# Cognizant Profit and Loss Questions with Solutions – merittrack

1.A dishonest shopkeeper uses a faulty measuring rod, which measures 90cm for a meter. Find the actual profit percent, if he claims to be selling at a profit of 10% only?

A) 20%
B) 22.22%
C) 18.33%
D) 15.5%
Explanation: Let cost price per cm = Rs 1,
Hence, cost price of 90cm = Rs 90
And, cost price of 100cm = Rs 100
Selling price of 100cm = 100 + 10% = Rs 110
∴ Actual profit percent = {(110 – 90)/90} × 100%
= (2/9) × 100% = 22.22%
Hence, the actual profit percent gained by the shopkeeper is 22.22%.

1. A trader advertises for selling the cloth at 5% loss, but by using a false meter scale he actually gains 20%. What is the actual length of the scale?

A) 0.75m
B) 0.8m
C) 0.6m
D) 0.5m
Explanation: Let the length of scale be ‘x’ metres
Let the cost price per meter cloth be Rs. 100
But actually he sells x meters for Rs. 95, and gains 20% profit
Cost price of 1 meter length of cloth is 100.
∴ Cost price of x meter length cloth = 100x
∵ Cost Price + Profit = Selling Price
⇒ 100x + 20% of 100x = 95
⇒ 100x + 20x = 95
⇒ 120x = 95
∴ x = 0.79 ≈ 0.80 m
Length of scale is 0.80 meter.

1. To make a profit of 20% the selling price of the good is Rs. 240. The cost price of the good is,

A) Rs. 200
B) Rs. 210
C) Rs. 220
D) Rs. 230
Explanation: We know that selling price of the good is Rs. 240 and the profit is 20% of the cost price Let cost price of the good be x
⇒ selling price = cost price + (profit%/100 × cost price)
⇒ 240 = x + (20x/100)
⇒ 120x/100 = 240
⇒ x = 200
∴ cost price of the good = Rs. 200

1. If the ratio of the cost price and the selling price of an article be 4 : 5, then the percentage of profit is:

A) 27½
B) 25
C) 15
D) 10
Explanation: Let the cost price (C.P.) and selling price (S.P.) of the article be 4x and 5x respectively.
⇒ Profit% = [(5x – 4x)/4x] × 100 = 25%
∴ Profit% = 25%

1. A pair of socks had been sold for Rs. 234 with a loss percentage of 6.4. If the same pair of socks were sold for Rs. 275 what is the gain percentage?

A) 10%
B) 15%
C) 25%
D) 20%
Explanation: Let the cost price of the socks be Rs. n.
With Rs. 234 loss percentage is 6.4
⇒ (n – 234)/n = 0.064
⇒ 0.936n = 234
⇒ n = Rs. 250
∴ With the selling price as Rs. 275 gain percentage = (275 – 250)/250 × 100 = 10%.

1. A man sold two paintings at Rs.1725 each. On one, he gains 15% and on the other, he loses 25%. The gain or loss % on the whole transaction is:

A) 16% gain
B) (14frac{1}{{63}}%) gain
C) 15% loss
D) (9frac{4}{{19}}%) loss
Explanation: Let the cost of first painting be x and that of second painting be y.
S.P. of each painting = Rs. 1725
∵ first painting is sold at 15% gain,
x + (15% of x) = 1.15x = 1725
⇒ x = 1725/1.15 = Rs. 1500
Second painting is sold at 25% loss.
∴ y – (25% of y) = 0.75y = 1725
⇒ y = 1725/0.75 = Rs. 2300
∴ total cost of both paintings = 1500 + 2300 = Rs. 3800
Total selling price of both paintings = 1725 × 2 = Rs. 3450
Here, S.P. < C.P. ⇒ Loss in overall transaction
Loss = 3800 – 3450 = Rs. 350
Loss% (= ;frac{{350}}{{3800}} times 100 = 9frac{4}{{19}})

1. Arun sold two TV sets for Rs.6000 each. On one he gained 20% and on the other he lost 20%. Loss or gain of Arun in the whole transaction is

