RRB JE Profit AND Loss Questions with Detailed Solutions

Given
Ratio of CP of X and Y = 3 : 7
Profit on X = 49%
Loss on Y = 16%
Formula Used
Selling Price (SP) = $$CP × (1 + \frac{Profit}{100})$$​​
Overall Profit % = $$\frac{Total SP - Total CP}{Total CP} × 100$$​​
Solution
Let CP of X = 300 and CP of Y = 700
Total CP = 300 + 700 = 1000
SP of X = 300 × 1.49 = 447
SP of Y = 700 × 0.84 = 588
Total SP = 447 + 588 = 1035
Overall Profit = 1035 - 1000 = 35
Profit % = $$\frac{35}{1000} × 100 = 3.5$$​​
Final Answer
So the correct answer is (d)

Given
Goods sold at cost price.
Profit percentage = 3 $$\frac{19}{27} \%$$​​
Claimed weight = 1 kg = 1000 g
Formula Used
Profit Percentage = $$\frac{\text{Error}}{\text{True Weight - Error}} × 100$$​​
True Weight - Error = False Weight used
Solution
Profit % =  $$\frac{81 + 19}{27} \% = \frac{100}{27} \%$$​​
Fractional gain = $$\frac{100}{27 × 100} = \frac{1}{27}$$​​
Let the false weight used be W.
Ratio of Selling Price to Cost Price = $$\frac{\text{True Weight}}{\text{False Weight}} = 1 + \frac{1}{27} = \frac{28}{27}$$​​
​$$\frac{1000}{W} = \frac{28}{27} \\\ \\W = \frac{1000 × 27}{28} = \frac{27000}{28}\\\ \\W = \frac{6750}{7} ≈ 964.2857 g\\\ \\$$​​
Rounded to 2 decimal places, the weight is 964.29 g.
Final Answer
So the correct answer is (b)

Given
Ratio of Cost Prices of X and Y = 1 : 2
Profit on X = 12%
Loss on Y = 36%
Formula Used
Selling Price = Cost Price × $$(1 + \frac{\text{Profit}}{100})$$​ for gain

Selling Price = Cost Price × $$(1 - \frac{\text{Loss}}{100})$$​ for loss

Overall Percentage =$$\frac{ \text{Total SP - Total CP}}{\text{Total CP}}$$​ × 100
Solution
Let the Cost Price of X be 100 and Cost Price of Y be 200.
Total Cost Price = 100 + 200 = 300
Selling Price of X = 100 × (1 + 0.12) = 112
Selling Price of Y = 200 × (1 - 0.36) = 200 × 0.64 = 128
Total Selling Price = 112 + 128 = 240
Since Total SP < Total CP, there is an overall loss.
Loss = 300 - 240 = 60
Loss Percentage = $$\frac{60}{300} × 100$$​​
Loss Percentage = 20%
Final Answer
So the correct answer is (a)

Given:
Cost price of 6 identical mobile phones = ₹45,000.
Selling price of 2 mobile phones = ₹42,000.
Formula Used:
Gain G = Selling price - Cost price
Gain % = $$\frac{Gain}{Cost\ price}$$​ × 100
where S is selling price and C is cost price.
Solution:
Cost price of 6 mobile phones = ₹45,000.
Cost price of 1 mobile phone = $$\frac{45000}{6}$$​ = 7500.
Cost price of 2 mobile phones C = 2 × 7500 = 15000.
Selling price of 2 mobile phones S = ₹42,000.
Gain G = 42000 - 15000 = 27000.
Calculating the gain percentage:
Gain % = $$\frac{27000}{15000} × 100$$​​ = $$\frac{9}{5} × 100 = 9 × 20 = 180\%.$$​​
Final Answer
So the correct answer is (c)

Given:
Purchase rate of 1st type = ₹2 for 3 apples.
Purchase rate of 2nd type = ₹6 per apple.
Equal numbers of both types are purchased.
Selling price of all apples = ₹6 per apple.
Formula Used:
Profit P = S - C
Profit % = $$\frac{P}{C} × 100$$​​
where S is total selling price and C is total cost price.
Solution:
Let the man buy 3 apples of each type.
Cost price of 3 apples of 1st type = ₹2.
Cost price of 3 apples of 2nd type = 3 × 6 = 18.
Total cost price C for 6 apples = 2 + 18 = 20.
Total selling price S for 6 apples at ₹6 each = 6 × 6 = 36.
Calculating total profit P:
P = 36 - 20 = 16.
Calculating profit percentage:
Profit % = $$\frac{16}{20}$$​× 100 = 16 × 5 = 80%.
Final Answer
So the correct answer is (b)

