If you’re preparing for a competitive exam, then you’re likely aware of the importance of mastering profit and loss problems. These types of questions are a staple in many exams, including those for banking, insurance, and management positions. By learning key concepts such as cost price, selling price, profit, and loss, and by using effective strategies to solve different types of problems, you can increase your accuracy and speed in solving these questions.
Assignment:1
Que 1: When an article is sold for Rs.703, there is a loss of 25% less than the profit earned when it is sold for Rs.836. What is the selling price of the article when it makes a profit of 20%?
(a) 900
(b) 860
(c) 912
(d) 960
Solution: Let the profit earned while selling at 836= 4k
Loss, while selling at 703= 3k (25% less)
Total gap= 4k+3k=7k
7k= 836–703= 133
k=19 (Profit and Loss Problems)
Now, in the first case: Cost Price+ 4k= 836
Cost Price= 836- 76= 760
New selling price= CP+ 20% of CP= 760+152= 912 rs
Option (c) is correct.
Que 2: What is the profit earned on an article with a cost price of 2128 rs, given that the ratio of its marked price and the selling price is 12:7, and the ratio of the discount given and the profit earned is 7:6?
(a) 3360 rs
(b) 2880 rs
(c) 3600 rs
(d) 2420 rs
Solution: SP: MRP= 7:12 (Profit and Loss Problems)
Given, The discount= 12k-7k=5k= 7 unit
7 unit=5k
1 unit=5k/7
Profit earned= 6 unit= 30k/7
CP= SP-Profit= 7k-30k/7=19k/7
CP:SP: MRP= 19/7: 7: 12= 19: 49: 84
Given, 19x= 2128
x= 112 (Profit and Loss Problems)
Profit= 49x-19x=30x= 3360 rs
Option (a) is correct.
Que 3: What is the profit percentage made by the retailer who sells a commodity at the cost price, given that he receives 22% more from the wholesaler than he paid for and then gives 20% less while selling to his customer?
(a) 42%
(b) 55.55%
(c) 52.5%
(d) 60.25%
Solution: Let the CP of the article= 1 rs/kg
Given, after paying Rs 100 to the wholesaler, the retailer received 122 kg of the article.
Total CP for retailer= 100 rs …………(i)
Now the retailer will sell it for Rs 100 per 80 kg. (Profit and Loss Problems)
80 kg⇒ 100 rs
1kg⇒ 10/8 rs
122 kg⇒ 1220/8 rs
Total SP for retailer= 1220/8 rs………..(ii)
CP: SP= 100: 1220/8= 40:61
Profit percentage= \frac{61-40}{40}\times 100=52.5%
Option (c) is correct.
Que 4: What is the retail price per mango that would yield a 60% profit, if the cost of purchasing 5 dozen mangoes at a certain price resulted in a gain of 3/10th of the total outlay when sold at Rs 156 per 5 dozen?
(a) 3.20 rs
(b) 2.80 rs
(c) 3.60 rs
(d) 2.75 rs
Solution: 5 dozen Mangoes⇒ 156 rs
CP: SP= 10: 13 (3/10th profit is given)
Let, CP= 10x (Profit and Loss Problems)
SP= 13x
13x= 156
x=12
So, CP of 5 dozen Mangoes= 12×10=120 rs
CP of 1 Mango= 120/(5×12)=2 rs
Retail Price of mango with 60% profit= 2+ 60% of 2= 3.2 rs
Option (a) is correct.
Que 5: What percentage increase in the cost price is required to set the selling price such that a profit of 20% is earned, taking into account a commission of 10% on the selling price?
(a) 25%
(b) 33.33%
(c) 30%
(d) 62.5%
Solution: MRP: SP= 10: 9
CP: SP=5: 6
CP: SP: MRP= 15: 18: 20
CP: MRP= 3: 4
Increment= 33.33%
Option (b) is correct.
Que 6: The cost of a bedsheet bought by a man was 450 rs, and he sold it at a profit of 10%, calculated based on the selling price. What was the selling price of the bedsheet?
(a) 460 rs
(b) 475 rs
(c) 480 rs
(d) 500 rs
Solution: CP: SP= 10-1: 10=9: 10
9 unit= 450 rs
10 unit= 500 rs
Option (d) is correct.
