Basic Terms / मूल शब्दावली
Cost Price — CP / क्रय मूल्य
The price at which an article is purchased is called its Cost Price.
जिस मूल्य पर कोई वस्तु खरीदी जाती है उसे क्रय मूल्य कहते हैं।
Selling Price — SP / विक्रय मूल्य
The price at which an article is sold is called its Selling Price.
जिस मूल्य पर वस्तु बेची जाती है उसे विक्रय मूल्य कहते हैं।
Marked Price — MP / अंकित मूल्य
The price printed or marked on an article before discount is called its Marked Price.
छूट देने से पहले वस्तु पर लिखा मूल्य अंकित मूल्य कहलाता है।
Profit / लाभ
When:
SP > CP
there is profit.
जब विक्रय मूल्य क्रय मूल्य से अधिक हो, तो लाभ होता है।
Profit = SP − CP
Profit Percentage
Profit% = (Profit/CP) × 100
Loss / हानि
When:
CP > SP
there is a loss.
Loss = CP − SP
Loss Percentage
Loss% = (Loss/CP) × 100
Profit or loss percentage is normally calculated on Cost Price, unless the question explicitly gives another base.
Important Direct Formulas
If profit is x%:
SP = CP × (100+x)/100
If loss is x%:
SP = CP × (100−x)/100
If SP and profit% are known:
CP = SP × 100/(100+Profit%)
If SP and loss% are known:
CP = SP × 100/(100−Loss%)
Discount / छूट
Discount = MP − SP
Discount% = (Discount/MP) × 100
Notice the difference:
Profit/Loss % → CP के आधार पर
Discount % → MP के आधार पर
This distinction is extremely important in SSC and Railway questions.
Successive Discounts / क्रमिक छूट
If two successive discounts are a% and b%:
Equivalent Discount = a + b − ab/100
Example:
20% and 10%
= 20+10−2
= 28%
Therefore, successive discounts of 20% and 10% are not 30%.
Same SP, Equal Profit and Loss %
A very important exam concept:
Two articles are sold at the same selling price. One gives x% profit and the other x% loss.
Overall result is always a loss.
Loss% = x²/100
Example:
20% profit and 20% loss:
Loss% = 400/100
= 4% loss
Dishonest Dealer Concept / बेईमान दुकानदार
Suppose a shopkeeper claims to sell at cost price but gives only 900 g instead of 1 kg.
He charges the cost of 1000 g while actually supplying 900 g.
If cost of 1 kg = ₹100:
Cost of 900 g = ₹90
SP = ₹100
Profit = ₹10
Profit%:
10/90 ×100
= 11.11%
Profit & Loss — 30 Questions
लाभ एवं हानि — 30 प्रश्न
Q1
An article is purchased for ₹500 and sold for ₹600. Profit percentage is:
₹500 में खरीदी वस्तु ₹600 में बेची गई। लाभ प्रतिशत क्या है?
A. 10%
B. 15%
C. 20%
D. 25%
Answer / उत्तर: C
Explanation: Profit=100. Profit%=100/500×100=20%.
Q2
CP=₹800 and SP=₹720. Loss percentage?
A. 8%
B. 10%
C. 12%
D. 15%
Answer: B
Q3
An article costing ₹1,200 is sold at 25% profit. SP?
A. ₹1,400
B. ₹1,450
C. ₹1,500
D. ₹1,600
Answer: C
Q4
An article costing ₹2,000 is sold at 15% loss. SP?
A. ₹1,600
B. ₹1,700
C. ₹1,750
D. ₹1,800
Answer: B
Q5
An article is sold for ₹1,320 at 10% profit. CP?
A. ₹1,100
B. ₹1,200
C. ₹1,250
D. ₹1,300
Answer: B
Q6
An article is sold for ₹1,600 at 20% loss. CP?
A. ₹1,800
B. ₹1,900
C. ₹2,000
D. ₹2,200
Answer: C
Q7
MP=₹1,000. Discount=20%. SP?
A. ₹700
B. ₹750
C. ₹800
D. ₹850
Answer: C
Q8
An article marked ₹2,000 is sold for ₹1,700. Discount percentage?
