Basic Definitions and Formulas for Profit and Loss
- Cost Price (CP) – This is the price at which an article is purchased.
- Selling Price (SP) – This is the price at which an article is sold.
- Profit or Gain – If the selling price is more than the cost price, the difference between them is the profit incurred.
- Profit or Gain = Selling price (SP) – Cost price (CP)
- Loss – If the selling price is less than the cost price, the difference between them is the loss incurred.
- Loss = Cost price (CP) – Selling price (SP)
- Gain on Rs. 100 is Gain Percent
- Gain% = (Gain * 100)/CP
- Loss on Rs. 100 is Loss Percent
- Loss% = (Loss * 100)/CP
- Profit or Loss is always calculated on the cost price.
- Marked Price – This is the price marked as the selling price on an article, also known as the listed price.
- Discount or Rebate – This is the reduction in price offered on the marked or listed price.
- If an article is sold at a gain of 10%, then SP = 110% of CP.
- If an article is sold at a loss of 10%, then SP = 90% of CP.
Profit and Loss Aptitude Problems and Solved Examples
Q.1: An article is bought for Rs. 675 and sold for Rs. 900. Find the gain percent?
A. 30 2/3%
B. 31 1/3%
C. 33 1/3%
D. 33 1/6%
Answer: B. 33 1/3%
Explanation: 900 – 675 = 225
225/675*100
= 33 1/3%
Q.2: A person buys a horse for 15 pounds. After one year, he sells it for 20 pounds. After one year, again he buys the same horse at 30 pounds and sells it for 40 pounds. What is the overall profit percent for that person over both the transactions?
A. 30.33%
B. 33.33%
C. 35.33%
D. 40.33%
Answer: B. 33.33%
Explanation: Total C.P. = 45
Total S.P. = 60
Profit% = (15/45) *100 = 33.33%
Profit and Loss Problems – Basic Concepts, Formulas, Math Tricks, Quantitative Aptitude Questions and Solutions
Q.3: A trader sells 85 m of cloth for Rs. 8,925 at the profit of Rs. 15/m of cloth. What is the cost price of 1 m of cloth?
A. Rs. 84
B. Rs. 90
C. Rs. 96
D. Rs. 102
Answer: B. Rs. 90
Explanation: SP of 1m of cloth = 8925/85 = Rs. 105
CP of 1m of cloth = SP of 1m of cloth – profit on 1m of cloth
= Rs. 105 – Rs. 15 = Rs. 90
Q.4: A, B and C enter into a partnership. A invests some money at the beginning, B invests double the amount after 6 months and C invests thrice the amount after 8 months. If the annual gain be Rs. 18,000. A's share is?
A. Rs. 5,750
B. Rs. 6,000
C. Rs. 7,200
D. Rs. 7,500
Answer: B. Rs. 6,000
Explanation: x*12 : 2x*6: 3x*4
1:1:1
1/3 * 18000 = 6000
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Q.5: By selling an article at Rs. 800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?
A. Rs. 460
B. Rs. 480
C. Rs. 500
D. Rs. 520
Answer: B. Rs. 480
Explanation: SP = 800, Profit = 25%
CP = (SP)*[100/(100+P)]
= 800 * [100/125] = 640
Loss = 25% = 25% of 640 = Rs. 160
SP = CP – Loss = 640 – 160 = Rs. 480
Q.6: Amit bought 160 shirts at the rate of Rs. 225/shirt. The transport expenditure was Rs. 1,400. He paid an octroi at the rate of Rs. 1.75/shirt and labour charges were Rs. 320. What should be the selling price of 1 shirt, if he wants a profit of 20%?
A. Rs. 260
B. Rs. 275
C. Rs. 280
D. Rs. 285
Answer: D. Rs. 285
Explanation: Total CP per shirt = 225 + 1400/160 + 1.75 + 320/160 = Rs. 237.5
SP = CP[(100 + profit%)/100]
= 237.5 * [(100 + 20)/100] = Rs. 285
Q.7: A man sold two houses for Rs. 7.8 lakhs each. On the one, he gained 5% and on the other, he lost 5%. What percent is the effect of the sale on the whole?