Que 7: Nisha purchased a certain quantity of oranges at the rate of 2 for 1 rupee and an equal amount at the rate of 3 for 1 rupee. To earn a profit of 20%, what should be the selling price of one dozen oranges?
(a) 6
(b) 8
(c) 10
(d) 12
Solution: LCM(2,3)=6
Type A⇒ 6 for 3 rs
Type B⇒ 6 for 2 rs
One dozen for 5 rs
CP: SP= 5:6
Option (a) is correct.
Que 8: Pooja intends to sell a watch at a 20% profit. She purchased it at a discount of 10% and sold it for 30 less than its actual selling price, yet she still earned a profit of 20%. What was the cost price of the watch?
(a) 240 rs
(b) 220 rs
(c) 225 rs
(d) 250 rs
Solution: CP: SP=5k: 6k
New CP= 4.5k
New SP= 6k-30
4.5k: 6k-30= 5: 6
27k= 30k-150
k=50
CP=5k=250 rs
Option (d) is correct.
Que 9: A fruit merchant earns a profit of 25% by selling mangoes at a particular price. If he increases the price of each mango by Re. 1, he would earn a profit of 50%. What was the initial price of one mango?
(a) 5 rs
(b) 7 rs
(c) 4 rs
(d) 6 rs
Solution: CP: SP= 4k: 5k
4k: 5k+1=2:3
12k= 10k+2
k=1
Initial price= 5k=5 rs
Option (a) is correct
Que 10: If bananas are purchased at the rate of 4 for 1 rupee, how many bananas must be sold for 1 rupee to earn a profit of 33.33%?
(a) 2.5
(b) 2
(c) 3
(d) 4
Solution: CP: SP=3: 4
1/4 : SP=3: 4
SP=1/3
Option (c) is correct
Assignment:2
Que 1: What is the cost price of an article if the profit on selling it for Rs. 425 is equal to the loss on selling it for Rs. 355?
(a) 410
(b) 380
(c) 400
(d) 390
Solution: CP-355=425-CP
CP=390
Option (d) is correct
Que 2: If the cost price of 10 articles is equal to the selling price of 15 articles, what is the percentage of profit or loss incurred on the transaction?
(a) 25.5%
(b) 35%
(c) 10%
(d) 33.33%
Solution: CP×10=SP×15
CP: SP=3:2
Loss=33.33%
Option (d) is correct
Que 3: If a trader incurred a loss of 10% on selling a cycle and could have gained 6% had the selling price been increased by Rs. 200, what was the cost price of the cycle?
(a) 1200 rs
(b) 1205 rs
(c) 1250 rs
(d) 1275 rs
Solution: 90%+200=106%
16%=200
1%=25/2
100%=1250
Option (c) is correct
Que 4: If A sold an article to B at a profit of 20% and B sold it to C at a loss of 15%, what profit or loss would A make if he had sold the article directly to C at the same selling price as B?
(a) 5% profit
(b) 2% profit
(c) 2% loss
(d) 5% loss
Solution: A: B=5: 6
B: C=20: 17
A: B: C= 100: 120: 102
A makes 2% profit
Option (b) is correct
Que 5: If goods are purchased for Rs. 976.50 and one-third of the goods are sold at a loss of 10%, what percentage of gain should be made on the remainder of the goods to achieve an overall profit of 20% on the whole transaction?
(a) 32%
(b) 35%
(c) 28%
(d) 30%
Solution:
x-20 : 30=1/3: 2/3 =1:2
2x-40=30
x=35
Option (b) is correct
Que 6: If a shopkeeper sells rice at a profit of 10% while using a weight that is 30% less than the actual measure, what is the percentage of profit that the shopkeeper earns?
(a) 57.67%
(b) 57.14%
(c) 57.40%
(d) 57.43%
Solution: SP= Price per unit× No. of Units
Weight⇒ 10: 7
SP⇒ 10: 11
Price= 10/10: 11/7= 7: 11
Percentage Profit= 400/7= 57(1/7)=57.14%
Option (b) is correct
Que 7: If a dishonest dealer defrauds by x% while both buying and selling goods by using a faulty weight, what will be the percentage of gain on his total outlay?
