Question

In a certain store, the regular price of the refrigerator is $ 600, how much money is saved by buying this refrigerator at 20 percent off the regular price rather than buying it on sale at 10 percent off the regular price with an additional discount of 10 percent off the sale price?
A) 6 dollars
B) 12 dollars
C) 24 dollars
D) 54 dollars
E) 60 dollars

Answer 1

Hint: Form the mathematical equation according to the given language in question.
A percentage is a number or ratio that represents a fraction of 100. It is denoted by the symbol “%”.
While solving ‘x% of y’, keep in mind that:
% means = divide by hundreds
of means = multiplication ‘$ \times $’
A discount is a decrease in price, so the percent discount is the percent decrease in price.
Increased or more than x% indicates the addition of x% of y to y (i.e. \[\left( {\dfrac{x}{{100}}} \right) \times y + y\]); reduced or less than x% indicates the subtraction of x% of y from y (i.e. \[y - \left( {\dfrac{x}{{100}}} \right) \times y\]).

Complete step by step solution:
Step 1: given that:
The regular price of the refrigerator = $600$ dollars
Step 2: calculate cost price of refrigerator for following cases
Case (i):
Buying refrigerator at 20% off the regular price:
Hence, rebate price on 20% off the regular price = 20% of 600
                                                                                     $ = \dfrac{{20}}{{100}} \times 600$
                                                                                     = $ 120$dollars
Therefore,
costs price of the refrigerator bought on 20% off the regular price = regular price – rebate price
                                                                                                                     = $ 600 - 120$
                                                                                                                     = $ 480 $ dollars
Case (ii):
Buying refrigerator at 10% off the regular price:
Hence, rebate price on 10% off the regular price = 10% of 600
                                                                                     $ = \dfrac{{10}}{{100}} \times 600$
                                                                                     = $ 60$
Therefore, costs price of the refrigerator bought on 10% off the regular price = regular price – rebate price
                                                                                                                     = $600 - 60$
                                                                                                                    = $ 540$
Further, discount of 10% on costs price of refrigerator:
Hence, discount price of 10% on costs price of refrigerator = 10% of costs price of refrigerator
                                                                                                       $ = \dfrac{{10}}{{100}} \times 540$
                                                                                                       = $ 54$ dollars
Now, costs price of the refrigerator after 10% discount on it = previous costs price – discount price
                                                                                                           = $ 540 - 54$
                                                                                                           = $ 486$ dollars

Step 8: find the saved money by subtracting:
Difference of costs prices in case (i) and case (ii)
= costs price after 10% off and discount 10% - costs price after 20% off
= $ 486 - 480$
= $ 6$ dollars

Therefore, $ 6 is saved by buying the refrigerator at 20 percent off the regular price rather than buying it on sale at 10 percent off the regular price with an additional discount of 10 percent off the sale price. The correct option is (A).

Note:
To convert from Percentage to fraction or decimal, it is divided by 100.
For example: convert 50% to decimal.
Solution $50\% = \dfrac{{50}}{{100}}$
                         = 0.5
Convert 50% to fraction
Solution $50\% = \dfrac{{5{0}}}{{10{0}}}$
                           $ = \dfrac{1}{2}$.
To convert decimal or fraction to percentage, it is multiplied by 100.
For example: convert 0.35 into percentage.
Solution $0.35{\text{ into percentage}} = 0.35 \times 100$
                                                        = 35%
Convert $\dfrac{2}{5}$into percentage.