Practice questions here, for every subject and every exam. Unlimited questions for unlimited attempts, given with answers and explanations.
Let $x$ be the original price paid by $P$
Selling price for $\mathrm{P}=\mathrm{x} \times \frac{100+20}{100}=1.2 \mathrm{x}$
Selling price of $Q=1.2 x \times \frac{100+30}{100}=1.56 x$
Given, $1.56 \mathrm{x}-1.2 \mathrm{x}=108$
$
\Rightarrow 0.36 \mathrm{x}=108
$
$
\Rightarrow \mathrm{x}=300
$
According to question
$
\begin{aligned}
&450 \times \frac{100-10}{100} \times \frac{100-x}{100} \times \frac{100-20}{100}=267.30 \\
&450 \times \frac{90}{100} \times \frac{100-x}{100} \times \frac{80}{100}=267.30 \\
&100-\mathrm{x}=\frac{267.30 \times 100 \times 100 \times 100}{450 \times 90 \times 80} \\
&100-\mathrm{x}=82.5 \\
&\mathrm{x}=17.5
\end{aligned}
$
$12.5 \%=\frac{1}{8}, \quad 15 \%=\frac{3}{20}$
MP of item $=805 \times \frac{8}{7}=$₹ 920
When he had not offered the discount, he would have earned a profit of $15 \%$.
So, cost price of the item $=920 \times \frac{20}{23}=$₹ 800
$
15 \%=\frac{3}{20}
$
Cost price of the article $==170 \times \frac{20}{17}=$₹ 200
Required profit $\%=\frac{206.40-200}{200} \times 100$
$
=\frac{6.40}{200} \times 100
$
= 3.2 %
After applying successive discounts of 10% and 5 % on the marked price of an article, it was sold for ₹ 3,420. Find the marked price of the article.
MP $\times \frac{90}{100} \times \frac{95}{100}=3420$
MP $=\frac{3420 \times 100 \times 100}{90 \times 95}$
MP $=$₹ 4000
Two successive discounts, with the first being 10%, were given on an article having the marked price of ₹ 7,500. Finally, it was sold for ₹ 5,805. What per cent was the second discount?
Selling price when first discount is given $=7,500-7,500 \times \frac{10}{100}$
$
=7,500-750=$₹ 6750
But the article was sold for ₹ 5,805
so, second discount percent $=\frac{6750-5805}{6750} \times 100$
$=\frac{945}{6750} \times 100=14 \% $
A trader purchased 360 packets of pencils at the rate of ₹ 15 per packet. He sold 60 % of the packets at the rate of ₹ 18 per packet and the remaining packets at the rate of ₹ 20 per packet. What is his gain per cent (up to one decimal place) in this transaction?
Cost price of 360 packets $=360 \times 15=5400$
Number of $60 \%$ packets $=360 \times \frac{60}{100}=216$
Selling price of 216 packets $=216 \times 18=3888$
Number of $40 \%$ packets $=360-216=144$
Selling price of 144 packets $=144 \times 20=2880$
Total SP $=3888+2880=6768$
Required gain $\%=\frac{6768-5400}{5400} \times 100=25.33 \%$
If the selling price of an article is ₹ 900 and the discount is 40%, then find its marked price (in ₹ ).
$
40 \%=\frac{2}{5}
$
Required Marked price $=900 \times \frac{5}{3}=1,500$
Alternative method
By selling 40 dozen bananas for ₹ 1,440, a man gains 20%. In order to gain 30 %, for how much should he sell 20 dozen bananas?
$
20 \%=\frac{1}{5}, 30 \%=\frac{3}{10}
$
Cost price of 40 dozen $=1440 \times \frac{5}{6}=$₹ 1200
Cost price of 1 dozen $=\frac{1200}{40}=$₹ 30
Cost price of 20 dozen $=30 \times 20=$₹ 600
Required selling price of 20 dozen bananas $=600 \times \frac{13}{10}=$₹ 780
By selling an article for ₹ 254.38, there is a gain of $10.6 \%$. If it is sold for ₹ 224.25, then the loss/gain percentage will be
There is a gain of $10.6 \%$ on the the article.
then, $110.6 \% \Rightarrow $₹ 254.38
$1 \% \Rightarrow 2.3$
$100 \% \Rightarrow 230$
So, Cost Price of article is ₹ 230.
