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Multiple choice maths money math different discounts successive discounts problems on discounts

A dealer buys a table listed at Rs 1500 and gets successive discounts of 20% and 10%. He spends Rs 20 on transportation and sells it a profit of 10%. Find the selling price of the table

  1. Rs $1800$
  2. Rs $1650$
  3. Rs $1188$
  4. Rs $1210$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\Rightarrow$  M.P of table is Rs. 1500

$\Rightarrow$  Discount percent allowed for first time is 20%
$\Rightarrow$  Price after discount = M.P - Discount 
$\Rightarrow$  Price after discount = $1500-\dfrac{20}{100}\times 1500=Rs.1200$
$\Rightarrow$  Discount percent allowed for the second time is 10%
$\Rightarrow$  Price after discount = $1200 - \dfrac{10}{100}\times 1200=Rs.1080$
$\Rightarrow$  Other cost = $Rs.20$
$\Rightarrow$  Total C.P = Rs. 1080 + Rs. 20 = Rs. 1100
$\Rightarrow$  Profit percent earned by selling the table is 10%.
$\therefore$    S.P of table = C.P + Profit
$\Rightarrow$  S.P of the table = $1100 + \dfrac{10}{100}\times 1100=Rs.1210$
$\therefore$   The selling price of table is $Rs.1210$.

Multiple choice maths money math different discounts successive discounts problems on discounts

A fan is listed at Rs. $1400$ and the discount offered is $10\%$. What additional discount must be given to bring the net selling price to Rs. $1200$?

  1. $16\dfrac {2}{3}\%$
  2. $5\%$
  3. $4\dfrac {16}{21}\%$
  4. $6\%$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

M.P. $=$ Rs. $1400$, discount rate $= 10\%$
$\therefore$ Net price after $1^{st}$ discount $= 90\%$ of Rs. $1400$
$=\dfrac {90}{100}\times 1400=$ Rs. $1260$
Final selling price $=$ Rs. $1200$
$\therefore$ Additional discount $=$ Rs. $1260 -$ Rs. $1200 =$ Rs. $60$
$\therefore$ Additional discount rate $=\left (\dfrac {60}{1260}\times 100\right )\% =4\dfrac {16}{21}\%$

Multiple choice maths money math different discounts successive discounts problems on discounts

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 second discount is

  1. $15\%$
  2. $18\%$
  3. $20\%$
  4. $25\%$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

M.P. $=$ Rs. $12$, discount rate $= 15\%$
$\therefore$ Net price after $1^{st}$ discount $=\dfrac {85}{100}\times  12=$ Rs. $10.20$
Final selling price $=$ Rs. $8.16$
$\therefore$ Additional discount $=$ Rs. $10.20-$ Rs. $8.16=$ Rs. $2.04$
$\therefore$ Additional discount rate $=\left (\dfrac {2.04}{10.20}\times 100\right )\% =20\%$.

Multiple choice maths money math different discounts successive discounts 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?

  1. Rs. $17000$
  2. Rs. $17010$
  3. Rs. $17100$
  4. Rs. $18000$
Reveal answer Fill a bubble to check yourself
C Correct answer
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$

Multiple choice maths money math different discounts successive discounts problems on discounts

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

  1. Rs. $3.50$
  2. Rs. $2.50$
  3. Rs. $1.50$
  4. Rs. $1.75$
Reveal answer Fill a bubble to check yourself
B Correct answer
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$

Multiple choice maths money math different discounts successive discounts problems on discounts

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

  1. $81\%$
  2. $31.4\%$
  3. $31.6\%$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
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$=100-68.40=31.6%$.

Multiple choice maths money math different discounts successive discounts problems on discounts

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%

  1. First

  2. Second

  3. Both first and second

  4. None
Reveal answer Fill a bubble to check yourself
B Correct answer
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

Multiple choice maths money math different discounts successive discounts problems on discounts

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

  1. 15%

  2. 18%

  3. 20%

  4. 25%
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $=20\%$.

Multiple choice maths money math different discounts successive discounts problems on discounts

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?

  1. 1st offer

  2. 2nd offer

  3. Both 1st offer and 2nd offer

  4. Cannot be determined
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

Multiple choice maths money math different discounts successive discounts problems on discounts

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 ?

  1. Rs.620

  2. Rs.600

  3. Rs.640

  4. Rs.680
Reveal answer Fill a bubble to check yourself
D Correct answer
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 $\displaystyle =Rs.\left ( \cfrac{612\times 100}{90} \right )=Rs.680$