Tag: problems on discounts

Questions Related to problems on discounts

Four dealers advertise the same list price for a TV set. Which one of the following discount series is more advantageous to the customer?

maths money math different discounts successive discounts problems on discounts

  1. 25% and 8%

  2. 22% and 8%

  3. 25% and 9%

  4. 25% and 10%

Show answer
Correct Option: D
Explanation:
Let the price of TV be $x$
A. $25\%$ and $8\%$ successive discounts
$\Rightarrow$ Net price $= \dfrac{(100-25)}{100} \times \dfrac{(100-8)}{100} x$
                      $= 0.69x$

B. $22\%$ and $8\%$ successive discounts
$\Rightarrow$ Net price $= \dfrac{(100-22)}{100} \times \dfrac{(100-8)}{100} x$
                      $= 0.7176x$

C. $25\%$ and $9\%$ successive discounts
$\Rightarrow$ Net price $= \dfrac{75}{100} \times \dfrac{91}{100}x$
                     $= 0.6825x$

D. $25\%$ and $10\%$ successive discounts
$\Rightarrow$ Net price $= \dfrac{75}{100} \times \dfrac{90}{100}x$
                     $= 0.675x$
$\therefore$ D is the most advantageous discount series for the customer.

Which discount series is profitable to the buyer $25\%, 12\%, 3\%$ or $18\%, 17\%, 5\%$?

maths money math different discounts successive discounts problems on discounts

  1. First

  2. Second

  3. Both

  4. Neither first nor second

Show answer
Correct Option: A
Explanation:

Let the sum be $x$.

Case 1:
Sum after 1st discount$=x-.25\times x$
                                       $=0.75\times x$
Remaining sum after 2nd discount $=0.75x-0.12\times 0.75x$
                                                          $=0.66x$
Remaining sum after 3rd discount$=0.66x-0.03\times 0.66x$
                                                          $=0.6402x$
$\therefore $Overall discount$=x-0.6402x$                 
                              $=0.3598x$                        
$\therefore$ Overall discount in %$=0.3598\times 100$
                                       $=35.98$%

Case 2:
Sum after 1st discount$=x-.18\times x$
                                       $=0.82\times x$
Remaining sum after 2nd discount $=0.82x-0.17\times 0.82x$
                                                          $=0.6806x$
Remaining sum after 3rd discount$=0.6806x-0.05\times 0.6806x$
                                                          $=0.64657x$
$\therefore $Overall discount$=x-0.64657x$                 
                              $=0.35343x$                        
$\therefore$ Overall discount in %$=0.35343\times 100$
                                       $=35.343$%
Thus, the first case is more profitable.