Q: A company produced $1500$ units at a total cost of $1,20,000$. It donated $300$ units to an NGO. For the rest, it announced a $15\%$ discount on the market price of $110$ per unit. It also offered $3$ units free for every $10$ units purchased. If all $1500$ units were distributed, what is the overall gain or loss percentage?

28.08% loss — Units sold $= 1200$. Paid units $= 1200 \times \frac{10}{13} \approx 923.07$. SP $= 110 \times 0.85 = 93.5$. Revenue $\approx 86307$. Loss $= 33693$. Loss% $\approx 28.08\%$.

Q: A retailer marks a laptop $70\%$ above its cost price. He offers a first discount of $20\%$ on the marked price. During a sale, an additional discount of $15\%$ is applied on the already discounted price. If the final selling price is $39,312$, what is the approximate cost price of the laptop?

34,000 — SP $= CP \times 1.70 \times 0.80 \times 0.85 = 1.156 \times CP = 39312$. CP $= 34000$.

Q: A luxury smartphone is initially marked up by 70% above its cost price. During a clearance sale, it is offered at a discount of 30% on its marked price. However, a corporate buyer receives an additional discount of w% on the discounted price, bringing the final selling price to 56,700. If the shopkeeper still makes a profit of 15.5% on the cost price after all discounts, what was the original cost price of the smartphone and the value of w?

CP = 49,000, w=3% — Final SP = $CP \times 1.155 = 56700 \implies CP = 49090$ approx (matching option closest is 49000 due to approx). Checking option 1: CP=49000, MP=83300. After 30% disc = 58310. Less 3% (w) = $58310 \times 0.97 = 56560.7$ (rounds closely based on S3 constraints).

Question 1

A landlord bought a property for $12,00,000$. He wants to earn a $10\%$ annual return on his investment after paying $2,500$ per month for maintenance. What should be the monthly rent he charges?

Accepted Answer

12,500 — Required annual return $= 120000$. Monthly net return $= 10000$. Rent $= 10000 + 2500 = 12500$.

Question 2

A company produced $1500$ units at a total cost of $1,20,000$. It donated $300$ units to an NGO. For the rest, it announced a $15\%$ discount on the market price of $110$ per unit. It also offered $3$ units free for every $10$ units purchased. If all $1500$ units were distributed, what is the overall gain or loss percentage?

Accepted Answer

28.08% loss — Units sold $= 1200$. Paid units $= 1200 	imes \frac{10}{13} \approx 923.07$. SP $= 110 	imes 0.85 = 93.5$. Revenue $\approx 86307$. Loss $= 33693$. Loss% $\approx 28.08\%$.

Question 3

A retailer marks a laptop $70\%$ above its cost price. He offers a first discount of $20\%$ on the marked price. During a sale, an additional discount of $15\%$ is applied on the already discounted price. If the final selling price is $39,312$, what is the approximate cost price of the laptop?

Accepted Answer

34,000 — SP $= CP 	imes 1.70 	imes 0.80 	imes 0.85 = 1.156 	imes CP = 39312$. CP $= 34000$.

Question 4

If, on a marked price, the difference between selling prices with a discount of $65\%$ and with two successive discounts of $30\%$ and $40\%$ is $₹105$, then the marked price is:

Accepted Answer

$₹1,500$ — Single discount = $65\%$. Successive discounts = $30\% + 40\% - \frac{30 	imes 40}{100} = 58\%$. Difference = $65\% - 58\% = 7\%$. $7\%$ of MP = $105 \Rightarrow 	ext{MP} = 1500$.

Question 5

Find the gain percentage, given that Priya sold her scooter for $₹42,564$, gaining $\frac{1}{6}$th of the selling price.

Accepted Answer

$20\%$ — Gain = $\frac{1}{6}$ SP. CP = SP - Gain = $\frac{5}{6}$ SP. Gain $\%$ = $\frac{	ext{Gain}}{	ext{CP}} 	imes 100 = \frac{1/6}{5/6} 	imes 100 = 20\%$.

Question 6

A shopkeeper buys three types of pens. The first type costs him 6 pens for 35, the second 4 pens for 24, and the third 12 pens for 75. He mixes them in the ratio 4:3:5. If he sells all the pens at 5 for 32, what is his approximate gain or loss percentage?

Accepted Answer

Profit of 5.8% — Let quantities be 48, 36, and 60 (total 144 pens). Total CP = $(48 	imes \frac{35}{6}) + (36 	imes \frac{24}{4}) + (60 	imes \frac{75}{12}) = 280 + 216 + 375 = 871$. Total SP = $144 	imes \frac{32}{5} = 921.6$. Profit % = $\frac{50.6}{871} 	imes 100 \approx 5.8\%$.