A) 3% loss
B) 4% gain
C) 3% gain
D) 4% loss
Explanation: Given, Arun sold two TV sets for Rs.6000 each.
Let the cost price of the TV be Rs a and Rs b respectively.
He gained 20% on one while lost 20% on the other.
∴ a + 20% of a = 6000 and b – 20% of b = 6000
⇒ 1.2a = 6000 and 0.8b = 6000
⇒ a = Rs. 5000 and b = Rs. 7500
Total cost price = Rs. 5000 + 7500 = Rs. 12500
Total selling price = Rs. 6000 + 6000 = Rs. 12000
Loss = 12500 – 12000 = Rs. 500
(Loss% = left( {frac{{loss}}{{costprice}} times 100% } right))
⇒ Loss% (= frac{{500}}{{12500}} times 100% = 4%)

1. A fruit seller purchased 50 kg of mangoes at the rate of Rs. 25 per kilo. He sold some of the mangoes at the rate of Rs. 40 per kilo and the rest at the rate of Rs. 15 per kilo. If he incurred 20% profit overall, the amount of mangoes sold at the rate of Rs. 15 per kilo is

A) 20 kg
B) 25 kg
C) 30 kg
D) 40 kg
Explanation: A fruit seller purchased 50 kg of mangoes at the rate of Rs. 25 per kilo.
Total cost price of the 50 kg of mangoes = 50 × 25 = 1250
If he incurred 20% profit overall then the selling price of 50 Kg of Mangoes (= 1250 times frac{{120}}{{100}})
= 1500
He sold some of the mangoes at the rate of Rs. 40 per kilo and the rest at the rate of Rs. 15 per kilo.Suppose he sold X kg of mangoes at the rate of Rs 40 and (50-X) Kg of sold at the rate of Rs15.
We can say that,
⇒ 40 × X + 15 × (50 – X) = 1500
⇒ 40X + 750 – 15X = 1500
⇒ 25X = 750
⇒ X = 30
So he sold 30 kg of mangoes at the rate of Rs 40 and (50-30) =20 Kg of sold at the rate of Rs 15.
Hence the answer is 20 kg

1. M and N enter into a partnership for a year. M contributes Rs 1500 and N contributes Rs 2000. After 4 months they admit R, who contributes Rs 2250. If N withdraws his contribution after 9 months, what would be the share of N after 1 year of partnership in a profit of Rs 900?

A) Rs 430
B) Rs 310
C) Rs 290
D) Rs 300
Explanation: From question, it is clear that M, N and R invest their amounts for 12, 9 and 8 months respectively.
∴ Ratio of their shares-
M’s share : N’s share : R’s share
= (1500 × 12) : (2000 × 9) : (2250 × 8)
= (15 × 12) : (20 × 9) : (22.5 × 8)
= 180 : 180 : 180
= 1 : 1 : 1
∴ Each of them gets = 900/3 = Rs 300.
Hence, the share of N in the profit is Rs 300.

10.Sunil invests Rs. 3000 for one year and Anand joins him four months later with Rs. 2000. At the end of the year, their income is Rs. 2600. Then what is the share of Anand?

A) Rs. 800
B) Rs. 1000
C) 750
D) Rs. 900
Ans:A
Explanation: Ratio of share in profit = Ratio of money invested.
Given, Sunil invests Rs. 3000 for one year and Anand joins him four months later with Rs. 2000.
Thus Sunil invested Rs. 3000 for 12months while Anand invested Rs. 2000 for 8 months.
Ratio of investment of Sunil to Anand (= frac{{3000 times 12}}{{2000 times 8}} = 9;:4)
Given, total income = Rs. 2600
Thus Anand’s share (= frac{4}{{9 + 4}} times 2600 = frac{4}{{13}} times 2600)
⇒ Anand’s share = Rs. 800

1. A, B, C enter into partnership with Rs. 35,000, Rs. 45,000 and Rs. 55,000 respectively. What is the share of A out of the profit of Rs. 40,500?

