A merchant purchases a cloth at a rate of Rs. 100 per meter and receives 5 ~cm length of cloth free for every 100 ~cm length of cloth purchased by him. He sells the same cloth at a rate of Rs. 110 per meter but cheats his customers by giving 95 ~cm length of cloth for every 100 ~cm length of cloth purchased by the customers. If the merchant provides a 5 % discount, the resulting profit earned by him is Option 1: 15.5% Option 2: 4.2% Option 3: 9.7% Option 4: 16%

Answer: 15.5%. Solution: The merchant has three sources of advantage: Getting extra cloth when buying (5 cm free per 100 cm), giving less cloth when selling (95 cm instead of 100 cm), and charging premium price (Rs. 110 vs Rs. 100 cost). Even after giving a 5% discount, let's see the final profit. What we pay: Rs. 100 for 100 cm of cloth What we actually get: 100 cm + 5 cm free = 105 cm Effective cost per cm: Rs. 100 ÷ 105 cm = Rs. 100/105 per cm Listed selling price: Rs. 110 per meter (100 cm) What customer actually gets: Only 95 cm (instead of 100 cm) Effective revenue per cm sold: Rs. 110 ÷ 95 cm = Rs. 110/95 per cm After 5% discount: Rs. 110/95 x 0.95 = 104.5/95 per cm For the 105 cm of cloth we actually have: Total Cost: Rs. 100 (what we paid) Total Revenue: 105 x 104.5/95 = 115.5 cm Profit: Rs. 115.5 - Rs. 100 = Rs. 15.5 Profit Percentage: 15.5/100 x 100 = 15.5% The reference solution uses a clever multiplier approach: Selling Price = 110 x (1 + 1/20) x (1 + 1/19) x 0.95 Where: (1 + 1/20) accounts for getting 5 cm free per 100 cm (1 + 1/19) accounts for giving 95 cm instead of 100 cm 0.95 accounts for the 5% discount Calculation: 110 x 21/20 x 20/19 x 95/100 = 110 x (21 x 20 x 95)/(20 x 19 x 100) = 115.5 Final Answer: The profit percentage is 15.5% Key Insight: Even after giving a 5% discount, we still make a healthy profit due to the combined effect of getting extra cloth when buying and giving less cloth when selling. This is a common type of profit calculation problem where multiple factors work together.

Arithmetic

Profit & Loss

Hard

A merchant purchases a cloth at a rate of Rs. $100$ per meter and receives $5 \mathrm{~cm}$ length of cloth free for every $100 \mathrm{~cm}$ length of cloth purchased by him. He sells the same cloth at a rate of Rs. $110$ per meter but cheats his customers by giving $95 \mathrm{~cm}$ length of cloth for every $100 \mathrm{~cm}$ length of cloth purchased by the customers. If the merchant provides a $5 \%$ discount, the resulting profit earned by him is

$15.5%$

$4.2%$

$9.7%$

$16%$

✅ Correct Option: 1

The merchant has three sources of advantage:

Getting extra cloth when buying (5 cm free per 100 cm), giving less cloth when selling (95 cm instead of 100 cm), and charging premium price (Rs. 110 vs Rs. 100 cost).

Even after giving a 5% discount, let's see the final profit.

What we pay: Rs. 100 for 100 cm of cloth

What we actually get: 100 cm + 5 cm free = 105 cm

Effective cost per cm: Rs. 100 ÷ 105 cm = Rs. $\dfrac{100}{105}$ per cm

Listed selling price: Rs. 110 per meter (100 cm)

What customer actually gets: Only 95 cm (instead of 100 cm)

Effective revenue per cm sold: Rs. 110 ÷ 95 cm = Rs. $\dfrac{110}{95}$ per cm

After 5% discount: Rs. $\dfrac{110}{95} \times 0.95 = \dfrac{104.5}{95}$ per cm

For the 105 cm of cloth we actually have:

Total Cost: Rs. 100 (what we paid)

Total Revenue: $105 \times \dfrac{104.5}{95} = 115.5$ cm

Profit: Rs. 115.5 - Rs. 100 = Rs. 15.5

Profit Percentage: $\dfrac{15.5}{100} \times 100 = 15.5\%$

The reference solution uses a clever multiplier approach:

Selling Price = $110 \times \left(1 + \dfrac{1}{20}\right) \times \left(1 + \dfrac{1}{19}\right) \times 0.95$

Where:

$\left(1 + \dfrac{1}{20}\right)$ accounts for getting 5 cm free per 100 cm

$\left(1 + \dfrac{1}{19}\right)$ accounts for giving 95 cm instead of 100 cm

$0.95$ accounts for the 5% discount

Calculation:

$110 \times \dfrac{21}{20} \times \dfrac{20}{19} \times \dfrac{95}{100} = 110 \times \dfrac{21 \times 20 \times 95}{20 \times 19 \times 100} = 115.5$

Final Answer: The profit percentage is 15.5%

Key Insight: Even after giving a 5% discount, we still make a healthy profit due to the combined effect of getting extra cloth when buying and giving less cloth when selling. This is a common type of profit calculation problem where multiple factors work together.

CAT 2021 Slot 1

Amal purchases some pens at ₹ $8$ each. To sell these, he hires an employee at a fixed wage. He sells $100$ of these pens at $₹ 12$ each. If the remaining pens are sold at $₹ 11$ each, then he makes a net profit of ₹ $300$ , while he makes a net loss of ₹ $300$ if the remaining pens are sold at ₹ $9$ each. The wage of the employee, in INR, is

2025 Slot 3

The monthly sales of a product from January to April were 120, 135, 150 and 165 units, respectively. The cost price of the product was Rs. 240 per unit, and a fixed marked price was used for the product in all the four months. Discounts of 20%, 10% and 5% were given on the marked price per unit in January, February and March, respectively, while no discounts were given in April. If the total profit from January to April was Rs. 138825, then the marked price per unit, in rupees, was

CAT 2019 Slot 2

Mukesh purchased $10$ bicycles in $2017$ , all at the same price. He sold six of these at a profit of $25 \%$ and the remaining four at a loss of $25 \%$ . If he made a total profit of Rs. $2000,$ then his purchase price of a bicycle, in Rupees, was

2025 Slot 1

A shopkeeper offers a discount of 22% on the marked price of each chair, and gives 13 chairs to a customer for the discounted price of 12 chairs to earn a profit of 26% on the transaction. If the cost price of each chair is Rs 100, then the marked price, in rupees, of each chair is

CAT 2017 Slot 2

The manufacturer of a table sells it to a wholesale dealer at a profit of $10 \%$ . The wholesale dealer sells the table to a retailer at a profit of $30\%$ . Finally, the retailer sells it to a customer at a profit of $50\%$ . If the customer pays Rs $4290$ for the table, then its manufacturing cost (in Rs) is

CAT 2018 Slot 1

Two types of tea, $A$ and $B$ , are mixed and then sold at Rs. $40$ per kg. The profit is $10 \%$ if A and B are mixed in the ratio $3: 2$ , and $5 \%$ if this ratio is $2: 3$ . The cost prices, per kg , of $A$ and $B$ are in the ratio

Solution

Related questions:

Keyboard Shortcuts

CAT Past Year Questions (Topic-Wise)