# Profit and Loss

## Profit And Loss

 Question 1 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
The price of an article reduces to 576 after two successive discounts. The markup is 80% above the cost price of Rs. 500. What is the new profit percentage if instead of two successive discounts the markup price was further increased successively two times by the same percentage?
 A 157% B 159.2% C 300% D 259.20%
Question 1 Explanation:
\begin{align} & {\text{CP}} = 500 \cr & {\text{SP}} = 576 \cr & {\text{MP}} = 900\left[ {80\% \,{\text{above}}\,{\text{the}}\,{\text{CP}}} \right] \cr & {\text{Now}}, \cr & {\text{SP}} = {\text{MP}} \times {\left[ {1 - \left( {\frac{R}{{100}}} \right)} \right]^2} \cr & \left[ {{\text{R = Rate}}\,{\text{of}}\,{\text{Discount}}} \right] \cr & 576 = 900 \times {\left[ {1 - \left( {\frac{R}{{100}}} \right)} \right]^2} \cr & R = 20\% \cr & \cr & {\text{Again}}, \cr & {\text{SP}} = {\text{MP}} \times {\left[ {1 + \left( {\frac{R}{{100}}} \right)} \right]^2} \cr & {\text{SP}} = 900 \times {\left[ {1 + \left( {\frac{{20}}{{100}}} \right)} \right]^2} \cr & {\text{SP}} = 1296 \cr & {\text{New}}\,{\text{Profit}}\,{\text{Percentage}}, \cr & = \left[ {\frac{{\left( {SP - CP} \right)}}{{CP}}} \right] \times 100 \cr & = \left[ {\frac{{\left( {1296 - 500} \right)}}{{500}}} \right] \times 100 \cr & = 159.2\% \cr\end{align}

 Question 2 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
The marked price of a shirt and trousers are in the ratio 1:2. The shopkeeper gives 40% discount on the shirt. If the total discount in the set of the shirt and trousers is 30%, the discount offered on the trousers is:
 A 30% B 15% C 20% D 25%
Question 2 Explanation:
Let the price of shirt and trouser be Rs. 100 and Rs. 200 respectively.

Then, price of set of shirt and trouser = Rs. 300.

After giving 30% discount on the set,

Selling Price = 300 - 30% of 300 = 210.

Total Discount on Set = 90.

And Discount on shirt is 20% alone,

SP of shirt alone = 100 - 40% of 100 = 60.

Rs. 40 is the discount on shirt then Rs. 50 must be the discount on the trouser.

So, discount on trouser = (50*100)/200 = 25%.

 Question 3 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
 A Rs. 2200 B Data inadequate C Rs. 2400 D Rs. 2000
Question 3 Explanation:
\begin{align} & {\text{Let}}\,{\text{C}}{\text{.P}}{\text{.}}\,{\text{be}}\,Rs.\,x \cr & {\text{Then}},\,\frac{{1920 - x}}{x} \times 100 = \frac{{x - 1280}}{x} \times 100 \cr & \Rightarrow 1920 - x = x - 1280 \cr & \Rightarrow 2x = 3200 \cr & \Rightarrow x = 1600 \cr & \therefore {\text{Required}}\,{\text{S}}{\text{.P}}{\text{.}}\, = 125\% \,{\text{of}}\,Rs.\,1600 \cr & = Rs.\,\left( {\frac{{125}}{{100}} \times 1600} \right) = Rs.\,2000 \cr\end{align}

 Question 4 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
If the profit per cent got on selling an article is numerically equal to its cost price in rupees and the selling price is Rs. 39, then cost price (in Rs.) will be:
 A 22 B 30 C 28 D 20
Question 4 Explanation:
SP = Rs. 39.

CP = x(let)

Profit % = CP

Or, [(39-x)/x] * 100 = x [% profit= (SP-CP)/CP]

3900-100x = x2

X2+100-3900 = 0

X = 30. (we cannot take negative value of x)

