Successive discounts - class-VII

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

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=$\frac{79\times 100}{250}= 31.6$%

M.P. of the shirt = Rs.700 

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

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 %.
 

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%

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

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
$= \dfrac {2590\times 100}{92\dfrac {1}{2} \times 87\dfrac {1}{2}} = Rs. 3,200$.

Marked price$=Rs.\ 150$

Let the discount price be$x$.

$ Assume MP =Rs 100$

After successive discounts $= 100 [1-\dfrac{20}{100}] [1-\dfrac{5}{100}][1-\dfrac{10}{100}]$

Discount from Marked Price $=100-68.4 =31.6$

% Discount $=\dfrac{31.6}{100} \times 100 =31.6$

The marked price of VCR is $Rs.12000.$

Sale Price = $250\left( 1-\cfrac { 20 }{ 100 }  \right) \left( 1-\cfrac { 15 }{ 100 }  \right) =250\left( \cfrac { 80 }{ 100 }  \right) \left( \cfrac { 85 }{ 100 }  \right) =250\left( \cfrac { 68 }{ 100 }  \right) $

To calculate the equivalent discount of 40% and 20%, use the formula: 100 - (100 * 0.6 * 0.8) = 100 - 48 = 52%.

Two successive discounts of 4% are calculated as: 100 - (100 * 0.96 * 0.96) = 100 - 92.16 = 7.84%.

Let the Marked price be $ x $
After $ 10 $ % discount, the Selling price becomes $ 0.9 x$
After further $ 15 $ % discount, the selling price becomes $ 0.85 \times 0.9x = 0.765x $

Given, SP $ = Rs 459 $
$ => 0.765 = Rs 459 $
$ => x = Rs  600 $

Hence, marked price is $ Rs  600 $

Marked Price of an article=Rs 800.
Price after 1st discount $=$ Rs $800-\cfrac { 10 }{ 100 } \times 800$
$=$Rs $720$
Price after 2nd discount $=$ Rs $720-\cfrac { 5 }{ 100 } \times 720$
$=$Rs $684$
Price after 3rd discount $=$ Rs $684-\cfrac { 3 }{ 100 } \times 684$
$=$ Rs $663.48$
Selling Price after three successive discounts $=$ Rs$ 663.48$

Let the original price =Rs.100

Given the Marked price is $ Rs 400 $
After $ 10 $ % discount, the Selling price becomes $ 0.9  \times 400 = Rs   360  $
After further $ x $ % discount, the selling price becomes $ \dfrac { (100-x)}{100} \times 360 $

Given, SP $ = Rs 306 $
$ => \dfrac { (100-x)}{100} \times 360 =  306 $
$ => 100 - x = 85 $
$ => x = 15 $
Hence, 2nd discount is  is $ 15 $ %

A discount of $40%$ on Rs. $1000 = \dfrac{40}{100}\times 1000$ 

M.P. $=$ Rs. $500$, $1^{st}$ discount $ = 20%$
Net price after $1^{st}$ discount $= 80%$ of Rs. $500=\dfrac {80}{100}\times 500=$ Rs. $400$
$2^{nd}$ discount $= 10%$
$\therefore$ Final S.P. after $2^{nd}$ discount $=\dfrac {90}{100}\times 400$
$=$ Rs. $360$

Let the M.P. $=$ Rs. $ 100$,
$\therefore$ S.P. $=80\%$ of $90\%$ of Rs. $ 100=$ Rs. $ \left (\dfrac {80}{100}\times \dfrac {90}{100}\times 100\right )=$ Rs. $  72$
$\therefore$ Single discount $=$ Rs. $ 100-$ Rs. $ 72=$ Rs. $ 28$
Single discount rate $=\dfrac {28}{100}\times 100=28\%$.

Given, M.P$=$ Rs. $80$

Two successive  Discount each $=5\%$

$\therefore $ S.P after first discount$=80-5\%$ of $80$

$\Rightarrow 80-\dfrac{5}{100}\times 80$

$\Rightarrow 80-4=$ Rs. $76$

Selling price after second discount $=76-5\% $ of $  76$

$\Rightarrow 76-\dfrac{5}{100}\times 76$

$\Rightarrow 76-3.80=$ Rs. $72.20$

$M.P. =Rs 800$, First discount $=$ 10%
$\therefore$ Net price after the first discount $= 90$% of $Rs 800 = 0.9 \times Rs 800 =Rs 720$
Final price after the second discount $=Rs 612$
$\therefore$ Second discount $=Rs 720 -Rs 612 =Rs 108$
$\Rightarrow$ Second discount rate $=\frac {108}{720}\times 100$% $= 15$%.

