formula, seeing the term effective discount in the question, students might divide the discount by effective cost instead of actual cost. So, this mistake must be avoided. We first need to determine the cost of 1 dupatta then calculate discount and discount % on that 1 dupatta.