 ## Profit And Loss Problems

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Basic Definitions

Cost price (C.P.): This is the price at which an article is purchased.

Selling price (S.P.): 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.

Loss: If the selling price is less than the cost price, the difference between them is the loss incurred.
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.

Important Formulas to Remember:

 Formula No. 1 15% Profit on an item means, Cost price = 100% Selling price = 115% Profit = 15% Formula No. 2 15% Loss on an item means, Cost price = 100% Selling price = 85% Loss = 15% Formula No. 3 Profit and Loss is always calculated on Cost Price or CP Formula No. 4 Gain Percentage: (Gain %) Gain % = (Gain x 100)/ C.P. Formula No. 5 Loss Percentage: (Loss %) Loss % = (Loss x 100)/ C.P. Formula No. 6 Selling Price: (S.P) SP = (100 + Gain %) /100 x C.P Formula No. 7 Selling Price: (S.P) SP = (100 – Loss %) /100 x C.P. Formula No. 8 Cost Price: (C.P.) C.P. = 100/ (100 + Gain %) x S.P. Formula No. 9 Cost Price: (C.P.) C.P. = 100/ (100 – Loss %)  x S.P.

Profit and Loss problems Question and Answers

Ques 1: If the cost price of 12 pens is equal to the selling price of 8 pens, the gain percent is ?

1)    12%
2)    30%
3)    50%
4)    60%

Explanation:

Friends, we know we will need gain amount to get gain percent, right. So lets get gain first.

Let the cost price of 1 pen is Re 1
Cost of 8 pens = Rs 8
Selling price of 8 pens = 12
Gain = 12 - 8 = 4
Gain%=(GainCost100)%=(48100)%=50%Gain%=(GainCost100)%=(48100)%=50%

Ques 2: The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, find out the value of x

1)    13
2)    14
3)    15
4)    16

Explanation:

Let the Cost Price of one article = Rs. 1
CP of x articles = Rs. x
CP of 20 articles = 20
Selling price of x articles = 20
Profit = 25% [Given]
(SP−CPCP)=25100=14(20−x)x=1480−4x=x5x=80x=805=16(SP−CPCP)=25100=14(20−x)x=1480−4x=x5x=80x=805=16

Ques 3: If the manufacturer gains 10 %, the wholesale dealer 15 % and the retailer 25 %, then find the cost of production of a table if the retail price was Rs 1265

1)    Rs. 750
2)    Rs. 800
3)    Rs. 850
4)    Rs. 900

Explanation:
Let the cost of Production = Rs. P
Then, as per question,
=>(125100115100110100P)=1265=>253160P=1265=>P=800=>(125100115100110100P)=1265=>253160P=1265=>P=800

Ques 4: Sahil purchased a machine at Rs 10000, then got it repaired at Rs 5000, then gave its transportation charges Rs 1000. Then he sold it with 50% of profit. At what price he actually sold it.

1)    Rs. 22000
2)    Rs. 24000
3)    Rs. 26000
4)    Rs. 28000

Explanation:

Question seems a bit tricky, but it is very simple.
Just calculate all Cost price, then get 150% of CP.
C.P. = 10000 + 5000 + 1000 = 16000
150% of 16000 = 150/100 * 16000 = 24000

Ques 5: A man gains 20% by selling an article for a certain price. If he sells it at double the price, the percentage of profit will be.

1)    130%
2)    140%
3)    150%
4)    160%

Explanation:

Let the C.P. = x,
Then S.P. = (120/100)x = 6x/5
New S.P. = 2(6x/5) = 12x/5

Profit = 12x/5 - x = 7x/5

Profit% = (Profit/C.P.) * 100
=> (7x/5) * (1/x) * 100 = 140 %

Ques 6: A plot is sold for Rs. 18,700 with a loss of 15%. At what price it should be sold to get profit of 15%.

1)    Rs 25300
2)    Rs 22300
3)    Rs 24300
4)    Rs 21300

Explanation:
This type of question can be easily and quickly solved as following:

Let at Rs x it can earn 15% pr0fit
85:18700 = 115:x [as, loss = 100 -15, Profit = 100 +15]

x = (18700*115)/85
= Rs.25300

Ques 7: A man buys an item at Rs. 1200 and sells it at the loss of 20 percent. Then what is the selling price of that item

1)    Rs. 660
2)    Rs. 760
3)    Rs. 860
4)    Rs. 960

Explanation:

Here always remember, whenever x% loss,
it means S.P. = (100 - x)% of C.P
whenever x% profit,
it means S.P. = (100 + x)% of C.P

So here will be (100 - x)% of C.P.
= 80% of 1200
= 80/100 * 1200
= 960
 Take a Test  Now

Ques 8. If the cost price is 25% of selling price. Then what is the profit percent.
1)    150%
2)    200%
3)    300%
4)    350%

Explanation:

Let the S.P = 100
then C.P. = 25

Profit = 75

Profit% = 75/25 * 100 = 3005

Ques 9: A bathing soap marked at Rs.80 is sold for Rs.68.Find the rate of discount.

