CAT — Profit, Loss & Discount
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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
520
525
510
515
525
Let the marked price per unit be M. Cost Price (CP) per unit = Rs. 240.
The selling prices in the four months are:
January: 80% of M = 0.8M
February: 90% of M = 0.9M
March: 95% of M = 0.95M
April: M
Step 2: Find the total revenue
Revenue in January = 120 × 0.8M = 96M
Revenue in February = 135 × 0.9M = 121.5M
Revenue in March = 150 × 0.95M = 142.5M
Revenue in April = 165 × M = 165M
Total revenue = 96M + 121.5M + 142.5M + 165M = 525M
Step 3: Find the total cost
Total units sold = 120 + 135 + 150 + 165 = 570
Total cost = 570 × 240 = Rs. 136800
Step 4: Use the given total profit
Profit = Total Revenue − Total Cost
138825 = 525M − 136800
525M = 275625
M = 275625 ÷ 525 = 525
− Bina incurs 19% loss when she sells a product at Rs. 4860 to Shyam, who in turn sells this product to Hari. If Bina would have sold this product to Shyam at the purchase price of Hari, she would have obtained 17% profit. Then, the profit, in rupees, made by Shyam is
Given:
Bina sells a product to Shyam for Rs. 4860 at a loss of 19%.
If Bina had sold the product at the price at which Hari purchased it, she would have earned a profit of 17%.
Find Shyam's profit.
Step 1: Find Bina's cost price
Since Rs. 4860 is 81% of the cost price,
Cost Price
= 4860/0.81
= Rs. 6000
Step 2: Find Hari's purchase price
If Bina had earned a profit of 17%,
Selling Price
= 117% of 6000
= 1.17 × 6000
= Rs. 7020
Thus, Hari purchased the product for Rs. 7020.
Step 3: Find Shyam's profit
Shyam purchased the product for Rs. 4860 and sold it for Rs. 7020.
Profit
= 7020 − 4860
= Rs. 2160
Answer: Rs. 2160
An item with a cost price of Rs. 1650 is sold at a certain discount on a fixed marked price to earn a profit of 20% on the cost price. If the discount was doubled, the profit would have been Rs. 110. The rate of discount, in percentage, at which the profit percentage would be equal to the rate of discount, is nearest to
16
18
14
12
14
Step 1: Find the selling price when the profit is 20%. Cost Price (CP) = Rs. 1650. Profit = 20% of 1650 = Rs. 330. Therefore, Selling Price (SP₁) = 1650 + 330 = Rs. 1980.
Step 2: Find the selling price when the discount is doubled. When the discount is doubled, the profit becomes Rs. 110. Therefore, Selling Price (SP₂) = 1650 + 110 = Rs. 1760.
Step 3: Find the marked price. Let the marked price be M and the original discount be d%. Then, SP₁ = M × (100 − d)/100 = 1980 and SP₂ = M × (100 − 2d)/100 = 1760. Subtracting: M × d/100 = 1980 − 1760 = 220 ... (1). From the first equation, M × (100 − d)/100 = 1980. Using equation (1), M = 1980 + 220 = Rs. 2200.
Step 4: Find the original discount percentage. Discount amount = 220. Marked Price = 2200. Discount percentage = (220/2200) × 100 = 10%.
Step 5: Let the required discount rate be x%. At this discount, Profit percentage = Discount percentage = x%. Selling Price = 1650 × (100 + x)/100. Also, Selling Price = 2200 × (100 − x)/100. Equating both: 1650(100 + x) = 2200(100 − x) → 165000 + 1650x = 220000 − 2200x → 3850x = 55000 → x = 55000/3850 = 100/7 ≈ 14.29%.
Step 6: The nearest percentage is 14%.
Gita sells two objects A and B at the same price such that she makes a profit of 20% on object A and a loss of 10% on object B. If she increases the selling price such that objects A and B are still sold at an equal price and a profit of 10% is made on object B, then the profit made on object A will be nearest to
42%
45%
47%
49%
47%
Let the initial common selling price of both objects be ₹S.
Step 1: Find the cost prices
For object A, Profit = 20% → CP of A = S/1.20 = 5S/6
For object B, Loss = 10% → CP of B = S/0.90 = 10S/9
Step 2: Increase the selling price
Now the new common selling price gives a profit of 10% on object
B.