(a) 2x%
(b) (10/x+x2)%
(c) (x+x2/100)%
(d) None
Solution: If the total expense is the same
The ratio of weight∝ 1/Ratio of Price
Let x=10%
The deal between the wholesaler and dealer
Weight⇒ 10: 11
Price⇒ 11: 10
This means the dealer pays the wholesaler Rs 10 for an item priced at Rs 11 (say 11 kg of an item at Rs 1/kg)
The deal between the dealer and the customer
Weight⇒ 10: 9
Price⇒ 9: 10
This means the dealer charges Rs 10 for an item worth Rs 9 (say 9 kg is sold for Rs 10)
9 kg⇒ 10 rs
1 kg⇒ 10/9 rs
11 kg⇒ 110/9 rs
CP: SP= 10: 110/9= 9:11
Profit= 200/9= 22.22%
Put x=10 in the options
Option (d) is correct
Que 8: Mohan bought 25 books for Rs. 2,000 and sold them at a profit equal to the selling price of 5 books. What is the selling price of one book?
(a) 100 rs
(b) 120 rs
(c) 150 rs
(d) 200 rs
Solution: 25×SP-2000=5×SP
SP=100
Option (a) is correct
Que 9: A fruit seller buys a certain number of oranges and sells 40% of them to realize the cost price of all the oranges. He reduces the price of the remaining oranges by half the previous rate of profit as they begin to grow over-ripe and sell 80% of them. The rest of the oranges are thrown away as they have become rotten. What is the overall percentage of profit earned by the fruit seller?
(a) 80
(b) 84
(c) 94
(d) 96
Solution: Let the Total oranges be 100 of 1 rs each
40 oranges sold for 100 rs
Profit percentage= 6000/40= 150%
80% of the remaining 60 oranges= 48
48 oranges sold at 75% profit= 84 rs
Total SP= 100+84= 184
CP: SP= 100: 184
Profit percentage= 84%
Option (b) is correct
Que 10: If two toys are sold for Rs. 723 each, and one toy brings the dealer a gain of 12% while the other toy causes a loss of 4%, what is the overall gain or loss percentage when both toys are sold together?
(a) 3(5/13)% profit
(b) 4(5/13)% profit
(c) 5(1/13)% profit
(d) 2(3/13)% profit
Solution: 12%=3/25 and 4%=1/25
(25: 28)×6= 150: 168
(25: 24)×7= 175: 168
CP: SP= 325: 336
Profit percentage= 1100/325= 3.38%
Option (a) is correct
Assignment:3
Que 1: What is the cost price of an item for a manufacturer if it is sold to a wholesale dealer at a profit of 18%, then to a retailer at a profit of 20%, and finally to a customer for 15045 with a profit of 25%?
(a) 8000 rs
(b) 8500 rs
(c) 9000 rs
(d) 10000 rs
Solution: 18%= 9/50, 20%=1/5, 25%=1/4
50: 59
5: 6
4: 5
Final ratio= 50×5×4: 59×6×5= 100: 177
177 unit= 15045 rs
1 unit= 85
100 unit= 8500 rs
Option (b) is correct
Que 2: What was the cost price of a bicycle for a dealer if he sold it at a profit of 10%, but if he had bought it at 10% less price and sold it for Rs. 60 more, he would have gained 25% profit?
(a) 2400 rs
(b) 2600 rs
(c) 2000 rs
(d) 2200 rs
Solution: 90%×5/4= 110%+60
112.5%-110%=60
2.5%=60
100%=2400 rs
Option (a) is correct
Que 3: If a milkman sells a mixture of milk and water at a price of Rs. 9 per liter and earns a profit of 20%, and the cost price of 1 liter of pure milk is Rs. 10, what is the ratio of milk and water in the mixture?
(a) 3:1
(b) 4:1
(c) 3:2
(d) 4:3
Solution: 20%=1/5
CP:SP=5: 6
6 unit= 9 rs
1 unit= 3/2 rs
CP of mixture= 5 unit=7.5 rs
Milk: Water= 7.5: 2.5= 3: 1
Option (a) is correct
Que 4: If a shopkeeper sells a book at a discount of 10% on the printed price and earns a profit of 12%, what is the ratio of the cost price and the printed price of the book?
(a) 99: 125
(b) 25:37
(c) 50: 61
(d) 45: 56
Solution: SP: MRP= 9: 10
CP: SP= 25: 28
CP: SP: MRP= 225: 252: 280
CP: MRP= 225: 280= 45: 56
Option (d) is correct
Que 5: If A invests Rs. 64,000 in a business and after a few months, B joins him with Rs. 48,000, and at the end of the year, they divide the total profit in the ratio of 2:1, after how many months did B join the business?
