Tag: problems on discounts

Questions Related to problems on discounts

For the purchase of a motorcar, a man has to pay Rs. $17000$ when a single discount of $15\%$ is allowed. How much will he have to pay for it if two successive discounts of $5\%$ and $10\%$ respectively are allowed?

maths money math different discounts successive discounts problems on discounts

  1. Rs. $17000$

  2. Rs. $17010$

  3. Rs. $17100$

  4. Rs. $18000$

Show answer
Correct Option: C
Explanation:

S.P. $=$ Rs. $ 17000$, discount $= 15\%$
$\therefore$ M.P. $=\dfrac {\text{S.P.}}{(100-\text{discount})}\times 100$
$=$ Rs. $ \dfrac {17000\times 100}{85}=$ Rs. $ 20000$.
Now $1^{st}$ discount $= 5\%$
$\therefore \text{S.P.} = 20000-\dfrac{5}{100}\times 20000=$ Rs. $19000$

Second discount $=10\%$
$\therefore \text{S.P.} =19000-\dfrac{10}{100}\times 19000$

$\Rightarrow 19000-1900=$ Rs. $ 17100$

Two shopkeepers sell a radio of similar brand and type at the same list price of Rs. $1000$. The first allows two successive discounts of $20\%$ and $10\%$ and the second allows two successive discounts $15\%$ and $15\%$. Find the difference in the discounts offered by the two shopkeepers

maths money math different discounts successive discounts problems on discounts

  1. Rs. $3.50$

  2. Rs. $2.50$

  3. Rs. $1.50$

  4. Rs. $1.75$

Show answer
Correct Option: B
Explanation:

S.P. of the $1^{st}$ shopkeeper
$=$ $80\%$ of $90\%$ of Rs. $ 1000$
$=\dfrac {80}{100}\times \dfrac {90}{100}\times$ Rs. $ 1000$
$=$ Rs. $ 720$
S.P. of the $2^{nd}$ shopkeeper
$= 85\%$ of $85\%$ of Rs. $1000$
$=\dfrac {85}{100}\times \dfrac {85}{100}\times$ Rs. $ 1000$
$=$ Rs. $ 722.50$
$\therefore$ Difference in discount $=$ Rs. $ 722.50 -$ Rs. $ 720$
$=$ Rs. $ 2.50$

What is a single discount equivalent to a series discount of $20\%, 10\%$ and $5\%$?

maths money math different discounts successive discounts problems on discounts

  1. $81\%$

  2. $31.4\%$

  3. $31.6\%$

  4. None of these

Show answer
Correct Option: C
Explanation:

Let the M.P is Rs. $100$

Then, S.P. $=[100-20\%] $ of $[100-10\%]$ of $[100-5\%]$ of $100$
$\Rightarrow 80\% $ of $  90\%   $ of $95\%  $ of $  100$
$\Rightarrow \dfrac{80}{100} \times \dfrac{90}{100}\times \dfrac{95}{100}\times 100$
$\Rightarrow 68.40$
Required Discount$=100-68.40=31.6%$.

What is more favourable for a buyer:

I)A discount series of 20%, 15% and 10% 
II)A discount series of 25%, 12% and 8%

maths money math different discounts successive discounts problems on discounts

  1. First

  2. Second

  3. Both first and second

  4. None

Show answer
Correct Option: B
Explanation:

Let the marked price $= Rs.100$

S.P. for the 1st discount series
$\displaystyle \frac{80}{100}\times \frac{85}{100}\times \frac{90}{100}\times 100=Rs.61.20$
S.P. for the 2nd discount series
$\displaystyle =\cfrac{75}{100}\times \cfrac{88}{100}\times \cfrac{92}{100}\times 100=Rs.60.72$
$\displaystyle \therefore$ The second discount series is more favourable

A pen is listed for Rs.12. A discount of 15% is given on it. A second discount is given bringing the price down to Rs.8.16. The rate of the second discount is

maths money math different discounts successive discounts problems on discounts

  1. 15%

  2. 18%

  3. 20%

  4. 25%

Show answer
Correct Option: C
Explanation:

The given C.P. of the pen $=Rs. 12$.

Then, after a dicount of 15% the S.P. $=Rs. \left( 12-12\times \cfrac { 15 }{ 100 }  \right) =Rs. \cfrac { 51 }{ 5 } $.
Let the second discount be $x\%$.
Then the final S.P.=$Rs. \left( \cfrac { 51 }{ 5 } -\cfrac { 51 }{ 5 } \times \cfrac { x }{ 100 }  \right) =Rs. \cfrac { 5100-51x }{ 500 } $.
But the final $S.P.=Rs. 8.16$.
$\therefore \cfrac { 5100-51x }{ 500 } =8.16\ \Longrightarrow 51x=1020\ \Longrightarrow x=20$.
So, the rate of the second discount $=20\%$.