A. 0.25 % loss
B. 0.25 % gain
C. 25 % loss
D. 25 % gain
Answer: A. 0.25 % loss
Explanation: Loss% = (5/10)^2 = 1/4% = 0.25%
Q.8: Profit after selling a commodity for Rs. 425 is same as loss after selling it for Rs.355. The cost of the commodity is:
A. Rs. 385
B. Rs. 390
C. Rs. 395
D. Rs. 400
Answer: B. Rs. 390
Explanation: Let C.P = Rs. X
425 – X = X – 355 (or)
2X = 780 or X = 390
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Q.9: If two mixers and one T.V cost Rs. 7000. While two T.V s and one mixer cost Rs. 9800. The value of one T.V is:
A. Rs. 3,200
B. Rs. 3,600
C. Rs. 4,200
D. Rs. 4,600
Answer: C. Rs. 4,200
Explanation: 2X + Y = 7000
X + 2Y = 9800
Solving (i) and (ii), we get Y = 4200
Q.10: Bhajan Singh purchased 120 reams of paper at Rs. 80 per ream. He spent Rs. 280 on transportation. Paid octrai at the rate of 40 paise per ream and paid Rs. 72 to the coolie. If he wants to have a gain of 8 %. What must be the selling price per ream?
A. Rs. 86
B. Rs. 88
C. Rs. 90
D. Rs. 92
Answer: C. Rs. 90
Explanation: C.P of 120 reams = Rs. (120 × 80 + 280 + 72 + 120 × 40) = Rs. 10000
C.P of 1 ream = (10000/120) = Rs. (250/3)
S.P of 1 ream = Rs. (108/100 × 250/3) = Rs. 90
Q.11: If an article is sold at a loss of 66 2/3%, what is the loss in terms of the selling price?
A. 50%
B. 100%
C. 150%
D. 200%
Answer: D. 200%
Explanation: Let the C. P. = 100
∴ Amount of loss = 66 2/3 or 200/3
⇒ S. P = 100 – 66 2/3 = 33 1/3 or 100/3
∴ Loss expressed in terms of S. P. = 100 × (200/3)/(100/3) 100 = 200%
Q.12: A shopkeeper bought 150 pen drives at the rate of Rs. 500 per pen drive. He spent Rs. 500 on transportation and packing. If the marked price of pen drive is Rs. 520 per pen drive and the shopkeeper gives a discount of 5% on the marked price then what will be the percentage profit gained by the shopkeeper?
A. 1.2%
B. 3.8%
C. 4.5%
D. 5.5%
Answer: B. 3.8%
Explanation: C.P. of 150 calculators = 150 * 500 = Rs. 75000
∴ Total C.P. = 75000 + 500 = Rs. 75500
Marked price of 150 calculator = 150 * 570 = Rs. 82500
Selling price after discount = 82500 * 95 / 100 = Rs. 78375
∴ percentage profit = [(78375 – 75500) / 75500] * 100 = 3.8%
Q.13: An article is sold at 25% profit. If the CP and the SP of the article are increased by Rs 60 and Rs 30 respectively, the profit% decreases by 15%. Find the cost price of the article.
A. Rs. 190
B. Rs. 240
C. Rs. 285
D. Rs. 305
Answer: B. Rs. 240
Explanation: CP = x, then SP = (125/100)*x = 5x/4
New CP = (x+60), new SP = (5x/4 + 30), new profit% = 25-15 = 10
So (5x/4 + 30) = (110/100) * (x+60)
Solve, x = 240
Q.14: A person sold a pen at Rs. 96 in such a way that his percentage profit is same as the cost price of the watch. If he sells it at twice the percentage
profit of its previous percentage profit then new selling price will be?
A. Rs. 132
B. Rs. 150
C. Rs. 180
D. Rs. 192
Answer: A. Rs. 132
Explanation: CP = x
Profit Percentage = x%
SP = x(100 + x)/100
x(100 + x)/100 = 96
x = 60
Profit Percentage = 60%
New SP = 60 * 220 / 100 = 132
Q.15: A and B, there are two companies, selling the packs of cold-drinks. For the same selling price A gives two successive discounts of 10% and 25%. While B sells it by giving two successive discounts of 15% and 20%. What is the ratio of their marked price?
A. 143 : 144
B. 19 : 11
C. 136 : 135
D. 73 : 77
Answer: C. 136 : 135
Explanation: A = 90/100*75/100
=> 0.675
B = 85/100*80/100
=> 0.68
=> 680 : 675
=> 136 : 135