Free Practice Questions for Profit-and-loss in Maths

Let

Cost price of TV  = $x$ Rs

According to Question

$750-x$ =$\frac{(400-x)\times 4}{3}$

2250 - $3x$ = 1600 - $4x$

$7x$ = 3850

$x$ = Rs 550

Selling price if sold at 20% profit

$\frac{550\times 6}{5}$

= Rs 660

$\text{ Here, }15\mathrm{\%}+10\mathrm{\%}=2250$

$\Rightarrow 25\mathrm{\%}=2250$

$\Rightarrow 100\mathrm{\%}=9000$

Hence, 9000 be the cost price of article.

$\Rightarrow \mathrm{CP}$ of $\mathrm{C}-\mathrm{CP}$ of $\mathrm{A}=140x-85x=55x$

$\Rightarrow 55x=231$

SP of $B=100\times \frac{110}{100}=110x$

Now, $55x=231$

$\therefore 110x=462$

Let, Cost Price is x
$x\times \frac{100+8}{100}+150=x\times \frac{100+14}{100}$
$108x+15000=114x$
$6x=15000$
$x=2500$
Gain $\mathrm{\%}=\frac{2650-2500}{2500}\times 100=6\mathrm{\%}$

Profit $=12.5-8=4.5$ 

$\text{ Profit}\mathrm{\%}=(\frac{4.5}{8}\times 100)\mathrm{\%}$

$\Rightarrow \frac{450}{8}=56\frac{1}{4}\mathrm{\%}$

Let the cost price of the item purchased by Shruti be $x$.

Now,

Marked price

$\Rightarrow x+x\times 25\mathrm{\%}$

$\Rightarrow x(1+0.25)$

$\Rightarrow (x\times 1.25)$

After $10\mathrm{\%}$ discount

$\Rightarrow (\mathrm{x}\times 1.25)-(\mathrm{x}\times 1.25)\times 10\mathrm{\%}$

$\Rightarrow (\mathrm{x}\times 1.25)(1-0.1)$

$\Rightarrow (\mathrm{x}\times 1.25)\times 0.9$

$\Rightarrow (\mathrm{x}\times 1.125)$

After addition $5\mathrm{\%}$ discount

$\Rightarrow (x\times 1.125)-(x\times 1.125)\times 5\mathrm{\%}$

$\Rightarrow (x\times 1.125)(1-0.05)$

$\Rightarrow (x\times 1.125)\times 0.95$

$\Rightarrow (x\times 1.06875)$

According to the question,

$(x\times 1.06875)=2394$

$\Rightarrow x=2394÷1.06875$

$x=2240$

Let the $\mathrm{CP}$ of $\mathrm{A}$ is $3x$ and that of $\mathrm{B}$ is $5x$, then $\mathrm{SP}=\mathrm{CP}\times \frac{(100+\text{ Profit })}{100}$
$\mathrm{SP}$ of $\mathrm{A}=3x\times \frac{120}{100}=3.6x$
$\mathrm{SP}$ of $\mathrm{B}=5x\times \frac{110}{100}=5.5x$
Given that
$5.5x-3.6x$=₹ $760$ 

$1.9x$ =₹ $760$
$x$ =₹ $400$
So, the difference of cost prices $=5x-3x=2x=$₹ $800$

Let the cost price of the articles is $100x$

Marked Price $=100x\times \frac{130}{100}=130x$

Selling Price $=$ Marked Price $\times \frac{(100-\text{ Discount })}{100}$

$\mathrm{SP}=130x\times \frac{(100-20)}{100}$

$\mathrm{SP}=130x\times \frac{80}{100}$

$\mathrm{SP}=104x$

Profit $\mathrm{\%}=\frac{(104x-100x)}{100x}\times 100=\frac{4x}{100x}\times 100=4\mathrm{\%}$

Selling price $=800\times \frac{(100-30)}{100}=800\times \frac{70}{100}=$₹ 560

Cost price = Selling price $-$ Profit

Cost price $=560-60=$ ₹ 500

Profit $\mathrm{\%}=\frac{60}{500}\times 100=12\mathrm{\%}$

$\mathrm{SP}=\mathrm{CP}\times \frac{(100-\text{ Loss })}{100}$
$600=CP\times \frac{(100-20)}{100}$
$CP=\frac{600\times 100}{80}=$₹ 750
$\mathrm{SP}=\mathrm{CP}\times \frac{(100+\text{ Profit })}{100}$
New SP $=750\times \frac{(100+10)}{100}=75\times 11=$₹ 825