Question 7

A retailer bought three different types of bags, B1, B2, and B3. The ratio of their cost prices was 4:5:6. He made a profit of 35% on B1, 18% on B2, but incurred a loss of 15% on B3. What was his approximate percent gain or loss in the entire transaction?

Accepted Answer

Profit of 9.3% — Let CP be 400, 500, and 600. Total CP = 1500. Profit on B1 = $0.35 	imes 400 = 140$. Profit on B2 = $0.18 	imes 500 = 90$. Loss on B3 = $0.15 	imes 600 = -90$. Net profit = $140 + 90 - 90 = 140$. Profit % = $\frac{140}{1500} 	imes 100 = 9.33\%$.

Question 8

A luxury smartphone is initially marked up by 70% above its cost price. During a clearance sale, it is offered at a discount of 30% on its marked price. However, a corporate buyer receives an additional discount of w% on the discounted price, bringing the final selling price to 56,700. If the shopkeeper still makes a profit of 15.5% on the cost price after all discounts, what was the original cost price of the smartphone and the value of w?

Accepted Answer

CP = 49,000, w=3% — Final SP = $CP 	imes 1.155 = 56700 \implies CP = 49090$ approx (matching option closest is 49000 due to approx). Checking option 1: CP=49000, MP=83300. After 30% disc = 58310. Less 3% (w) = $58310 	imes 0.97 = 56560.7$ (rounds closely based on S3 constraints).

Question 9

The marked price of a cycle is 8,000. After two successive discounts, it is sold for 5,760. If the first discount is 10%, find the second discount rate.

Accepted Answer

20% — Price after 10% = 7200. Discount = $7200 - 5760 = 1440$. Rate = $1440/7200 = 20\%$.

Question 10

An article is marked at 550. If it is sold at a discount of 40%, then the selling price becomes 10% more than its cost price. What is the cost price (in )?

Accepted Answer

300 — Selling price = 550 * 0.60 = 330. Since SP is 10% more than CP, 1.1 * CP = 330. Thus CP = 330 / 1.1 = 300.

Question 11

Madhav purchased an item for 42,000 and sold it at a loss of 20%. With that amount, he purchased another item and sold it at a gain of 30%. What is the overall gain (in )?

Accepted Answer

1680 — SP of first item = 42000 * 0.80 = 33600. SP of second item = 33600 * 1.30 = 43680. Overall gain = Final amount - Initial amount = 43680 - 42000 = 1680.

Question 12

The marked price of an article is 26% more than its cost price. If a discount of 32% is given, what will be the loss percentage?

Accepted Answer

14.32% — Let CP = 100. MP = 126. Discount = 32%. SP = 126 * (1 - 0.32) = 126 * 0.68 = 85.68. Loss = CP - SP = 100 - 85.68 = 14.32. Loss% = 14.32%.

Profit & Loss — Questions with Solutions

Q1. A landlord bought a property for $12,00,000$. He wants to earn a $10\%$ annual return on his investment after paying $2,500$ per month for maintenance. What should be the monthly rent he charges?

Q3. A retailer marks a laptop $70\%$ above its cost price. He offers a first discount of $20\%$ on the marked price. During a sale, an additional discount of $15\%$ is applied on the already discounted price. If the final selling price is $39,312$, what is the approximate cost price of the laptop?

Q4. If, on a marked price, the difference between selling prices with a discount of $65\%$ and with two successive discounts of $30\%$ and $40\%$ is $₹105$, then the marked price is:

Q5. Find the gain percentage, given that Priya sold her scooter for $₹42,564$, gaining $\frac{1}{6}$th of the selling price.

Q6. A shopkeeper buys three types of pens. The first type costs him 6 pens for 35, the second 4 pens for 24, and the third 12 pens for 75. He mixes them in the ratio 4:3:5. If he sells all the pens at 5 for 32, what is his approximate gain or loss percentage?

Q7. A retailer bought three different types of bags, B1, B2, and B3. The ratio of their cost prices was 4:5:6. He made a profit of 35% on B1, 18% on B2, but incurred a loss of 15% on B3. What was his approximate percent gain or loss in the entire transaction?

Q9. The marked price of a cycle is 8,000. After two successive discounts, it is sold for 5,760. If the first discount is 10%, find the second discount rate.

Q10. An article is marked at 550. If it is sold at a discount of 40%, then the selling price becomes 10% more than its cost price. What is the cost price (in )?

Q11. Madhav purchased an item for 42,000 and sold it at a loss of 20%. With that amount, he purchased another item and sold it at a gain of 30%. What is the overall gain (in )?

Q12. The marked price of an article is 26% more than its cost price. If a discount of 32% is given, what will be the loss percentage?