A) Rs. 10500
B) Rs. 13500
C) Rs. 16500
D) Rs. 11,000
Ans:A
Explanation: The share with which A, B and C entered into partnership is 35,000 , 45,000 and 55,000 respectively.
The ratio of A, B and C is
A: B: C = 35,000 : 45,000: 55,000 = 7: 9 :11
Total share = Sum of all the ratio’s = 7 + 9 + 11= 27
A’s share out of profit of Rs. 40,500 (= left( {40,500 times frac{7}{{27}}} right) = Rs10,500)

1. A and B started a business in partnership investing Rs. 30000 and Rs. 25000 respectively. After six month C joined them with Rs. 40000. What will be C’s share in total profit of Rs. 34000 earned at the end of 2 years from the starting of the business,

A) Rs. 15000
B) Rs.10000
C) Rs. 18000
D) Rs. 12000
Ans:D
Explanation: Given,
Investment of A = Rs. 30000,
Investment of B = Rs. 25000
Investment of C = Rs. 40000
Total time of investment = 2 years = 24 months
A and B invested for the whole investment period i.e 2 years
Time of investment for C = (24 – 6) months = 18 months
∴ Ratio of shares of A,B and C
= 30000 × 24: 25000 × 24: 40000 × 18
= 120: 100: 120
= 6: 5: 6
Given, Total profit = Rs. 34000
∴ C’s share = (6/17) × 34000 = Rs. 12000

1. Three glasses of capacity 4 liters, 7 liters and 10 liters are completely filled with mixture of milk and water. Milk concentrations in the mixtures are 70%, 80% and 70% respectively. The mixture of three glasses are emptied in a large vessel. Find the ratio of milk to water in the vessel?

A) 11 : 4
B) 4 : 11
C) 23 : 56
D) 44 : 24
Explanation: Three glasses of capacity 4 liters, 7 liters and 10 liters are completely filled with mixture of milk and water.
In first glass it is of capacity 4 liters and milk concentration is 70%
Quantity of milk in that first glass = 70% of 4 liters (= ;4 times frac{{70}}{{100}} = 2.8;{rm{liters}})
Water quantity in that first glass = 4 – 2.8 = 1.2 liters
In second glass it is of capacity 7 liters and milk concentration is 80%
Quantity of milk in that second glass = 80% of 7 liters (= ;7 times frac{{80}}{{100}} = 5.6;{rm{liters}})
Water quantity in that second glass = 7 – 5.6 = 1.4 liters
In third glass it is of capacity 10 liters and milk concentration is 70%
Quantity of milk in that third glass = 70% of 10 liters (= ;10 times frac{{70}}{{100}} = 7;{rm{liters}})
Water quantity in that third glass = 10 – 7 = 3 liters
If the mixture of three glasses are emptied in a large vessel.
Then total milk = Milk of the first glass + Milk of the second glass + Milk of the third glass
= 2.8 + 5.6 + 7
= 15.4 liters
Total water in the large vessel = Water in the first glass + Water in the second glass + Water in the third glass
= 1.2 + 1.4 + 3
= 5.6 liters
Hence the ratio of milk to water in that vessel = 15.4 : 5.6 = 11:4

1. Two equal glasses filled with milk and water in the proportions 4:1 and 3:2 are emptied into a third glass. The proportion of milk and water in the third glass will be

A) 7 : 5
B) 7 : 3
C) 3 : 7
D) 5 : 7
Explanation: Let there be 100 ml of liquid in both the glass,
Since the milk and water are in the ratio of 4 : 1 in first glass,
Hence amount of milk = (frac{4}{{4 + 1}} times 100)= 80 ml
Amount of water = 100 – 80 = 20 ml
Similarly, amount of water in glass 2 = (frac{2}{{2 + 3}} times 100)= 40 ml
Amount of milk in second glass = 100 – 40 = 60 ml
Total milk in third glass = 80 + 60= 140 ml
Total water in third glass = 20 + 40 = 60 ml
The proportion of milk and water in the third glass will be 140 : 60= 7 : 3

1. A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 45%. The percentage of water in mixture

A) 35%
B) 39%
C) 31%
D) 33.33%
Explanation: Given,
Let, Cost price of 1 litre of milk = Rs. x
Amount of water mixed with 1 litre milk = y litre
Amount of milk in 1 litre of milk water mixture = (1 – y) litre
Cost price of (1 – y) litre milk = x(1 – y)
Actual cost price of 1 litre of mixture selling = Cost price of (1 – y) litre milk = x(1 – y)
Gain per 1 litre selling = Cost price of y litre of milk = y × x
Gain per cent
= (Gain per litre selling/Actual Cost per litre selling) × 100
(= frac{{xy}}{{xleft( {1 – y} right)}} times 100 = frac{{100y}}{{1 – y}})
Given, Gain percentage = 45%
∴ 100y/(1 – y) = 45
⇒ 100y = 45 –45y
⇒ y = 45/145 = 0.3103 litre
∴ Percentage amount of water in mixture
= (0.3103/1) × 100 = 31.03% = 31%