Let the M.P. $=$ Rs. $ 100$
Then, S.P. after $1^{st}$ discount of $30%$
$=100-30%$ of Rs. $ 100 =100-\dfrac{30}{100}\times 100=$ Rs. $ 70$
S.P. after $2^{nd}$ discount of $20%$
$\Rightarrow 70-$ $20%$ of Rs. $ 70 =70-\dfrac{20}{100}\times 70$
$\Rightarrow 70-14=$ Rs. $ 56$
Net S.P. after $3^{rd}$ discount of $10%$
$=56- 10%$ of Rs. $ 56=56-\dfrac{10}{100}\times 56$

CP, of the car $=$ $95\%$ of $90\%$ of Rs. $ 200000$

$\Rightarrow \dfrac{95}{100}\times \dfrac{90}{100}\times 200000$
$\Rightarrow 95\times 90\times 20=Rs 171000$
S.P. of the car $=$ Rs. $ 179550$
$\therefore$ Profit $\%$ $=\left (\dfrac {(179550-171000)}{171000}\times 100\right )$ $\%$
$=\left (\dfrac {8550}{171000}\times 100\right )$% $=$ $5$%

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

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 $=\left (\dfrac {60}{1260}\times 100\right )% =4\dfrac {16}{21}%$

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 $=\left (\dfrac {2.04}{10.20}\times 100\right )% =20%$.

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$

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$

Let the M.P is Rs. $100$

Let the marked price $= Rs.100$

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

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

M.P. = Rs.800 

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

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 $

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

Let the first discount be x%.
Then, $87.5%:of:(100-x)%:of:150=105$

$\displaystyle\frac{87.5}{100}\times\frac{100-x}{100}\times150=105$

or $\displaystyle(100-x)=\frac{105\times100\times100}{150\times87.5}=80$
$x=100-80=20$
$\therefore$ First discount $=20%$

Let the bill amount be 100.
One discount $=35$

Two successive discounts $\displaystyle\left(100-\frac{100\times80\times30}{100\times100}\right)(100-64)=36$

Difference $=36-35=1$

If the difference is 1, the bill amount is 100.
If the difference is 22, the bill amount will be $22\times100=2200$.

Two successive discounts on 15% on MP 80. Therefore,

$\displaystyle SP=80\times\frac{95}{100}\times\frac{95}{100}=72.20$

Let the selling price of the cold drink is Rs. $100$

Listed Price of mobile phone $=$ Rs. $19450$

Total discount of $20%$ and $40% =$ $20+40-\dfrac{800}{100}=52$ $%$
Discount $= 52%$ of marked price
$=\dfrac{52}{100}\times 2000=1040$
Selling price $=$ marked price $-$ discount
$= 2000 - 1040 =$ Rs. $960$

First total discount of $10%$ and $20%$ $=$ $10+20-\dfrac{200}{100}=28%$
Secondly total discount of $28%$ and $30% =$ $28+30-\dfrac{840}{100}=49.6%$
Therefore, the single equivalent discount to three successive discount of $10%, 20%$ and $30% = 49.6%$.

$\Rightarrow$  The original price of CD is $Rs.500$

Let the cost price be Rs. $100$

$100\times (\cfrac{70}{100})\times (\cfrac{80}{100})\times (\cfrac{90}{100})=\cfrac{7\times 8\times 9}{10}=\cfrac{7\times 72}{10}=50.4$
$100-50.4=49.6$

Total discount $=$ $20+45-\dfrac{450}{100}=60.5%$
The single discount equivalent to two discount $ = 60.50%$ 

Given, marked price $=$ Rs. $1250$ and discount $=6%$

Given, $P$ is the original price of item and get $20%$ discount. 

There is a initial 30% discount on a $$ 100$ speaker. This reduces its cost to $$ 70$. 

Listed price of house $=200,000$ USD

Single equivalent discount of two successive discounts of $36%$ and $4%,,:$

$\Rightarrow$  Single equivalent discount for successive discount of $10%$ and $20%$.

Let $x$ is the factor by which successive discount was given.

$SP=MP-$discount$\times MP$

$\Rightarrow$  Let $x$ be the first discount $50%$ and $y$ be the second discount $20%$.

$\Rightarrow$  Single discount equivalent for successive discounts of $20%$ and $10%$.

$\Rightarrow$  Let $x$ be the first discount $50%$ and $y$ be the second discount $50%$.

Let the discount price be$x$.

$\Rightarrow$  Let $x$ be the first discount $50%$ and $y$ be the second discount $40%$.

$\Rightarrow$  Single discount equivalent for successive discounts of $50%$ and $10%$.

Let the marked price be $M$

Discount of $60%$ on $500 = 0.6\times 500=300$

Since a single discount D, equal to three successive discounts $D _1,
D _2 and D _3$ is $D = D _1 + D _2 + D _2 - D _1D _2 - D _2D _3 - D _3D _1 +
D _1D _2D _3$, then the choices are
$0.20 + 0.20 + 0.10 - 0.04 - 0.02 - 0.02 + 0.004 = 0.424$ and $0.40 + 0.05 + 0.05 - 0.02 - 0.02 - 0.0025 + 0.001 = 0.4585.$
The saving is $0.0345.10,000 = 345 rupees$

$40$% of $Rs. 10,000$ is $Rs. 4,000; 36$% of $Rs. 10,000$ is $Rs. 3,600; 4$% of $(Rs. 10,000 - Rs. 3,600)$ is $Rs. 256. Rs. 3,600 + Rs. 256 = Rs. 3,856$;
$\therefore$ the difference is $Rs. 4,000 - Rs. 3,856 = Rs. 144$; or two successive discounts of $36$% and $4$% are equivalent to one discount of $38.56$%.

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.