XAT Profit and Loss Questions [Most Important]
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Question 1: A single discount equivalent to three simple discounts of 10%, 12%, and 15% is:
a) 32.68%
b) 34.17%
c) 37%
d) 35.36%
1) Answer (A)
Solution:
The successive discounts are 10%,12% and 15%
Let the Initial value be 100.
According to question, $100\times\ \frac{\left(100-10\right)}{100}\times\ \frac{\left(100-12\right)}{100}\times\ \frac{\left(100-15\right)}{100}$
i.e; $100\times\ \frac{90}{100}\times\ \frac{88}{100}\times\ \frac{85}{100}$
Discounted value = 67.32 %
Equivalent discount = initial value – discounted value
= 100 – 67.32 = 32.68 .
Hence option A is correct.
Another method :
Discount is also called successive decrease
if x and y are two successive discounts then ,
$x\ +\ y\ -\frac{\left(x\times\ y\right)}{100}$
first we take first two discount 10% and 12%
$\therefore\ 10\ +\ 12\ -\frac{10\times\ 12}{100}=\ 20.8\ \%$
Now we take,
20.8% and 15% ,
$\therefore\ 20.8\ +\ 15\ -\frac{20.8\times\ 15}{100}=\ 32.68\ \%$
Question 2: A shopkeeper sold an article for ₹455 at a loss (in ₹). If he sells it for ₹490, then he would gain an amount four times the loss. At what price (in ₹) should he sell the article to gain 25%?
a) 575
b) 577.50
c) 570.50
d) 115.50
2) Answer (B)
Solution:
Let the loss when the shopkeeper sold the article for ₹455 = L
and the Cost price of the article = C
$\Rightarrow$ C – 455 = L
$\Rightarrow$ C = L + 455……(1)
According to the problem, when the shopkeeper sells it for ₹490, then he would gain an amount four times the loss.
$\Rightarrow$ 490 – C = 4L
$\Rightarrow$ 490 – (L + 455) = 4L
$\Rightarrow$ 35 = 5L
$\Rightarrow$ L = 7
From (1),
C = L + 455 = 7 + 455 = ₹462
Cost price of the article = ₹462
Selling price of the article when the shopkeeper sells at 25% gain = $\frac{125}{100}\times$C
= $\frac{125}{100}\times$462
= ₹577.50
Hence, the correct answer is Option B
Question 3: A shopkeeper marks an article at a price such that after giving a discount of x%, he gains 20%. If the cost price and the marked price of the article are ₹920 and ₹1472 respectively, then what is the value of x?
a) 18
b) 30
c) 20
d) 25
3) Answer (D)
Solution:
Cost price of the article = ₹920
Gain = 20%
Selling price of the article = $\frac{120}{100}\times$920
= ₹1104
Marked price of the article = ₹1472
Discount = x%
Selling price of the article = $\frac{100-x}{100}\times$1472
1104 = $\frac{100-x}{100}\times$1472
69 = $\frac{100-x}{100}\times$92
6900 = 9200 – 92x
92x = 2300
x = 25
Hence, the correct answer is Option D
Question 4: In festival season, a shopkeeper allows a discount of 10% on every item. Even after giving the discount, he makes a profit of 20%. If he does not give any discount, then what will be his profit percent? (correct to 2 decimal places)
a) 33
b) 25
c) 33.33
d) 33.43
4) Answer (C)
Solution:
Let the cost price of the article = 100C
Profit = 20%
Selling price of the article = $\frac{120}{100}\times$100C = 120C
Discount = 10%
$\frac{90}{100}\times$Marked price = 120C
Marked price of the article = $\frac{400}{3}$C
When no discount is provided,
Selling price = $\frac{400}{3}$C
Profit% = $\frac{\frac{400}{3}C-100C}{100C}\times100$
= 33.33%
Hence, the correct answer is Option C
Question 5: A trader bought 640 kg of rice. He sold a part of rice at 20% profit and the rest at 5% loss. He earned a profit of 15% in the entire transaction. What is the quantity (in kg) of rice that he sold at 5% loss?