New SP = 110% of CP of B = 1.10 × 10S/9 = 11S/9
Step 3: Find the profit on object A
CP of A = 5S/6
New SP = 11S/9
Profit % = [(11S/9 − 5S/6) ÷ (5S/6)] × 100
Take LCM of 9 and 6, 11S/9 − 5S/6 = (22S − 15S)/18 = 7S/18
Therefore, Profit % = [(7S/18) ÷ (5S/6)] × 100 = (7/18) × (6/5) × 100 = 7/15 × 100 = 46.67% ≈ 47%
Answer:
C. 47%
Minu purchases a pair of sunglasses at Rs.1000 and sells to Kanu at 20% profit. Then, Kanu sells it back to Minu at 20% loss. Finally, Minu sells the same pair of sunglasses to Tanu. If the total profit made by Minu from all her transactions is Rs.500, then the percentage of profit made by Minu when she sold the pair of sunglasses to Tanu is
35.42%
52%
31.25%
26%
35.42%
Step 1: First transaction
CP = Rs. 1000. Sold at 20% profit.
SP = 1000 × 1.2 = Rs. 1200. Profit = Rs. 200.
Step 2: Kanu sells back to Minu
Kanu incurs 20% loss: SP = 1200 × 0.8 = Rs. 960
Minu buys back for Rs. 960.
Step 3: Find the final selling price
Total profit = Rs. 500. Already earned Rs. 200.
Profit in final transaction = 500 − 200 = Rs. 300
Final SP = 960 + 300 = Rs. 1260
Step 4: Calculate percentage profit in final sale
Profit % = (300/960) × 100 = 31.25%
Gopi marks a price on a product in order to make 20% profit. Ravi gets 10% discount on this marked price, and thus saves Rs 15. Then, the profit, in rupees, made by Gopi by selling the product to Ravi, is
10
25
15
20
10
Given:
Gopi marks the price of a product to earn a 20% profit.
Ravi gets a 10% discount on the marked price and saves Rs. 15.
Find Gopi's profit.
Step 1: Find the marked price
Since the discount is 10%,
10% of the marked price = 15
Marked Price
= 15/0.10
= Rs. 150
Step 2: Find the selling price
Selling Price
= 150 − 15
= Rs. 135
Step 3: Find the cost price
The marked price gives a profit of 20%.
Hence,
Marked Price = 120% of Cost Price
Cost Price
= 150/1.20
= Rs. 125
Step 4: Find the profit
Profit
= Selling Price − Cost Price
= 135 − 125
= Rs. 10
Answer:
A. 10
The selling price of a product is fixed to ensure 40% profit. If the product had cost 40% less and had been sold for 5 rupees less, then the resulting profit would have been 50%. The original selling price, in rupees, of the product is
15
14
10
20
14
Step 1: Let the original cost price be x.
Original selling price = 140% of x = 1.4x
Step 2: Form the second condition
New cost price = 60% of x = 0.6x
New selling price = 1.4x − 5
Since the new profit is 50%:
New selling price = 150% of new cost price = 1.5 × 0.6x = 0.9x
Therefore: 1.4x − 5 = 0.9x
Step 3: Solve for x
0.5x = 5 → x = 10
Step 4: Find the original selling price
Original selling price = 1.4 × 10 = Rs. 14
Jayant bought a certain number of white shirts at the rate of Rs 1000 per piece and a certain number of blue shirts at the rate of Rs 1125 per piece. For each shirt, he then set a fixed market price which was 25% higher than the average cost of all the shirts. He sold all the shirts at a discount of 10% and made a total profit of Rs.51000. If he bought both colors of shirts, then the maximum possible total number of shirts that he could have bought is
Let x = white shirts, y = blue shirts. Step 1: Find the total cost Marked price = 1.25 × Average Cost Selling price per shirt = 0.9 × 1.25 = 1.125 × Average Cost Total profit = (1.125 − 1) × Total Cost = (1/8) × Total Cost Given profit = Rs. 51,000 → Total Cost = 51,000 × 8 = Rs. 4,08,000 Step 2: Form the equation 1000x + 1125y = 408000 Divide by 125: 8x + 9y = 3264 Step 3: Maximize x + y Since 9 ≡ 1 (mod 8), y must be a multiple of 8. Let y = 8k (k ≥ 1): x = (3264 − 72k)/8 = 408 − 9k x + y = (408 − 9k) + 8k = 408 − k To maximize, take k = 1: y = 8, x = 399 Total = 399 + 8 = 407
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
Let marked price = M. Discounted price per chair = 0.78M. Revenue = 12×0.78M = 9.36M.
Cost of 13 chairs = ₹1300. With 26% profit: SP = 1300×1.26 = ₹1638.
9.36M = 1638 → M = ₹175.
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