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In a grocery shop, customers were asked to stand in a queue in order to buy the goods. It was noticed that the first customer bought 10 kg of rice and then 1/5th of whatever remained in the rice container. The second customer bought 20 kg of rice and then 1/5th of whatever remained. The third customer bought 30 kg of rice plus 1/5th of whatever remained in the container and this went on for each customer in the queue. It was noticed that finally each customer had bought the same amount of rice.
Which of following statements is/are true?
i. Each customer buys 40 kg of rice.
ii. Initially there was 260 kg of rice.
iii. There were exactly 5 customers standing in the queue.
  • a)
    Only ii
  • b)
    Only i
  • c)
    Both i and iii
  • d)
    All of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
In a grocery shop, customers were asked to stand in a queue in order t...
Let x be the amount of rice present in the shop initially.
The amount of rice bought by the first customer = 10 + 0.2(x- 10) = 8 + 0.2x
The amount of rice bought by the second customer = 20 + 0.2[x- (20+ 8 + 0.2x)] = 14.4 + 0.16x Now, as each customer buys equal amount of rice, we get, 8 + 0.2x = 14.4 + 0.16x x = 160 Initially there was 160 kg of rice.
Rice bought by each customer = 8 + 0.2x = 40 kg There were exactly 4 customers standing in the queue as they buy 40 kg rice each.
Only statement (i) is correct.
Hence, option 2.
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Most Upvoted Answer
In a grocery shop, customers were asked to stand in a queue in order t...
Given information:
- The first customer bought 10 kg of rice and then 1/5th of whatever remained in the rice container.
- The second customer bought 20 kg of rice and then 1/5th of whatever remained.
- The third customer bought 30 kg of rice plus 1/5th of whatever remained in the container.
- This pattern continued for each customer in the queue.
- Finally, each customer had bought the same amount of rice.

To determine:
Which of the following statements is/are true?
i. Each customer buys 40 kg of rice.
ii. Initially there was 260 kg of rice.
iii. There were exactly 5 customers standing in the queue.

Solution:
Let's assume that there were 'n' customers standing in the queue.

Step 1: Analyzing the first customer's purchase
- The first customer bought 10 kg of rice and then 1/5th of whatever remained in the container.
- Let's assume 'x' kg of rice remained after the first customer's purchase.
- After buying 10 kg of rice, the first customer took 1/5th of (x - 10) kg of rice.
- So, the first customer bought a total of 10 + (1/5)(x - 10) kg of rice.

Step 2: Analyzing the second customer's purchase
- The second customer bought 20 kg of rice and then 1/5th of whatever remained.
- After the first customer's purchase, there were (x - 10) kg of rice remaining.
- The second customer bought 20 kg of rice and then 1/5th of (x - 10) kg of rice.
- So, the second customer bought a total of 20 + (1/5)[(x - 10) - 20] kg of rice.

Step 3: Analyzing the third customer's purchase
- The third customer bought 30 kg of rice plus 1/5th of whatever remained in the container.
- After the second customer's purchase, there were [(x - 10) - 20] kg of rice remaining.
- The third customer bought 30 kg of rice and then 1/5th of [(x - 10) - 20] kg of rice.
- So, the third customer bought a total of 30 + (1/5)[[(x - 10) - 20] - 30] kg of rice.

Step 4: Generalizing the pattern for the 'n'th customer
- The 'n'th customer buys 'n * 10' kg of rice and then 1/5th of whatever remains.
- After the ('n' - 1)th customer's purchase, there are [((x - 10) - 20) - 30] kg of rice remaining.
- The 'n'th customer buys 'n * 10' kg of rice and then 1/5th of [((x - 10) - 20) - 30] kg of rice.
- So, the 'n'th customer buys a total of 'n * 10' + (1/5)[[((x - 10) - 20)
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In a grocery shop, customers were asked to stand in a queue in order to buy the goods. It was noticed that the first customer bought 10 kg of rice and then 1/5th of whatever remained in the rice container. The second customer bought 20 kg of rice and then 1/5th of whatever remained. The third customer bought 30 kg of rice plus 1/5th of whatever remained in the container and this went on for each customer in the queue. It was noticed that finally each customer had bought the same amount of rice.Which of following statements is/are true?i. Each customer buys 40 kg of rice.ii. Initially there was 260 kg of rice.iii. There were exactly 5 customers standing in the queue.a)Only iib)Only ic)Both iand iiid)All of theseCorrect answer is option 'B'. Can you explain this answer?
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In a grocery shop, customers were asked to stand in a queue in order to buy the goods. It was noticed that the first customer bought 10 kg of rice and then 1/5th of whatever remained in the rice container. The second customer bought 20 kg of rice and then 1/5th of whatever remained. The third customer bought 30 kg of rice plus 1/5th of whatever remained in the container and this went on for each customer in the queue. It was noticed that finally each customer had bought the same amount of rice.Which of following statements is/are true?i. Each customer buys 40 kg of rice.ii. Initially there was 260 kg of rice.iii. There were exactly 5 customers standing in the queue.a)Only iib)Only ic)Both iand iiid)All of theseCorrect answer is option 'B'. 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 In a grocery shop, customers were asked to stand in a queue in order to buy the goods. It was noticed that the first customer bought 10 kg of rice and then 1/5th of whatever remained in the rice container. The second customer bought 20 kg of rice and then 1/5th of whatever remained. The third customer bought 30 kg of rice plus 1/5th of whatever remained in the container and this went on for each customer in the queue. It was noticed that finally each customer had bought the same amount of rice.Which of following statements is/are true?i. Each customer buys 40 kg of rice.ii. Initially there was 260 kg of rice.iii. There were exactly 5 customers standing in the queue.a)Only iib)Only ic)Both iand iiid)All of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a grocery shop, customers were asked to stand in a queue in order to buy the goods. It was noticed that the first customer bought 10 kg of rice and then 1/5th of whatever remained in the rice container. The second customer bought 20 kg of rice and then 1/5th of whatever remained. The third customer bought 30 kg of rice plus 1/5th of whatever remained in the container and this went on for each customer in the queue. It was noticed that finally each customer had bought the same amount of rice.Which of following statements is/are true?i. Each customer buys 40 kg of rice.ii. Initially there was 260 kg of rice.iii. There were exactly 5 customers standing in the queue.a)Only iib)Only ic)Both iand iiid)All of theseCorrect answer is option 'B'. Can you explain this answer?.
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