Required loss when it is sold at ₹ 224.25 $=\frac{230-224.25}{230} \times 100$
$=\frac{5.75}{230} \times 100=2.5 \%$
Selling Price $=$ Cost price $+$ profit
Selling price $=100 \%+20 \%=120 \%$
According to question
$20 \% \rightarrow 30.80$
$10 \% \rightarrow 15.40$
Hence, $120 \% \rightarrow 12 \times 15.4=$₹ 184.80
Total cost price $=22000+3000=25000$
Selling price $=25000 \times \frac{112}{100}=$₹ 28000
New selling price $=28000-500=$₹ 27500
Profit $\%=\frac{(27500-25000)}{25000} \times 100=\frac{2500}{250}=10 \%$
By selling 36 m of jute, a shopkeeper gains an amount equal to the selling price of 12 m of jute. Find the gain percentage.
According to question
$
36 \mathrm{SP}=36 \mathrm{CP}+12 \mathrm{SP}
$
$
\begin{aligned}
&24 \mathrm{SP}=36 \mathrm{CP} \\
&\frac{S P}{C P}=\frac{36}{24} \\
&\frac{S P}{C P}=\frac{3}{2}
\end{aligned}
$
Profit % $=\frac{3-2}{2} \times 100$
$
\begin{aligned}
&=\frac{1}{2} \times 100 \\
&=50 \%
\end{aligned}
$
A chair is sold for ₹ 720 after giving a discount of 10 % on its marked price. The cost price of the chair is ₹ 640. If it is sold at the marked price, then the profit percentage will be:
Given, Selling price $=$₹ 720
Cost price $=$₹ 640
Market price $=720 \times \frac{100}{90}=$₹ 800
Required profit $\%=\frac{800-640}{640} \times 100$
$
=\frac{160}{640} \times 100
$
$
=25 \%
$
Successive Discount formula $=A+B-\frac{A \times B}{100}$
For $12 \%$ and $5 \%$
$12+5-\frac{12 \times 5}{100}=17-0.60=16.4 \%$
Now for $16.4 \%$ and $7 \%$
$16.4+7-\frac{16.4 \times 7}{100}=23.4-1.148=22.252 \%$
A man incurred 8% loss by selling a TV for ₹ 18,400. At what price should the TV be sold to earn 5% profit?
Selling Price $=$ Cost Price $\times \frac{(100-\text { Loss })}{100}$
$18400=$ Cost Price $\times \frac{(100-8)}{100}$
Cost Price $=\frac{18400 \times 100}{92}=$₹ 20000
New selling price $=20000 \times \frac{(100+5)}{100}=200 \times 105=$₹ 21000
Let total goods be 12 , then
$\frac{1}{3} \times 12=4$ goods at $15 \%$ profit
$\frac{25}{100} \times 12=3$ goods at $20 \%$ profit
$12-(4+3)=5$ goods at $10 \%$ loss
Overall profit/loss $\%=\frac{4 \times 15 \%+3 \times 20 \%+5 \times(-10 \%)}{12}=\frac{60 \%+60 \%-50 \%}{12}=\frac{70 \%}{12}$
According to question
$\frac{70 \%}{12}=$₹ 350
$1 \%=$₹ 60
$100 \%=$₹ 6000
By selling a guitar for ₹ 846 , Rakhi loses 6%. For how much should Rima sell it to gain 8% ?
Selling Price $=$ Cost Price $\times \frac{(100-\text { Loss })}{100}$
$846=$ Cost Price $\times \frac{(100-6)}{100}$
Cost Price $=\frac{846 \times 100}{94}=$₹ 900
New selling price $=900 \times \frac{(100+8)}{100}=9 \times 108=$₹ 972
In a sale, perfumes are available at a discount of 25% on the selling price. If a perfume costs ₹ 6,873 in the sale, what is the original selling price of the perfume?
Let the original selling price be $x$.
According to question
$x \times \frac{(100-25)}{100}=$₹ 6873
$x=\frac{6873 \times 4}{3}=$₹ 9164
Hence, Original selling price of a perfume is ₹ 9164 .
As per the question,
Cost price of 18 oranges $=\frac{151.2}{80} \times 100=189 \mathrm{rs}$
So, Cost price of 1 orange $=\frac{189}{18}=$₹ 10.5
For $30 \%$ profit, selling price of 1 orange $=\frac{10.5}{100} \times 130=$₹ 13.65
No of oranges $=\frac{819}{13.65}=60$ oranges