Two shopkeepers sell the machines at the same marked price. The f
Two shopkeepers sell the machines at the same marked price. The first shopkeeper allows two successive discounts of 30% and 6%, and the second shopkeeper allows 20% and 16%. Which discount series is most advantageous to the purchaser?
A. First discount series
B. Second discount series
C. Both of these equally advantageous
D. None of these
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
Let the marked price of the machine be Rs.100
Then the price of the machine after first discount at the first shopkeeper will be,
\(\Rightarrow 100 - \frac{{100 \times 30}}{{100}} = {\rm{Rs}}.\;70\)
Now, price of the machine after second discount
\(\Rightarrow 70 - \frac{{70\; \times \;6}}{{100}} = {\rm{Rs}}.{\rm{}}\;65.8\) .......(1)
The price of the machine after first discount at the second shopkeeper will be,
\(\Rightarrow 100 - \frac{{100 \times 20}}{{100}} = {\rm{Rs}}.\;80\)
Now, price of the machine after second discount
\(\Rightarrow 80 - \frac{{80\; \times \;16}}{{100}} = {\rm{Rs}}.{\rm{\;}}67.2\) ......(2)
Comparing equation (1) and (2) we see that first series of discount is more profitable
∴ First discount series is most advantageous to the purchaser.