# 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