A. 10%
B. 12%
C. 15%
D. 20%
Answer: C
Q9
Successive discounts of 20% and 10% are equivalent to:
A. 26%
B. 28%
C. 30%
D. 32%
Answer: B
Q10
Successive discounts of 10% and 20% on ₹1,000 give final price:
A. ₹700
B. ₹720
C. ₹750
D. ₹800
Answer: B
Q11
A shopkeeper marks an article 25% above CP and gives 10% discount. Profit percentage?
A. 10%
B. 11.5%
C. 12.5%
D. 15%
Answer: C
Explanation: Assume CP=100. MP=125. SP=112.5. Profit=12.5%.
Q12
A trader marks goods 40% above CP and gives 20% discount. Profit percentage?
A. 10%
B. 12%
C. 15%
D. 20%
Answer: B
Q13
If SP is doubled, profit becomes three times the original profit. Find original profit%.
A. 50%
B. 75%
C. 100%
D. 125%
Answer: C
Explanation: Let CP=C and original SP=S. S−C=P. New profit=2S−C=3P=3(S−C). Hence C=S/2, so S=2C. Original profit=C=100%.
Q14
A trader sells an article at 20% profit. If CP increases by 25% but SP remains unchanged, the result is:
A. 4% profit
B. 4% loss
C. 5% loss
D. No profit, no loss
Answer: B
Q15
A shopkeeper sells two articles for ₹1,200 each. On one he gains 20%, and on the other he loses 20%. Overall:
A. 4% profit
B. 4% loss
C. No profit/loss
D. 8% loss
Answer: B
Q16
An article is sold at 25% profit. If both CP and SP increase by ₹100, profit becomes 20%. Original CP?
A. ₹300
B. ₹400
C. ₹500
D. ₹600
Answer: B
Q17
A trader sells an article for ₹540 and loses 10%. To gain 20%, he should sell it for:
A. ₹660
B. ₹700
C. ₹720
D. ₹750
Answer: C
Q18
A person buys 20 articles for ₹1,600 and sells each for ₹100. Profit percentage?
A. 20%
B. 25%
C. 30%
D. 40%
Answer: B
Q19
A trader buys 10 items for ₹8 each and sells 8 items for ₹10 each. Overall result?
A. 20% profit
B. 25% profit
C. No profit/loss
D. 20% loss
Answer: C
Q20
By selling an article for ₹450, a trader loses 10%. At what price should it be sold for 20% profit?
A. ₹550
B. ₹575
C. ₹600
D. ₹625
Answer: C
Q21
An article is sold for ₹690 after a 25% discount. Marked price?
A. ₹900
B. ₹920
C. ₹940
D. ₹960
Answer: B
Q22
A seller allows 20% discount but still earns 20% profit. If CP=₹800, MP is:
A. ₹1,000
B. ₹1,100
C. ₹1,200
D. ₹1,250
Answer: C
Q23
A trader sells at cost price but uses 800 g instead of 1 kg. Profit percentage?
A. 20%
B. 25%
C. 30%
D. 40%
Answer: B
Q24
A dishonest dealer claims 10% loss but uses 800 g instead of 1 kg. Actual profit percentage?
A. 10%
B. 11.25%
C. 12.5%
D. 15%
Answer: C
Q25
A shopkeeper earns 20% profit after giving 20% discount. Marked price is what percent above CP?
A. 40%
B. 45%
C. 50%
D. 60%
Answer: C
Q26
If an article is sold at 10% loss instead of 10% profit, the seller receives ₹120 less. CP?
A. ₹500
B. ₹600
C. ₹700
D. ₹800
Answer: B
Q27
A trader gains 25% by selling an article for ₹1,000. If he sells it for ₹880, profit percentage?
A. 8%
B. 10%
C. 12%
D. 15%
Answer: B
Q28
A seller wants 25% profit after giving 20% discount. If CP=₹640, MP?
A. ₹900
B. ₹950
C. ₹1,000
D. ₹1,050
Answer: C
Q29
A person sold an article at 20% loss. If he had sold it for ₹200 more, he would have gained 20%. CP?
A. ₹400
B. ₹500
C. ₹600
D. ₹800
Answer: B
Q30
A trader marks an article 60% above CP and allows successive discounts of 20% and 10%. His profit percentage is:
A. 12%
B. 15.2%
C. 16%
D. 18%
Answer: B
Explanation: CP=100 → MP=160 → after 20%=128 → after 10%=115.2. Profit=15.2%.