Given:
Original list price of washing machine = ₹87,200.
Successive discounts given to retailer = 9% and 50%.
Desired profit percentage for retailer = 25%.
Discount allowed by retailer to customer = 48%.
Formula Used:
Effective price after discounts $$d_{1}$$​ and $$d_{2}:$$​​
Price = $$P × (1 - \frac{d_{1}}{100}) × (1 - \frac{d_{2}}{100})$$​​
Selling price for desired profit p:
​$$S = C × (1 + \frac{p}{100})$$​​
New list price L after allowing discount d:
​$$L = \frac{S}{1 - \frac{d}{100}}$$​​
Solution:
Calculating the cost price C for the retailer:
C = 87200 × $$(1 - \frac{9}{100}) × (1 - \frac{50}{100})$$​​

C = 87200 × $$\frac{91}{100} × \frac{50}{100}$$​​

C = 87200 × 0.91 × 0.5 = 39676.

Retailer's cost price C = ₹39,676.

Calculating the required selling price S to earn 25% profit:
S = 39676 × $$(1 + \frac{25}{100})$$​​

S = 39676 × $$\frac{5}{4}$$​ = 9919 × 5 = 49595.
Required selling price S = ₹49,595.
Let the new list price be L.
Since a discount of 48% is offered on L:
​$$L × (1 - \frac{48}{100}) = 49595$$​​

L × 0.52 = 49595

L = $$\frac{49595}{0.52}$$​ = 95375.
Therefore, the retailer should list the washing machine at ₹95,375.
Final Answer
So the correct answer is (a)

Given
Discount = 8%
Free articles = 3 for every 18 articles bought (Total 21 given)
Overall Profit = 38%
Formula Used
Selling Price (SP) = Marked Price (MP) × $$\frac{100 - \text{Discount}}{100}$$​​
Cost Price (CP) = SP × $$\frac{100}{100 + Profit}$$​​
Solution
Let the Cost Price (CP) of 1 article = 100
Total CP for 21 articles given to the customer = 21 × 100 = 2100
The trader gains an overall profit of 38% on his total investment.
Total Selling Price (SP) for the transaction = 2100 × 1.38 = 2898
The customer pays for exactly 18 articles at the discounted price.
Total SP of 18 articles = 2898
SP of 1 article = $$\frac{2898}{18} = 161$$​​
The discount given is 8% on the Marked Price (MP).
MP of 1 article = $$\frac{161}{1 - 0.08} = \frac{161}{0.92} = 175$$​​

Markup percentage = $$\frac{175 - 100}{100} × 100 = 75$$​​
Final Answer
So the correct answer is (b)

Given
Cost price (CP) of 24 articles = Selling price (SP) of 15 articles
Formula Used
Profit % = $$\frac{SP - CP}{CP} × 100$$​​
Solution
24 × CP = 15 × SP
​$$\frac{SP}{CP} = \frac{24}{15} = \frac{8}{5}$$​​
Let SP = 8 units and CP = 5 units
Profit = 8 - 5 = 3 units
Profit % = $$\frac{3}{5} × 100 = 60\%$$​​
Final Answer
So the correct answer is (a)

Given:
Selling price of 20 books = Cost price of 31 books
Formula Used:
Gain% = $$\frac{SP - CP}{CP}$$​ × 100
Solution:
Let the cost price of 1 book be CP and the selling price of 1 book be SP.
According to the question:
20 × SP = 31 × CP
​$$\frac{SP}{CP} = \frac{31}{20}$$​​
Here, SP is greater than CP, which indicates a gain.
Gain = 31 - 20 = 11 units.
Gain % = $$\frac{11}{20}$$​ × 100 = 55% 
Final Answer
So the correct answer is (a)

Given:
Claimed selling price = Cost price
Promised weight = 1000 grams
Actual weight delivered = 902 grams
Formula Used:
Profit % = $$\frac{Gain}{Cost Value}$$​ × 100
Solution:
Let the cost price of 1 gram be 1 unit.
Cost price of 902 grams = 902 units.
Selling price charged for 1000 grams = 1000 units.
Profit = 1000 - 902 = 98 units.
Profit % = $$\frac{98}{902} × 100 = 10.864\% ≈ 10.86\%$$​​
Final Answer
So the correct answer is (d)

