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

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

$\Rightarrow 25 \%=2250 $

$\Rightarrow 100 \%=9000$

Hence, 9000 be the cost price of article.

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

$\Rightarrow 55 x=231$

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

Now, $55 x=231$

$\therefore 110 x=462$

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

Profit $=12.5- 8 =  4.5$ 

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

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

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

Now,

Marked price

$\Rightarrow x+x \times 25 \% $

$\Rightarrow x(1+0.25) $

$\Rightarrow(x \times 1.25)$

After $10 \%$ discount

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

$\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 $5 \%$ discount

$\Rightarrow(x \times 1.125)-(x \times 1.125) \times 5 \%$

$\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 \div 1.06875 $

$x=2240$

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

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

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

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

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

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

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

$\mathrm{SP}=104 x$

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

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

$\mathrm{SP}=\mathrm{CP} \times \frac{(100-\text { Loss })}{100}$
$600=C P \times \frac{(100-20)}{100}$
$C P=\frac{600 \times 100}{80}=$₹ 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
$35 x \rightarrow $ ₹ 1050
$x \rightarrow $₹ 30
So,
CP, $100 x \rightarrow $₹ 3000
Profit earned on selling the article for ₹ 4000
Profit $=4000-3000=$₹ 1000
Profit $\%=\frac{1000}{3000} \times 100=33 \frac{1}{3} \%$

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 $20 \%$ loss
$=\frac{80}{100} \times 640=$₹ 512

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

For P -
Selling Price $=$ Cost Price $\times \frac{(100-\text { Loss } \%)}{100}$
$18000=$ Cost Price $\times \frac{(100-20)}{100}$
Cost Price $=\frac{18000}{80} \times 100=$₹ 22500
If $P$ gets a profit of $8 \%$, 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 $\%$ of $Q=\frac{(24300-18000)}{18000} \times 100=\frac{6300}{180}=35 \%$

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

$8 \%, 15 \%$ and $20 \%$ is $37 \%$.

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

Profit % = 19  , Discount % = 15 

$
\frac{M P}{C P}=\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 \% \text { discount }=700 \times \frac{25}{100}=175
$
So selling price of the article $=700-175=525$
Profit $\%=\frac{25}{500} \times 100=5 \%$

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

Total CP                  =   4ltr    =  ₹ 150

$1 \mathrm{ltr}=\frac{150}{4}=$₹ 37.5

SP of 1 ltr =₹60

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

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