(a) 8
(b) 4
(c) 6
(d) 7
Solution: 64000×12: 48000×k= 2:1
4×12: 3×k=2:1
6k=48
k=8 months
B joins after 4 months
Option (b) is correct
Que 6: If Rs. 864 is divided among A, B, and C such that 8 times A’s share is equal to 12 times B’s share and also equal to 6 times C’s share, how much money did B receive?
(a) 399 rs
(b) 192 rs
(c) 288 rs
(d) 72 rs
Solution: 8A=12B=6C
LCM(8,12,6)=24
Divide the given equation by 24
A/3=B/2=C/4
A:B:C=3:2:4
9 unit= 864 rs
2 unit= 192 rs
Option (b) is correct
Que 7: In a business partnership among A, B, C, and D, the investment ratio is A:B=B:C=C:D= 1:3. If the total profit of the business is Rs. 400,000, what is the share of C in the profit?
(a) 1,12,500 rs
(b) 1,37,500 rs
(c) 90,000 rs
(d) 2,70,000 rs
Solution: A:B:C:D=1:3:9:27
40 unit= 400000
1 unit= 10000
9 unit= 90000
Option (c) is correct
Que 8: If a sum of Rs. 1,170 was distributed among A, B, and C in the ratio 2:3:4, by mistake, in place of 1/2:1/3:1/4, who among A, B, and C benefited the most and by how much?
(a) B, 220 rs
(b) C, 250 rs
(c) B, 270 rs
(d) A, 280 rs
Solution: A:B:C= 2:3:4 (by mistake)= 9 unit
A:B:C= 6:4:3 (Actual)= 13 unit
(2:3:4)×13=26:39:52
(6:4:3)×9=54:36:27
C gains= 52-27= 25 unit
117 unit= 1170 rs
25 unit= 250 rs
Option (b) is correct
Que 9: If a shopkeeper gains 20% while buying goods and 30% while selling them, what is his total gain percentage?
(a) 50%
(b) 62.5%
(c) 75%
(d) 56%
Solution: 20%=2/10 and 30%=3/10
Let, the manufacturing cost be 1 rs/kg
While buying⇒ 10 rs paid for 12 kg
While selling⇒ 10 kg sold in 13 rs
12 kg= 13×12/10= 15.6 rs
CP: SP for shopkeeper= 10: 15.6
Profit percentage= 56%
Option (d) is correct
Que 10: If a trader’s balance weighs 20% less than it should be, and he still marks up his goods to achieve an overall profit of 35%, what is the markup percentage on the cost price?
(a) 7.14%
(b) 8%
(c) 9%
(d) 6.67%
Solution: 35%= 7/20
Weight= 5: 4
Price= 4: 5 …..(i)
CP: SP= x: y …..(ii)
4x: 5y= 20: 27
x:y= 25: 27
Mark up percentage= 200/25= 8%
Option (b) is correct
LCM and HCF Concepts: Click Here
Assignment: 4
Que 1: A dishonest dealer marks up the price of his goods by 30% and gives a discount of 20% to the customer. Besides, he also cheats both his supplier and his buyer by 100 grams while buying or selling 1 kilogram. Find the percentage profit earned by the shopkeeper.
(a) 28.12%
(c) 23.12%
(b) 25.54%
(d) 27.11%
Solution: CP:SP:MRP= 50:52:65
CP:SP= 25:26 …….(i)
10% cheating both sides
CP:SP= 9:11 …….(ii)
Combined effect
25×9: 26×11=225:286
Profit= (61/225)×100=27.11%
Option (d) is correct
Que 2: A trader while buying takes 20% extra but while selling, gives 20% less. He claims to make 10 % profit on this transaction. Find the actual gain made by the trader.
(a) 44%
(b) 56.25%
(c) 65%
(d) 66.66%
Solution: From wholesaler: Paid 10 rs and got 12 kg
To customer: 8 kg sold for 11 rs
8 kg= 11 rs
1 kg= 11/8
12 kg= 132/8=16.5
CP:SP (for retailer)= 10:16.5
65% profit
Option (c) is correct