Tag: problems on discounts

Questions Related to problems on discounts

Choose the most appropriate option.
A shop gives $15\%$ discount on the purchase of a T.V. If paid for in cash immediately, a further discount of $12\%$ is given. If the marked price is Rs. $15,000$, what is the price of the T.V if cash purchase is made?

maths money math different discounts successive discounts problems on discounts

  1. Rs. $12,750$

  2. Rs. $11,220$

  3. Rs. $10,950$

  4. Rs. $11,475$

Show answer
Correct Option: B
Explanation:

The marked price of T.V. $=Rs.15,000$ 

Price of T.V after $15\%$ discount $=Rs.\left(15,000-\dfrac{15}{100}\times 15000\right)$

                                                      $=Rs.\left(15,000-2250\right)$
                                                      $=Rs.12,750$
Price of T.V. again after $12\%$ discount $=Rs\left(12,750-\dfrac{12}{100}\times 12750\right)$

                                                               $=Rs.\left(12750-1530\right)$
                                                               $=Rs.11,220$

$\therefore$  The price of the T.V if cash purchase is made is $Rs.11,220.$

Find the single discount which is equivalent to three successive discounts of 20%, 10% and 5%.
Hence, find the selling price of an article marked at Rs. 250. 

maths money math different discounts successive discounts problems on discounts

  1. 31.6%; Rs. 171

  2. 31.8%; Rs. 171

  3. 31.6%; Rs. 178

  4. 31.6%; Rs. 71

Show answer
Correct Option: A,B
Explanation:

Given marked price is Rs 250
Selling price after Ist discount =100-20=80 Rs
Selling price after 1st discount=$\frac{80\times 250}{100}= 200$Rs
Selling price after 2nd discount=Selling price after 2nd discount=$\frac{90\times 200}{100}= 180$Rs
Selling price after third discount=$\frac{95\times 280}{100}= 171$Rs
Total discount = 250-171=79 Rs
% of total discuont =Selling price after 2nd discount=$\frac{79\times 100}{250}= 31.6$%

Two shopkeepers announce the same price of Rs.700 for a shirt. The first offers successive discounts of 30% and 6% while the second offers successive discounts of 20% and 16%. The shopkeeper who offers better discounts charges ______ less than the other shopkeeper.

maths money math different discounts successive discounts problems on discounts

  1. Rs. 22.40

  2. Rs. 16.80

  3. Rs. 9.80

  4. Rs. 36.40

Show answer
Correct Option: C
Explanation:

M.P. of the shirt = Rs.700 

S.P. of the shirt 1st shoopkeeper = 70% of 94% of Rs.700
$\displaystyle =\frac{70}{100}\times \frac{94}{100}\times Rs.700=Rs.460.60$
S.P. of the shirt offered by the 2nd shopkeeper = 80% of 84% of Rs.700
$\displaystyle =\frac{80}{100}\times \frac{84}{100}\times Rs.700=Rs.470.40$
$\displaystyle \therefore$ 1st shopkeeper offers better discounts and 
Required difference $= Rs.470.40 - Rs. 460.60 = Rs.9.80 $

A single discount equal to a discount series of 10% and 20% is

maths money math different discounts successive discounts problems on discounts

  1. 25%

  2. 30%

  3. 35%

  4. 28%

Show answer
Correct Option: D
Explanation:

$100\, \times\, \displaystyle\frac{100\,-\,10}{100}\, \times\, \frac{100\, -\, 20}{100}$


 = $100\, \times\, \displaystyle\frac{90}{100}\, \times\, \frac{80}{100}\,=\, 72$

$\therefore$ Single discount $= 100 - 72 = 28 \%$

The price of an article is raised by 30% and then two successive discounts of 10% each are allowed ultimately, the price of the article is

maths money math different discounts successive discounts problems on discounts

  1. decreased by 5.3%

  2. increased by 3%

  3. increased by 5.3%

  4. increased by 10%

Show answer
Correct Option: C
Explanation:

Let the original price=100 Rs.
Then marked price=130 Rs.
First discount=10%
Then 10% of 130=$\frac{10}{100}\times 130=13  Rs$
Price of article after first discount=$130-13=117  Rs$
Second discount=10%
Then 10% of 117=$\frac{10}{100}\times 117=11.70  Rs.$
Price of article after second discount =$117-11.70=105.30 Rs.$
$\therefore  increase  in  price=105.30-100=5.30$
$increased  percentage=\frac{5.30}{100}\times 100=5.30$
Hence the price of article increased by 5.30 %.
 

