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A dishonest shopkeeper mixes pure sugar with some sugar like substance to gain extra profit. The cost price of sugar like substance is 2/3 times the pure sugar. If the shopkeeper wants to gain a profit of 30 % on selling the mixture at the cost price of pure sugar, then find the ratio of sugar like substance to pure sugar in the mixture.
  • a)
    5 : 6
  • b)
    7 : 5
  • c)
    9 : 4 
  • d)
    5 : 9
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A dishonest shopkeeper mixes pure sugar with some sugar like substance...
Let the cost price of 1 kg of pure sugar be Rs. x.
The cost price of 1 kg sugar like substance = Rs. 2x / 3 The selling price of one kg of mixture = Rs. x.
Let the amount of pure sugar in 1 kg of mixture be y.
The amount of sugar like substanace = (1 —y)
The cost price of mixture = xy + (2x / 3) x (1 - y) = (x / 3) x (2 + y)
x / [(x / 3) x (2 + y)] = 1.3
y = 4/13
Thus, the ratio of sugar like substance to pure sugar = 1 - y : y = 9 : 4 
Hence, option 3.
This question is part of UPSC exam. View all CAT courses
Most Upvoted Answer
A dishonest shopkeeper mixes pure sugar with some sugar like substance...
Given:
Cost price of sugar like substance = (2/3) * cost price of pure sugar
Shopkeeper wants to gain 30% profit on selling the mixture at cost price of pure sugar

To find: Ratio of sugar like substance to pure sugar in the mixture

Let's assume that the shopkeeper mixes x units of pure sugar and y units of sugar like substance to get a mixture.

Cost price of the mixture = (x+y) * cost price of pure sugar

To gain a profit of 30%, the selling price of the mixture should be 1.3 times the cost price of pure sugar. So,

Selling price of the mixture = 1.3 * cost price of pure sugar

Profit = Selling price - Cost price
Profit = (1.3 * cost price of pure sugar) - ((x+y) * cost price of pure sugar)

Profit = 0.3 * cost price of pure sugar

As the shopkeeper wants to gain a profit of 30%, we can equate the profit equation to 0.3 times the cost price of the mixture.

0.3 * cost price of the mixture = 0.3 * cost price of pure sugar

0.3 * (x+y) * cost price of pure sugar = 0.3 * cost price of pure sugar

0.3 * (x+y) = 1

x+y = 10/3

We know that the cost price of sugar like substance is (2/3) times the cost price of pure sugar. So,

Cost price of sugar like substance = (2/3) * cost price of pure sugar
=> (y/(x+y)) * cost price of mixture = (2/3) * cost price of pure sugar

Substituting x+y = 10/3, we get

(y/(10/3)) * cost price of mixture = (2/3) * cost price of pure sugar

Simplifying, we get

y/x = 9/4

Therefore, the ratio of sugar like substance to pure sugar in the mixture is 9:4. Hence, option C is the correct answer.
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A dishonest shopkeeper mixes pure sugar with some sugar like substance to gain extra profit. The cost price of sugar like substance is 2/3 times the pure sugar. If the shopkeeper wants to gain a profit of 30 % on selling the mixture at the cost price of pure sugar, then find the ratio of sugar like substance to pure sugar in the mixture.a)5 : 6b)7 : 5c)9 : 4d)5 : 9Correct answer is option 'C'. Can you explain this answer?
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A dishonest shopkeeper mixes pure sugar with some sugar like substance to gain extra profit. The cost price of sugar like substance is 2/3 times the pure sugar. If the shopkeeper wants to gain a profit of 30 % on selling the mixture at the cost price of pure sugar, then find the ratio of sugar like substance to pure sugar in the mixture.a)5 : 6b)7 : 5c)9 : 4d)5 : 9Correct 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 A dishonest shopkeeper mixes pure sugar with some sugar like substance to gain extra profit. The cost price of sugar like substance is 2/3 times the pure sugar. If the shopkeeper wants to gain a profit of 30 % on selling the mixture at the cost price of pure sugar, then find the ratio of sugar like substance to pure sugar in the mixture.a)5 : 6b)7 : 5c)9 : 4d)5 : 9Correct 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 A dishonest shopkeeper mixes pure sugar with some sugar like substance to gain extra profit. The cost price of sugar like substance is 2/3 times the pure sugar. If the shopkeeper wants to gain a profit of 30 % on selling the mixture at the cost price of pure sugar, then find the ratio of sugar like substance to pure sugar in the mixture.a)5 : 6b)7 : 5c)9 : 4d)5 : 9Correct answer is option 'C'. Can you explain this answer?.
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