a) 128
b) 132
c) 154
d) 256
5) Answer (A)
Solution:
Using mixture and alligation method,
Ratio of the quantity of rice sold at 20% profit and 5% loss = 20 : 5
= 4 : 1
Quantity of rice sold at 5% loss = $\frac{1}{4+1}\times$640
= 128 kg
Hence, the correct answer is Option A
Question 6: The cost price of an article is ₹280. A shopkeeper sells it by allowing 16% discount on its marked price and still gains 20%. What is the marked price(in ₹) of the article?
a) 400
b) 360
c) 420
d) 350
6) Answer (A)
Solution:
The cost price of article = ₹280
Gain = 20%
Selling price of the article = $\frac{120}{100}\times$280
= ₹336
Let the marked price of the article = M
Discount = 16%
Selling price of the article = $\frac{84}{100}$M
$\Rightarrow$ 336 = $\frac{84}{100}$M
$\Rightarrow$ M = 400
Marked price of the article = ₹400
Hence, the correct answer is Option A
Question 7: A shop keeper sold an article at four-fifth of the marked price and suffered a loss of $3 \frac{1}{3}\%$. Find the profit percent, if he sold the article at the marked price. (correct to nearest integer)
a) 22
b) 18
c) 21
d) 20
7) Answer (C)
Solution:
Let the cost price of the article = 100C
Loss = $3 \frac{1}{3}\%$ = $\frac{10}{3}\%$
Selling price of the article = 100C – $\frac{\frac{10}{3}}{100}\times$100C
= $\frac{290}{3}$C
Shop keeper sold the article at four-fifth of the marked price.
$\frac{290}{3}$C = $\frac{4}{5}\times$Marked price of the article
Marked price of the article = $\frac{725}{6}$C
Profit percentage when article is sold at marked price = $\frac{\frac{725}{6}C-100C}{100C}\times100$
= $\frac{125C}{6\times100C}\times100$
= 20.833%
= 21% (approximately)
Hence, the correct answer is Option C
Question 8: Trader A gives a single discount of 25% and Trader B gives two successive discounts of 20% and 5% on an identical item. If the discount given by A is ₹320 more than the discount given by B, then what is the marked price (in ₹) of the item?
a) 3200
b) 32000
c) 30000
d) 25000
8) Answer (B)
Solution:
Let the marked price of the item = M
i) Trader A gives a single discount of 25%.
Discount = $\frac{25}{100}$M = $\frac{1}{4}$M
ii) Trader B gives two successive discounts of 20% and 5%.
Price of the item after 20% discount = $\frac{80}{100}\times$M
Price of the item after 5% discount = $\frac{95}{100}\times\frac{80}{100}\times$M = $\frac{19}{25}$M
Total discount given trader B = M – $\frac{19}{25}$M = $\frac{6}{25}$M
According to the problem, discount given by A is ₹320 more than the discount given by B.
$\frac{1}{4}$M = $\frac{6}{25}$M + 320
$\frac{25M-24M}{100}=320$
M = ₹32000
Hence, the correct answer is Option B
Question 9: A customer wanted to purchase an item marked for ₹10000. Shopkeeper offered two types of discounts, 25% flat discount or successive discounts of 14% and 12%. Which is the better offer for the customers and by how much?
a) first offer by ₹68
b) second offer by ₹68
c) first offer by ₹32
d) second offer by ₹100
9) Answer (A)
Solution:
25% flat discount
Selling price of the item = $\frac{75}{100}\times10000$ = ₹7500
Successive discounts of 14% and 12%
Price of the item after 14% discount = $\frac{86}{100}\times10000$ = ₹8600
Price of the item after 12% discount = $\frac{88}{100}\times8600$ = ₹7568
Difference between selling prices = 7568 – 7500 = ₹68
First offer is better by ₹68.