1. An electronic weighing machine can show correct weight within the range of ± 10 grams. Nathan used this machine and sells items at the cost price. If Nathan sells items only in the form of 400 grams packets, then what is the maximum loss he can suffer? (in %)

A) 1.43
B) 2.04
C) 1.74
D) 2.44
Explanation: Nathan will suffer maximum loss when Machine shows 410 grams as 400 grams
He will get price for 400 grams but will give 410 grams
Maximum Loss percentage = (410 – 400)/410 × 100 = 2.44%

17.A merchant mixes two types of oil one costing Rs. 180 per kg and the other costing Rs. 220 in the ratio 3 : 1. What is the approximate profit percent if he sells this at Rs. 210 per kg.

A) 9.8%
B) 11%
C) 7.6%
D) 5%
Explanation: Cost price of the oil = (3/4)×C.P of first oil + (1/4)×C.P second oil
= (3/4)×180+(1/4)×220
= 135 + 55 = Rs. 190 per kg
⇒ Selling price of the oil = Rs. 210 per kg
∴ Profit on 1 kg of oil = S.P – CP
= 210 – 190
= Rs. 20
Profit percentage = [Profit/(C.P)]×100
= (20/190)×100
= (20/19)×10
≃ 10.5%

18.A shopkeeper sells a pair of sunglasses at a profit of 25%. If he had bought it at 25% less and sold it for Rs. 20 less, then he would have gained 40%. The cost price of the pair of sunglasses is:

A) Rs. 125
B) 50
C) Rs. 160
D) Rs. 100
Answer:Det the sunglasses were brought for Rs 100.
Selling price be ‘x’ .such that gain% = 25%
Selling price = Rs 100+ Rs 25 = Rs 125
Now if he had bought them at 25% less would mean
⇒ 100 – 25% of 100 = 100 – 25 = Rs 75
Hence let the cost price be Rs 75 and new SP be ‘y’ then
Gain% = 40%
⇒ (SP – CP)/CP × 100 = 40
(Rightarrow frac{{y;-;75}}{{75}} times 100 = 40;)
⇒ y – 75 = 30
⇒ y = 75 + 30 = 105 Rs
Now if he sells for Previous SP – new SP = Rs. 125 – Rs 105 = Rs 20 less
Then CP = Rs 100
If he sells for Rs 20 less, then C.P. (= frac{{100}}{{20}} times 20 = Rs.;100;)

19.A man sells an article at a loss of 20%. Had he bought it 20% less and sold it for Rs. 60 more, he could have gained 50%. What is the cost price of the article?

A) Rs. 200
B) Rs. 225
C) Rs. 150
D) None of these
Explanation: Let the cost price of the article, C.P1 = Rs. X.
We know that,
⇒ Selling Price = Cost price × (1 ± Profit or loss %)
Earlier the article was sold at a loss of 20% thus its selling price
(Rightarrow S.{P_1} = C.Pleft( {1 – frac{{20}}{{100}}} right))
⇒ S.P1 = 0.8X
Now, if the article is bought at 20% less then,
⇒ New cost price, (;C.{P_2} = C.{P_1} – frac{{20}}{{100}}C.{P_1})
(= X – frac{{20}}{{100}}X)
= 0.8X
Also if the article is sold at a price Rs. 60 more than earlier then,
⇒ New selling price, S.P2 = S.P1 + 60
= 0.8X + 60
Since the new profit percentage is 50%. Hence,
⇒Profit percent (= frac{{Selling;price – Cost;price}}{{Cost;price}} times 100;)
(Rightarrow 50 = frac{{0.8X + 60 – 0.8X}}{{0.8X}} times 100)
(Rightarrow frac{{50}}{{100}} times 0.8X = 60)
⇒ X =Rs. 150
Hence, the cost price of the article is Rs. 150.

20.A man bought a number of oranges at 3 for rs 1 and an equal number at 2 for rs 1. At what price per dozen should he sell them to make a profit of 20%?

A) Rs 4
B) Rs 5
C) Rs 6
D) Rs 7