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A shopkeeper sells four qualities of rice A, B, C and D having cost price ₹ 40/kg, ₹ 55/kg, ₹ 50/kg and ₹ 65/kg respectively. Ankit purchased ‘a’ kg of A and ‘b’ kg of B to make ‘a + b’ kg of a new quality ‘E’ of rice worth ₹ 50/kg. Then he purchased ‘c’ kg of C and ‘d’ kg of D to make ‘c + d’ kg of a new quality ‘F’ of rice worth ₹ 60/kg.
Finally he took ‘x’ kg of rice and ‘y’ kg of rice from ‘E’ quality of rice and ‘F’ quality of rice respectively to make ‘x + y’ kg of rice worth ₹ 53/kg. Ensuring that a, b, c, d, x and y are all integers then what is the minimum value of a + b + c + d + x + y in kg?
(2014)
  • a)
    28
  • b)
    22
  • c)
    16
  • d)
    26
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A shopkeeper sells four qualities of rice A, B, C and D having cost pr...
By Allegation,

⇒ 1 : 2
Hence a : b = 1 : 2

⇒ 1 : 2
Hence, c : d = 1 : 2
Also,

Hence, x : y = 7 : 3
So, minimum weight of x (= 7 kg) and y (= 3 kg)
we need (a + b) ≥ 7 and (c + d) ≥ 3.
Hence, minimum a + b = 9 (as it has to be in the ratio of 1 : 2 it must be a multiple of 3)
So, Minimum value of c + d = 3
∴ Minimum value of a + b + c + d + x + y
= 9 + 3 + 7 + 3  = 22 kg.
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Community Answer
A shopkeeper sells four qualities of rice A, B, C and D having cost pr...
To calculate the cost of Ankit's purchase, we need to know the quantity of each quality of rice he purchased.
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A shopkeeper sells four qualities of rice A, B, C and D having cost price 40/kg, 55/kg, 50/kg and 65/kg respectively. Ankitpurchased ‘a’ kg of A and ‘b’ kg of B to make ‘a + b’ kg of a new quality ‘E’ of rice worth 50/kg. Then he purchased ‘c’ kg of Cand ‘d’ kg of D to make ‘c + d’ kg of a new quality ‘F’ of rice worth 60/kg.Finally he took ‘x’ kg of rice and ‘y’ kg of rice from ‘E’ quality of rice and ‘F’ quality of rice respectively to make ‘x + y’ kg of rice worth 53/kg. Ensuring that a, b, c, d, x and y are all integers then what is the minimum value of a + b + c + d + x + y in kg?(2014)a)28b)22c)16d)26Correct answer is option 'B'. Can you explain this answer?
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A shopkeeper sells four qualities of rice A, B, C and D having cost price 40/kg, 55/kg, 50/kg and 65/kg respectively. Ankitpurchased ‘a’ kg of A and ‘b’ kg of B to make ‘a + b’ kg of a new quality ‘E’ of rice worth 50/kg. Then he purchased ‘c’ kg of Cand ‘d’ kg of D to make ‘c + d’ kg of a new quality ‘F’ of rice worth 60/kg.Finally he took ‘x’ kg of rice and ‘y’ kg of rice from ‘E’ quality of rice and ‘F’ quality of rice respectively to make ‘x + y’ kg of rice worth 53/kg. Ensuring that a, b, c, d, x and y are all integers then what is the minimum value of a + b + c + d + x + y in kg?(2014)a)28b)22c)16d)26Correct answer is option 'B'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A shopkeeper sells four qualities of rice A, B, C and D having cost price 40/kg, 55/kg, 50/kg and 65/kg respectively. Ankitpurchased ‘a’ kg of A and ‘b’ kg of B to make ‘a + b’ kg of a new quality ‘E’ of rice worth 50/kg. Then he purchased ‘c’ kg of Cand ‘d’ kg of D to make ‘c + d’ kg of a new quality ‘F’ of rice worth 60/kg.Finally he took ‘x’ kg of rice and ‘y’ kg of rice from ‘E’ quality of rice and ‘F’ quality of rice respectively to make ‘x + y’ kg of rice worth 53/kg. Ensuring that a, b, c, d, x and y are all integers then what is the minimum value of a + b + c + d + x + y in kg?(2014)a)28b)22c)16d)26Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A shopkeeper sells four qualities of rice A, B, C and D having cost price 40/kg, 55/kg, 50/kg and 65/kg respectively. Ankitpurchased ‘a’ kg of A and ‘b’ kg of B to make ‘a + b’ kg of a new quality ‘E’ of rice worth 50/kg. Then he purchased ‘c’ kg of Cand ‘d’ kg of D to make ‘c + d’ kg of a new quality ‘F’ of rice worth 60/kg.Finally he took ‘x’ kg of rice and ‘y’ kg of rice from ‘E’ quality of rice and ‘F’ quality of rice respectively to make ‘x + y’ kg of rice worth 53/kg. Ensuring that a, b, c, d, x and y are all integers then what is the minimum value of a + b + c + d + x + y in kg?(2014)a)28b)22c)16d)26Correct answer is option 'B'. Can you explain this answer?.
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