Hence, the correct answer is Option A
Question 10: If selling price of 75 articles is equal to cost price of 60 articles, then the approximate loss or gain percent is:
a) Profit of 25%
b) No profit no loss
c) Loss of 30%
d) Loss of 20%
10) Answer (D)
Solution:
Let the cost price of 60 articles = C
Cost price of 1 article = $\frac{C}{60}$
Selling price of 75 articles = C
Selling price of 1 article = $\frac{C}{75}$
Loss% = $\frac{\frac{C}{60}-\frac{C}{75}}{\frac{C}{60}}\times100$
= $\frac{\frac{5C-4C}{300}}{\frac{C}{60}}\times100$
= $\frac{60}{300}\times100$
= 20%
Hence, the correct answer is Option D
Question 11: The marked price of an article is ₹180. Renu sells it after 20% discount on its marked price and still gains 25%, The cost price (in ₹) of the article is:
a) 120.80
b) 110.80
c) 115.20
d) 125.50
11) Answer (C)
Solution:
Marked price of an article is ₹180.
Discount = 20%
Selling price of the article = $\frac{80}{100}\times$180 = ₹144
Let the cost price of the article = C
Profit = 25%
Selling price of the article = $\frac{125}{100}$C
$\frac{125}{100}$C = 144
C = $\frac{576}{5}$
C = 115.2
Cost price of the article = ₹115.20
Hence, the correct answer is Option C
Question 12: The cost price of an article is ₹250. A shopkeeper gains 20% by selling it at a discount of 36% on its marked price. What is the marked price (in ₹) of the article?
a) 450
b) 380.50
c) 475
d) 468.75
12) Answer (D)
Solution:
Cost price of the article is ₹250.
Profit = 20%
Selling price of the article = $\frac{120}{100}\times$250 = ₹300
Let the marked price of the article = M
Discount = 36%
$\frac{64}{100}\times$M = 300
M = 468.75
Marked price of the article = ₹468.75
Hence, the correct answer is Option D
Question 13: Radha bought a fridge and a washing machine together for ₹57300. She sold the fridge at a profit of 15% and washing machine at a loss of 24% and both are sold at the same price. The cost price of washing machine(in ₹) is:
a) 28650
b) 34500
c) 24500
d) 22800
13) Answer (B)
Solution:
Let the cost price of fridge = x
Profit = 15%
Selling price of fridge = $\frac{115}{100}$x
Cost price of washing machine = 57300 – x
Loss = 24%
Selling price of washing machine = $\frac{76}{100}\left(57300-\text{x}\right)$
According to the problem, both are sold at same price.
$\frac{115}{100}$x = $\frac{76}{100}\left(57300-\text{x}\right)$
115x + 76x = 76$\times$57300
191x = 76$\times$57300
x = 76$\times$300
x = 22800
Cost price of fridge = ₹22800
Cost price of washing machine = 57300 – x
= 57300 – 22800
= ₹34500
Hence, the correct answer is Option B
Question 14: The marked price of an article is ₹5320. It is subject to two successive discounts, the first being 15%, and the second at a rate of 20% of the first. What is the selling price (to nearest ₹) of the article?
a) ₹4522
b) ₹4127
c) ₹4000
d) ₹4386
14) Answer (D)
Solution:
The marked price of an article is ₹5320.
First discount = 15%
Price of the article after 15% discount = $\frac{85}{100}\times5320$ = ₹4522
Second discount = 20% of 15% = $\frac{20}{100}\times$15% = 3%
Selling price of the article after 3% discount = $\frac{97}{100}\times4522$ = ₹4386.34
= ₹4386 (approximately)
Hence, the correct answer is Option D
Question 15: Hari suffered a loss of 8% by selling an article. If he had sold it for ₹300 more, he would have made a profit of 4%. Find his CP (in ₹).
a) 2400
b) 2250
c) 2575
d) 2500
15) Answer (D)
Solution:
Let the cost price of article = 100C
Hari suffered a loss of 8% by selling an article.
Selling price of the article = $\frac{92}{100}\times$100C = 92C
If he had sold it for ₹300 more, he would have made a profit of 4%.
92C + 300 = $\frac{104}{100}\times$100C
92C + 300 = 104C
12C = 300
C = 25
The cost price of article = ₹2500
Hence, the correct answer is Option D