 Question 5 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
If selling price is doubled, the profit triples. Find the profit percent.
 A 120 B 66 2/3 C 105 1/3 D 100
Question 5 Explanation:
\begin{align} & {\text{Let}}\,{\text{C}}{\text{.P}}{\text{.}}\,{\text{be}}\,{\text{Rs}}{\text{.}}\,x\,{\text{and}}\,{\text{S}}{\text{.P}}{\text{.}}\,{\text{be}}\,{\text{Rs}}.\,y \cr & {\text{Then}},\,3\left( {y - x} \right) = \left( {2y - x} \right) \cr & \Rightarrow y = 2x \cr & {\text{Profit}} = Rs.\,\left( {y - x} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {2x - x} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,x \cr & \therefore {\text{Profit}}\,\% \cr & = \left( {\frac{x}{x} \times 100} \right)\% \cr & = 100\% \cr\end{align}

 Question 6 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
Find the selling price of goods if two salesmen claim to make 25% profit each, one calculating it on cost price while another on the selling price, the difference in the profits earned being Rs. 100 and selling price being the same in both the cases?
 A Rs. 2400 B Rs. 1200 C Rs. 3000 D Rs. 1600
Question 6 Explanation:
Let CP's be Rs. 1000 each, their respective SP will be,

1000==25%↑==> 1250 [person calculating profit on the CP]

1000 ==33.33%↑==> 1333.33 [The person calculating his profit on SP: 25% of SP = 33.33% of CP]

The difference turned out to be = 83.33. this has occured when we have assumed the CP as 1000. But, we are given difference of Rs. 100.

So, on comparing,

83.33 = 1000

1 = [1000/83.33]

100 = [1000/83.33] *100 = Rs. 1200.

 Question 7 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
Find the difference of amount if 40% discount is given on Rs. 500 and two consecutive discount 30% and 10% are given on the same amount.
 A Rs. 0 B Rs. 20 C Rs. 10 D Rs. 15
Question 7 Explanation:
40% discount on 500 = (40 *500)/100 = Rs. 200.

Two successive discount on 500,

= 30% of 500 + 10% of (500 - 30% of 500).

= 150 + 10% of 350.

= 150 + 35 = Rs. 185.

Difference in Discount = 200 - 185 = Rs. 15

 Question 8 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
A company charges a fixed rental of Rs. 350 per month. It allows 200 calls free per month. Each call is charge at Rs. 1.4 when the number of calls exceed 200 per month and it charges Rs. 1.6 when the number of calls exceeds 400 per month and so on. A customer made 150 calls in February and 250 calls in march. By how much percent each call is cheaper in March than each call in February.
 A 28% B 18.50% C 16% D 25%
Question 8 Explanation:
\begin{align} & {\text{Charge per call in February}} \cr & = \frac{{350}}{{150}} = \frac{7}{3} = 2.33 \cr & {\text{Charge per call in March}} \cr & = \frac{{\left[ {350 + \left( {50 \times 1.4} \right)} \right]}}{{250}} \cr & = \frac{{420}}{{250}} = \frac{{42}}{{25}} = 1.68 \cr & \% {\text{ Cheaper call rate in March}}. \cr & = \left[ {\frac{{\left( {2.33 - 1.68} \right)}}{{2.33}}} \right] \times 100 \cr & = 28\% \cr\end{align}
 Question 9 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
A dishonest dealer marks up the price of his goods by 20% and gives a discount of 10% to the customer. Besides, he also cheats both his supplier and his buyer by 100 grams while buying or selling 1 kilogram. Find the percentage profit earned by the shopkeeper?
 A 46.66% B 50% C 32% D 25%
Question 9 Explanation:

Suppose he bought 1100 grams for Rs. 1000.

While selling,

He sells only 900 grams when he takes the money for 1 kg.

Now, according to the problem,

he sells at a 8% profit (20% markup, 10% discount).

Hence, his selling price is Rs. 1080 for 900 grams.

Now,

1100grams for Rs. 1000

Hence, 1188 grams for Rs. 1080

Selling: 900 grams for Rs. 1080.

Hence, % profit = 288/900 = 32%.

(using goods left by goods sold formula).

 Question 10 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
A tradesman marks his goods at 25% above the cost price and allows purchasers a discount of 25/2%, his profit is:
 A 9.375% B 8.50% C 8.63% D 8%
Question 10 Explanation:

Let his CP = Rs. 100.

Marked Price = 100 + 25% of 100 = 125.

Now, discount = 25/2% on MP.

So, SP = 125 - (25/2)% of 125 = Rs. 109.375.

%Gain = 9.375%.

Alternatively use graphic change method:

100(CP)==25% Up==>125(MP)==12.5%down ==>109.375.

%Profit = 9.375%.

There are 10 questions to complete.