Costs of petrol, ethanol and kerosene are Rs. 80, Rs. 50 and Rs. 30 per litre respectively. A clever dealer mixes petrol with e litres of ethanol and k litres of kerosene and sells at Rs. 75 making a profit of 20%. He has used 10 barrels of petrol each containing 15 litres. Which of the following options shows the quantity of kerosene he had used? (Note that e and k are integer values. The total mixture with him is less than 250 litres.)a)20 litresb)55 litresc)70 litresd)None of theseCorrect answer is option 'C'. Can you explain this answer?

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Costs of petrol, ethanol and kerosene are Rs. 80, Rs. 50 and Rs. 30 per litre respectively. A clever dealer mixes petrol with ‘e’ litres of ethanol and ‘k’ litres of kerosene and sells at Rs. 75 making a profit of 20%. He has used 10 barrels of petrol each containing 15 litres. Which of the following options shows the quantity of kerosene he had used? (Note that e and k are integer values. The total mixture with him is less than 250 litres.)

a)
20 litres
b)
55 litres
c)
70 litres
d)
None of these

Correct answer is option 'C'. Can you explain this answer?

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Costs of petrol, ethanol and kerosene are Rs. 80, Rs. 50 and Rs. 30 pe...

S.R of the mixture = Rs. 75 per litre
As profit = 20%; C.P. of mixture = 75/1.2 = Rs. 62.5 per litre
The ratio of petrol to ethanol that will give mixture that costs Rs. 62.5 is:

The ratio of petrol to kerosene that will give mixture that costs Rs. 62.5 is:

Assume that 12x litres of mixture containing petrol and ethanol is mixed with 20y litres of mixture containing petrol and kerosene. The resultant mixture will cost Rs. 62.5 per litre.

Petrol in the mixture = 5x + 13y = 150
Ethanol in the mixture; e = 7x
Kerosene in the mixture; k = 7y
x and y are integers as e and k are integers.
5x + 13y = 150 holds true for x = 4 and y = 10
Thus, quantity of kerosene the dealer had used = 7 * 10 = 70 litres
Hence, option 3.

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Most Upvoted Answer

Costs of petrol, ethanol and kerosene are Rs. 80, Rs. 50 and Rs. 30 pe...

Given:
Cost of petrol = Rs. 80 per litre
Cost of ethanol = Rs. 50 per litre
Cost of kerosene = Rs. 30 per litre
Dealer sells the mixture at Rs. 75 per litre with a profit of 20%
10 barrels of petrol, each containing 15 litres, are used

To find: Quantity of kerosene used in the mixture

Assume that the dealer has used e litres of ethanol and k litres of kerosene in the mixture.

Cost price of 1 litre of mixture = Cost of e litres of ethanol + Cost of k litres of kerosene + Cost of 1 litre of petrol
Cost price of 1 litre of mixture = (50 x e) + (30 x k) + 80

Selling price of 1 litre of mixture = Rs. 75

Profit percentage = 20%

Profit earned on 1 litre of mixture = Selling price - Cost price
Profit earned on 1 litre of mixture = 75 - [(50 x e) + (30 x k) + 80]
Profit earned on 1 litre of mixture = - (50e + 30k - 5)

As the dealer makes a profit, the value of (50e + 30k) must be less than 80.

Let's consider the options:

Option A: Quantity of kerosene used = 20 litres
Substituting k = 20 in the equation (50e + 30k), we get (50e + 600)
(50e + 600) is greater than 80, which is not possible. Hence, option A is not the answer.

Option B: Quantity of kerosene used = 55 litres
Substituting k = 55 in the equation (50e + 30k), we get (50e + 1650)
(50e + 1650) is greater than 80, which is not possible. Hence, option B is not the answer.

Option C: Quantity of kerosene used = 70 litres
Substituting k = 70 in the equation (50e + 30k), we get (50e + 2100)
(50e + 2100) is less than 80, which is possible. Hence, option C is the answer.

Option D: None of these
We have already shown that options A, B, and C are not the answer. Hence, option D is also not the answer.

Therefore, the correct answer is option C, i.e., the dealer used 70 litres of kerosene in the mixture.

Answered by Wizius Careers · View profile

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Costs of petrol, ethanol and kerosene are Rs. 80, Rs. 50 and Rs. 30 per litre respectively. A clever dealer mixes petrol with e litres of ethanol and k litres of kerosene and sells at Rs. 75 making a profit of 20%. He has used 10 barrels of petrol each containing 15 litres. Which of the following options shows the quantity of kerosene he had used? (Note that e and k are integer values. The total mixture with him is less than 250 litres.)a)20 litresb)55 litresc)70 litresd)None of theseCorrect answer is option 'C'. Can you explain this answer?

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Costs of petrol, ethanol and kerosene are Rs. 80, Rs. 50 and Rs. 30 per litre respectively. A clever dealer mixes petrol with e litres of ethanol and k litres of kerosene and sells at Rs. 75 making a profit of 20%. He has used 10 barrels of petrol each containing 15 litres. Which of the following options shows the quantity of kerosene he had used? (Note that e and k are integer values. The total mixture with him is less than 250 litres.)a)20 litresb)55 litresc)70 litresd)None of theseCorrect answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Costs of petrol, ethanol and kerosene are Rs. 80, Rs. 50 and Rs. 30 per litre respectively. A clever dealer mixes petrol with e litres of ethanol and k litres of kerosene and sells at Rs. 75 making a profit of 20%. He has used 10 barrels of petrol each containing 15 litres. Which of the following options shows the quantity of kerosene he had used? (Note that e and k are integer values. The total mixture with him is less than 250 litres.)a)20 litresb)55 litresc)70 litresd)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Costs of petrol, ethanol and kerosene are Rs. 80, Rs. 50 and Rs. 30 per litre respectively. A clever dealer mixes petrol with e litres of ethanol and k litres of kerosene and sells at Rs. 75 making a profit of 20%. He has used 10 barrels of petrol each containing 15 litres. Which of the following options shows the quantity of kerosene he had used? (Note that e and k are integer values. The total mixture with him is less than 250 litres.)a)20 litresb)55 litresc)70 litresd)None of theseCorrect answer is option 'C'. Can you explain this answer?.

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