The $MP$ of a watch was $720$. A man bought the same for $550.80$ after getting two successive discounts, the first being $10%$. What was the second discount rate?

maths money math different discounts successive discounts problems on discounts

  1. $12%$

  2. $14%$

  3. $15%$

  4. $18%$

Show answer
Correct Option: C
Explanation:
Given:
The Marked Price, $MP$ of the watch is $Rs.\ 720$.
The Selling Price, $SP$ of the watch is $Rs.\ 550.80$.
The first discount is $10\%$.


Let the second discount be $x\%$.

According to the question,

$550.8=720\times \dfrac{90}{100}\times \dfrac{(100-x)}{100}$
$55080=(72\times 9)\dfrac{(100-x)}{100}$
$55080=64800-648x$
$x=\dfrac{9720}{648}$
$x=15\%$


Hence, the second discount is $15\%$.

Find the single discount equivalent to two successive discounts of 20% and 10%

maths money math different discounts successive discounts problems on discounts

  1. 28%

  2. 29%

  3. 30%

  4. 26%

Show answer
Correct Option: A
Explanation:

Let the marked price of an article be Rs. 100
Then first discount on it =Rs. 20
Price after discount =Rs. (100-20)=Rs. 80
Second discount on it =10% of Rs. 80
$Rs.(80\times \frac{10}{100})=Rs.8$
Price after second discount =Rs. (80-8)=Rs. 72
Net selling price =Rs. 72
Single discount equivalent to given successive discounts =(100-72)%=28%

Find the successive discount equivalent to $10\%$ and $5\%$.

maths money math different discounts successive discounts problems on discounts

  1. $14.5\%$

  2. $15\%$

  3. $15.5\%$

  4. $16\%$

Show answer
Correct Option: A
Explanation:

$\Rightarrow$  Let A = First discount = 10% and B = Second discount = 5%.

$\Rightarrow$  Equivalent Discount = $(A+B)-(\dfrac{A\times B}{100})$

$\Rightarrow$  Equivalent Discount = $(10+5)-(\dfrac{10\times 5}{100})=15-0.5=14.5\%$

Successive discounts of $12\dfrac {1}{2}$% and $7\dfrac {1}{2}$% are given on the marked price of a cupboard. If the customer pays $Rs. 2,590$, then what is the marked price?

maths money math different discounts successive discounts problems on discounts

  1. $Rs. 3,108$

  2. $Rs. 3,148$

  3. $Rs. 3,200$

  4. $Rs. 3,600$

Show answer
Correct Option: C
Explanation:

Let the marked price be $Rs. 100$
Price after $1st$ discount $= Rs. 87\dfrac {1}{2}$
Price after $2nd$ discount $= Rs. 87\dfrac {1}{2} - 7 \dfrac {1}{2}$% of $87\dfrac {1}{2}$
$\therefore$ Customer pays $= 92\dfrac {1}{2}$% of $Rs. 87\dfrac {1}{2}$
When the customers pay $Rs. 2590$, then the marked price
$= \dfrac {2590\times 100}{92\dfrac {1}{2} \times 87\dfrac {1}{2}} = Rs. 3,200$.

A shopkeeper marked his price for $Rs. 150$. He pays a customer $10$% discount and second discount $5$%. What does he get?

maths money math different discounts successive discounts problems on discounts

  1. $Rs. 122.50$

  2. $Rs. 125$

  3. $Rs. 128.25$

  4. $Rs. 172.50$

Show answer
Correct Option: C
Explanation:

Marked price$=Rs.\ 150$

First discount$=10\%$
Hence, price after first discount$=150-\dfrac{10}{100}\times 150=150-15=Rs.\ 135$.
Now, second discount$=5\%$
Hence, price after second discount$=135-5\%\ of\ 135=135-6.75=Rs.\ 128.25$
So, he get $Rs.\ 128.25$