Two dealers offer an article at the same list price. The first allows discount 20%, 10%, and 5% and the other of 15%, 12%, and 8%. Which is a better offer for the customer?

maths money math different discounts successive discounts problems on discounts

  1. 1st offer

  2. 2nd offer

  3. Both 1st offer and 2nd offer

  4. Cannot be determined

Show answer
Correct Option: A
Explanation:

Let the cost price of the article $=Rs100.$


FIRST CASE-
First discount $=20\%$.
So the first $S.P.=Rs(100-20)=Rs 80.$
Second successive discount $=10\%$.
So the second $S.P.=Rs. 80\left( 1-\cfrac { 10 }{ 100 }  \right) =Rs72.$

Third successive discount $=5\%$.
So the third $S.P.=Rs. 72\left( 1-\cfrac { 5 }{ 100 }  \right) =Rs68.4.$


SECOND CASE-

First discount $=15\%$.
So the first $S.P.=Rs(100-15)=Rs 85.$
Second successive discount $=12\%$.
So the second $S.P.=Rs. 85\left( 1-\cfrac { 12 }{ 100 }  \right) =Rs74.8.$
Third successive discount $=8\%$.
So the third $S.P.=Rs. 74.8\left( 1-\cfrac { 8 }{ 100 }  \right) =Rs68.82.$

$\therefore $ The first offer is the better offer for the customer since the final S.P. is less than that of the second offer.

An article listed at Rs.800 is sold at successive discounts of 25% and 15%. The buyer desires to sell it off at a profit of 20% after allowing a 10% discount. What would be his list price ?

maths money math different discounts successive discounts problems on discounts

  1. Rs.620

  2. Rs.600

  3. Rs.640

  4. Rs.680

Show answer
Correct Option: D
Explanation:

M.P. = Rs.800 

C.P. of the buyer = 75% of 85% of Rs.800 
$\displaystyle =\cfrac{75}{100}\times \cfrac{85}{100}\times Rs.800=Rs.510$ 

Profit = 20%
$\displaystyle \therefore$ S.P. of the buyer $\displaystyle =Rs.\left ( \cfrac{510\times 120}{100} \right )=Rs.612$ 
Discount = 10%
$\displaystyle \therefore$ List price of the buyer $\displaystyle =Rs.\left ( \cfrac{612\times 100}{90} \right )=Rs.680$

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. Increased by 10%

  2. Increased by 5.3%

  3. Decreased by 3%

  4. Decreased by 5.3%

Show answer
Correct Option: B
Explanation:

Let the original cost of the article be Rs.$x$ 

Raising it by 30% M.P. $\displaystyle =x\times \frac{130}{100}=Rs.\frac{13x}{10}$

After allowing two discounts each of 10% the price of the article $\displaystyle =\frac{13x}{10}\times \frac{90}{100}\times \frac{90}{100}=Rs.\frac{1053x}{1000}$

Per cent increase in the cost of the article $\displaystyle =\frac{\left ( \frac{1053x}{1000} \right )}{x}\times 100=\frac{53x}{1000x}\times 100=5.3\%$

The price of a VCR is marked at Rs. 12,000. If successive discounts of 15%, 10% and 5% be allowed, then at what price does a customer buy it ?

maths money math different discounts successive discounts problems on discounts

  1. Rs. 8400

  2. Rs. 8721

  3. Rs. 8856

  4. None of these

Show answer
Correct Option: B
Explanation:

Marked price$=$Rs $12000 .$
First discount =$15$%
Then 15% of 12000=$\frac{15}{100}\times 12000=$Rs $1800  .$
Price of VCR after first discount=$12000-1800=$Rs $10200 $
Second discount=$10$%
Then 10% of 10200=$\frac{10}{100}\times 10200=$Rs $1020  .$
Price of VCR aftr second discount=$10200-1020=$ Rs $9180  .$
Third discount=5%
Then 5% of 9180=$\frac{5}{100}\times 9180=$Rs $ 459 $
Price of VCR that customer pay=$9180-459=$Rs $8721 $

Two shopkeepers announce the same price of $Rs. 700$ for a sewing machine. The first offers successive discounts of $30%$ and $6%$ while the second offers successive discounts of $20%$ and $16%$. The shopkeeper that offers better discount, charges ........ less than the other shopkeeper.

maths money math different discounts successive discounts problems on discounts

  1. $Rs. 9.80$

  2. $Rs. 16.80$

  3. $Rs. 22.40$

  4. $Rs. 36.40$

Show answer
Correct Option: A
Explanation:

Price of sewing machine=700
First shopkeeper offers 30% and 6% discount
Then$\frac{30}{100}\times \frac{6}{100}\times 700=12.60$
Second shopker offers 20% and 16% discount
Then$\frac{20}{100}\times \frac{16}{100}\times 700=22.40$
Difference of discount=$22.04-12.06=9.80  Rs.$
Hence ,Second shopkeeper offers  better discount, charges 9.80  less than the first  shopkeeper