Given:
Marked price of each item = ₹700
Total items purchased = 5
Scheme applied = Buy 4 get 1 free
Additional trade discount = 16%
Formula Used:
Discounted Price = Marked Price ×$$(1 - \frac{Discount \%}{100})$$​​
Solution:
Under the "Buy 4 get 1 free" scheme, out of 5 items, the customer only pays the marked price for 4 items.
Effective marked price before trade discount = 4 × 700 = 2800
Now, apply the 16% trade discount on this amount:
Final Price = $$2800 × (1 - \frac{16}{100})$$​​

​$$= 2800 × \frac{84}{100}$$​​

= 28 × 84 = 2352

Thus, the total discounted price the customer pays is ₹2352.
Final Answer
So the correct answer is (b)

Given
Total eggs purchased = 1200
Cost price (CP) per egg = ₹4.50
Percentage of broken eggs = 8%
Selling price (SP) per remaining egg = ₹6.00
Formula Used
Total CP = Number of eggs $$\times$$​CP per egg
Profit Percentage = $$\frac{\text{Total SP} - \text{Total CP}}{\text{Total CP}} \times 100$$​​
Solution
Total CP for all 1200 eggs = 1200 $$\times$$​ 4.50 = 5400.
Number of eggs broken = $$8\% of 1200 = 1200 \times 0.08 = 96.$$​​
Remaining good eggs to sell = 1200 - 96 = 1104.
Total SP from the remaining eggs = $$1104 \times 6.00 = 6624.$$​​
Overall Profit = 6624 - 5400 = 1224.
Profit Percentage = $$\frac{1224}{5400} \times 100 = \frac{1224}{54}$$​​ = $$22 \frac{2}{3} \%.$$​​
Final Answer
So the correct answer is (c)

Given
50% goods sold at 19% profit.
20% of remaining goods sold at 40% profit.
Rest of the goods sold at 25% loss.
Overall profit = x%
Formula Used
Total SP = Sum of individual Selling Prices
Overall Profit % = $$\frac{\text{Total SP} - \text{Total CP}}{\text{Total CP}} \times 100$$​​
Solution
Let total quantity of goods be 100 and total Cost Price (CP) be 100.
Part 1: 50% of goods = 50 items. Profit = 19%.
SP of Part 1 = 50 $$\times$$​1.19 = 59.5
Remaining goods = 100 - 50 = 50.
Part 2: 20% of remaining goods = 20% of 50 = 10 items. Profit = 40%.
SP of Part 2 = 10$$\times$$​ 1.40 = 14
Part 3: Still remaining goods = 100 - (50 + 10) = 40 items. Loss = 25%.
SP of Part 3 = 40$$\times$$​(1 - 0.25) =$$40 \times 0.75 = 30$$​​
Total SP = 59.5 + 14 + 30 = 103.5
Overall Profit = 103.5 - 100 = 3.5
Overall Profit Percentage (x) = 3.5%
Final Answer
So the correct answer is (d)

Given
Selling Price 1 (SP1) = 76% of Marked Price (MP)
Loss at SP1 = 20%
New Selling Price (SP2) = 99% of MP
Formula Used
SP = CP $$\times (1 - \frac{\text{Loss\%}}{100})$$​​

Profit Percentage = $$\frac{SP - CP}{CP} \times 100$$​​
Solution
Let the Marked Price (MP) be 100.
Then SP1 = 76.
Since there is a 20% loss, SP1 is 80% of CP.
​$$0.8 \times CP = 76 \\CP = \frac{76}{0.8} = 95.$$​​
Now, if the article is sold at 99% of its marked price, SP2 = 99.
Profit = SP2 - CP = 99 - 95 = 4.
Profit Percentage = $$\frac{4}{95} \times 100 = \frac{400}{95}$$​​= $$4 \frac{4}{19} \%.$$​​
Final Answer
So the correct answer is (c)

Given
Cost of 6 mobile phones = ₹72,000
Selling price of 2 mobile phones = ₹42,000
Formula Used
Profit Percentage = (Profit / Cost Price) × 100
Solution
Cost Price of 1 phone = $$\frac{72000}{6} = 12000.$$​​

Selling Price of 1 phone = $$\frac{42000}{2} = 21000.$$​​
Profit on 1 phone = 21000 - 12000 = 9000.
Gain Percentage = $$(\frac{9000}{12000}) \times 100 = 75\%.$$​​
Final Answer
So the correct answer is (c)