Solution: Marked price = (M.P) = Rs.80
Selling price = (S.P) = Rs.68
Discount amount = Rs. 80 – 68 = Rs.12
Therefore, Rate of discount = Discount x 100 / M.P
= 12 x 100 / 80 = 120 / 8 = 15%

Ques 10: Rahul bought a computer for Rs.52,000 and spent Rs.4000 on its repairs. If he sells at Rs.47,000 then what will be his loss percentage?

Solution: Rahul bought the computer at Rs.52, 000
Amount for repairing = Rs.4000
Total Cost price of the computer = Rs.52, 000 + Rs.4000 = Rs.56,000
Selling price = Rs.47,000
Therefore the amount of loss = CP _ SP = 56,000 – 47,000 = Rs.9000
Loss % = loss x 100 /CP = 9000 x 100 / 56,000 = 900/56
225/14 % = 16 1/14 %

Ques 11: A seller gains the cost of 40 dozen apples by selling 25 dozen of apples. Then the gain percent is:

Solution: Given that the cost price (CP) of 40 dozen of apples is equal to selling of 25 dozen of apples.
Let the CP of 1 dozen of apple = Rs.1
Therefore CP of 40 dozen apples = Rs.40
Given, SP of 25 dozen apples = Rs.40
Then SP of 1 dozen apples = Rs.40/25 = Rs.8/5
Therefore profit of 1 dozen apples = Rs.(8/5 – 1) (SP – CP)
= Rs.3/5
Then profit % = 3/5 x 100 = 60%

Ques 12: Madhesh bought 100 dozen of pins at Rs.10 per dozen. He spent Rs.500 on a particular tax and he sold them at Rs. 1 per each pin. What was his profit or loss percent?

Solution: Cost price of 1 dozen of pins = Rs.10
Cost price of 100 dozen of pins = Rs. 100 x 10 = Rs.1000
Aamount of tax paid = Rs.500
Therefore total cost price = 1000 + 500 = Rs.1, 500
Selling price of total number of pins = 100 x 12 x 1 = Rs. 1,200
Therefore, loss = C.P – S.P = 1500 – 1200 = Rs.300
And loss % = loss x 100 / c.p = 100 x 100 / 1500 = 100/15 %
= 20/3 % = 6 2/3 %

Ques 13: Samy sold his dining table set at a loss of 20%. If he had sold it for Rs 800 more, he would have received a profit of 5%. Find the cost price.

Solution: Let the cost price be Rs 100
So when C.P = 100, loss of 20% means
S.P = 100 – 20 = 80
Profit of 5% means S.P = 100 + 5 = 105
The difference of two S.P = 105 – 80 = 25
If the difference is 25, C.P = Rs 100
If the difference is Rs 800, C.P = (100 / 25) x 800
C.P = Rs 3200

Ques 13: A shopkeeper sold an article for Rs 2564.36. Approximately what was his profit percent if the cost price of the article was Rs 2400

1)    4%
2)    5%
3)    6%
4)    7%

Explanation:
Gain % = (164.36*100/2400) = 6.84 % = 7% approx

Ques 14: A TV is purchased at Rs. 5000 and sold at Rs. 4000, find the lost percent.