Let the cost price of the article is 100x, then

Selling price, when it was sold at 20% loss = 80x

And selling price, when it was sold at 15% profit = 115x

Difference between selling prices in both cases= 115x - 80x = 35x

Given that
$35x\to$ ₹ 1050
$x\to$₹ 30
So,
CP, $100x\to$₹ 3000
Profit earned on selling the article for ₹ 4000
Profit $=4000-3000=$₹ 1000
Profit $\mathrm{\%}=\frac{1000}{3000}\times 100=33\frac{1}{3}\mathrm{\%}$

Let the Cost price of the article is $\mathrm{x}$ and the profit and loss on it is a, then $x+a=832$ and $x-a=448$
$x=\frac{832+448}{2}=640$
So, Cost price of the article is ₹ 640 .
Selling price of the article, when it was sold at $20\mathrm{\%}$ loss
$=\frac{80}{100}\times 640=$₹ 512

Selling Price = Cost Price $\times \frac{(100+\text{ Profit }\mathrm{\%})}{100}$
$1020=$ Cost Price $\times \frac{(100+20)}{100}$
Cost Price $=\frac{1020\times 100}{120}=$₹ 850

For P -
Selling Price $=$ Cost Price $\times \frac{(100-\text{ Loss }\mathrm{\%})}{100}$
$18000=$ Cost Price $\times \frac{(100-20)}{100}$
Cost Price $=\frac{18000}{80}\times 100=$₹ 22500
If $P$ gets a profit of $8\mathrm{\%}$, then
$\text{ Selling Price }=22500\times \frac{(100+8)}{100}=225\times 108=$₹ 24300
So, Q sold the article to $R$ at ₹ 24300
Hence, Profit $\mathrm{\%}$ of $Q=\frac{(24300-18000)}{18000}\times 100=\frac{6300}{180}=35\mathrm{\%}$

Successive Discount $=A+B-\frac{A\times B}{100}$
For $15\mathrm{\%}$ and $20\mathrm{\%}$ -
$15+20-\frac{15\times 20}{100}=35-\frac{300}{100}=35-3=32\mathrm{\%}$
For $32\mathrm{\%}$ and $8\mathrm{\%}$ -
$32+8-\frac{32\times 8}{100}=40-\frac{256}{100}=40-2.56=37.44\mathrm{\%}$
Hence, Approximate single discount equivalent to three successive discounts of

$8\mathrm{\%},15\mathrm{\%}$ and $20\mathrm{\%}$ is $37\mathrm{\%}$.

Let the Cost price of the book is $100\mathrm{\%}$.
Cost price of the book $=\frac{625}{125}\times 100=$₹ 500
In order to gain $35\mathrm{\%}$ profit, the selling price $=\frac{500}{100}\times 135=$₹ 675

Profit % = 19  , Discount % = 15 

$\frac{MP}{CP}=\frac{100+19}{100-15}=\frac{119}{85}=\frac{7}{5}$
Let the Marked price and cost price of article 700 and 500 respectively.
As per the question,
$25\mathrm{\%}\text{ discount }=700\times \frac{25}{100}=175$
So selling price of the article $=700-175=525$
Profit $\mathrm{\%}=\frac{25}{500}\times 100=5\mathrm{\%}$

In this question the cost price of the articles is same so we can use average method to find overall profit or loss $\mathrm{\%}=\frac{12-15+6}{3}=\frac{3}{3}=1\mathrm{\%}$
So overall profit $\mathrm{\%}=1\mathrm{\%}$

Total CP                  =   4ltr    =  ₹ 150

$1\mathrm{ltr}=\frac{150}{4}=$₹ 37.5

SP of 1 ltr =₹60

profit $\mathrm{\%}=\frac{60-37.5}{37.5}\times 100$

$=\frac{22.5}{37.5}\times 100=60\mathrm{\%}$