1)    10%
2)    20%
3)    25%
4)    28%

Explanation:
We know, C.P. = 5000
S.P. = 4000
Loss = 5000 - 4000 = 1000
Loss%=(LossCost100)%=(10005000100)%=20%
Loss%=(LossCost100)%=(10005000100)%=20%

Ques 15: In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit

1)    70%
2)    80%
3)    90%
4)    None of above

Explanation:
Let C.P.= Rs. 100.
Then, Profit = Rs. 320,
S.P. = Rs. 420.
New C.P. = 125% of Rs. 100 = Rs. 125
New S.P. = Rs. 420.
Profit = Rs. (420 - 125) = Rs. 295
Required percentage = (295/420) * 100
= 70%(approx)

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Ques 16: A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 1 less, he would have made a profit of 10%. The C.P. of the article was

1)    Rs 100
2)    Rs 150
3)    Rs 200
4)    Rs 250

Explanation:
Let original Cost price is x
Its Selling price = 105/100 * x = 21x/20
New Cost price = 95/100 * x = 19x/20
New Selling price = 110/100 * 19x/20 = 209x/200
[(21x/20) - (209x/200)] = 1
=> x = 200

Ques 17: A fruit seller sells mangoes at the rate of Rs.9 per kg and thereby loses 20%. At what price per kg, he should have sold them to make a profit of 5%

1)    Rs 8.81
2)    Rs 9.81
3)    Rs 10.81
4)    Rs 11.81

Explanation:
85: 9 = 105: x
x= (9×105/85)
= Rs 11.81

Ques 18: Akhil purchased 70kg vegetable at Rs. 420, then sold them at the rate of Rs. 6.50 per kg, find the profit percent.

1)    813%
2)    713%
3)    613%
4)    513%

Explanation:
Please note in this type of questions, get the value of 1 kg to solve this question, lets solve it.
C.P. of 1 Kg = 420/70 = Rs. 6
Selling Price = 6.50
Gain = Rs. 0.50
Gain%=.506100=813%

Ques19: A man bought some toys at the rate of 10 for Rs. 40 and sold them at 8 for Rs. 35. Find his gain or loss percent.

Solution: Cost price of 10 toys = Rs. 40 CP of 1 toy = Rs. 4.
Selling price of 8 toys = Rs. 35 SP of 1 toy = Rs. 35/8
Therefore, Gain = 35/8 – 4 = 3/8.
Gain percent = (3/8)/4 * 100 = 9.375%

Ques 20: The cost price of 10 pens is the same as the selling price of n pens. If there is a loss of 40%, approximately what is the value of n?

Solution: Let the price of each pen be Re. 1.
Then the cost price of n pens is Rs. n and the selling price of n pens is Rs. 10.
Loss = n-10.
Loss of 40% (loss/CP)*100 = 40
Therefore, [(n-10)/n]*100 = 40 n = 17 (approx)

Profit and Loss Arithmetic Ability Solved Examples

Ques 1: A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:

1)    No profit, no loss
2)    5%
3)    8%
4)    10%

Explanation:

C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600.
S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680.
Gain: (80/1600 *100) % =5%

Ques 2: By selling 45 lemons for Rs 40, a man loses 20 %. How many should he sell for Rs 24 to gain 20 % in the transaction?

1)    16
2)    18
3)    20
4)    22

Explanation:
Let S.P. of 45 lemons be Rs. x.
Then, 80: 40 = 120: x or   x = = 60
For Rs.60, lemons sold = 45
For Rs.24, lemons sold = 18.

Ques 3: If books bought at prices ranging from Rs. 200 to Rs. 350 are sold at prices ranging from Rs. 300 to Rs. 425, what is the greatest possible profit that might be made in selling eight books?

1)    600
2)    1200
3)    1800
4)    none of these

Explanation:
Least Cost Price = Rs. (200 * 8) = Rs. 1600.
Greatest Selling Price = Rs. (425 * 8) = Rs. 3400.
Required profit = Rs. (3400 - 1600) = Rs. 1800.

Ques 4: A man buys oranges at Rs 5 a dozen and an equal number at Rs 4 a dozen. He sells them at Rs 5.50 a dozen and makes a profit of Rs 50. How many oranges does he buy?

1)    30 dozens
2)    40 dozens
3)    50 dozens
4)    60 dozens

Explanation:
Cost Price of 2 dozen oranges Rs. (5 + 4) = Rs. 9.
Sell price of 2 dozen oranges = Rs. 11.
If profit is Rs 2, oranges bought = 2 dozen.
If profit is Rs. 50, oranges bought = (2/2) * 50 dozens = 50 dozens.

Ques 5: A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 1 less, he would have made a profit of 10%. The C.P. of the article was

1)    Rs 100
2)    Rs 150
3)    Rs 200
4)    Rs 250

Explanation:
Let original Cost price is x
Its Selling price = (105/100) * x = 21x/20
New Cost price = (95/100) * x = 19x/20
New Selling price = (110/100)* (19x/20)= 209x/200
[(21x/20) - (209x/200)] = 1
=> x = 200

Final words:

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