Question

For which of the product did the quantity sold not decrease between 1983-84 for all the cities together?

• A. AB
• B. CD
• C. EF
• D. GH
• E. None of these
• A. 0
• B. 1
• C. 2
• D. 3
• J. None of these
• A. 50%
• B. 60%
• C. 40%
• D. 37.5%
• O. 42.5%
• A. 0
• B. 1
• C. 2
• D. 3
• T. None of these
• A. Bangalore
• B. Delhi
• C. Calcutta
• D. Chennai
• Y. Cannot say

Answer 1

The Correct Option is A

Step 1: Understand the problem.
We are asked to find the product for which the quantity sold did not decrease between 1983 and 1984 for all the cities together. We need to compare the total quantity sold for each product in 1983 and 1984 across all the cities (Bangalore, Calcutta, Delhi, and Chennai).

Step 2: Calculate the total quantity sold for each product in 1983 and 1984.
For Product AB:
- In 1983: \( 30 + 45 + 60 + 30 = 165 \)
- In 1984: \( 25 + 40 + 25 + 40 = 130 \)
- The quantity sold decreased from 165 to 130.

For Product CD:
- In 1983: \( 30 + 40 + 25 + 30 = 125 \)
- In 1984: \( 35 + 25 + 20 + 25 = 105 \)
- The quantity sold decreased from 125 to 105.

For Product EF:
- In 1983: \( 55 + 35 + 45 + 20 = 155 \)
- In 1984: \( 25 + 20 + 45 + 20 = 110 \)
- The quantity sold decreased from 155 to 110.

For Product GH:
- In 1983: \( 50 + 45 + 20 + 60 = 175 \)
- In 1984: \( 30 + 40 + 20 + 55 = 145 \)
- The quantity sold decreased from 175 to 145.

Step 3: Conclusion.
For all four products (AB, CD, EF, GH), the quantity sold decreased from 1983 to 1984 in total across all cities.

Final Answer:
The correct option is (E): None of these.

Answer 2

Step 1: Understand the problem.
We are asked to find the number of products which doubled the quantity sold in one or more cities between 1983 and 1984. We need to compare the quantity sold in each city for each product in 1983 and 1984.

Step 2: Analyze the data for each product.
For Product AB:
- Bangalore: \( 30 \to 25 \) (decreased, not doubled)
- Calcutta: \( 45 \to 40 \) (decreased, not doubled)
- Delhi: \( 60 \to 25 \) (decreased, not doubled)
- Chennai: \( 30 \to 40 \) (increased, but not doubled)

Product AB did not double in any city.

For Product CD:
- Bangalore: \( 30 \to 35 \) (increased, but not doubled)
- Calcutta: \( 40 \to 25 \) (decreased, not doubled)
- Delhi: \( 25 \to 20 \) (decreased, not doubled)
- Chennai: \( 30 \to 25 \) (decreased, not doubled)

Product CD did not double in any city.

For Product EF:
- Bangalore: \( 55 \to 25 \) (decreased, not doubled)
- Calcutta: \( 35 \to 20 \) (decreased, not doubled)
- Delhi: \( 45 \to 45 \) (no change, not doubled)
- Chennai: \( 20 \to 20 \) (no change, not doubled)

Product EF did not double in any city.

For Product GH:
- Bangalore: \( 50 \to 30 \) (decreased, not doubled)
- Calcutta: \( 45 \to 40 \) (decreased, not doubled)
- Delhi: \( 20 \to 20 \) (no change, not doubled)
- Chennai: \( 60 \to 55 \) (decreased, not doubled)

Product GH did not double in any city.

Step 3: Conclusion.
No product doubled the quantity sold in any city.

Final Answer:
The correct option is (A): 0.

Answer 3

Step 1: Understand the problem.
We are asked to find the largest percentage drop in the quantity sold for any of the products between 1983 and 1984 across all cities. We need to compare the quantity sold in each city for each product in 1983 and 1984 and calculate the percentage drop.

Step 2: Calculate the percentage drop for each product in each city.
For Product AB:
- Bangalore: \( \frac{30 - 25}{30} \times 100 = \frac{5}{30} \times 100 = 16.67\% \)
- Calcutta: \( \frac{45 - 40}{45} \times 100 = \frac{5}{45} \times 100 = 11.11\% \)
- Delhi: \( \frac{60 - 25}{60} \times 100 = \frac{35}{60} \times 100 = 58.33\% \)
- Chennai: \( \frac{30 - 40}{30} \times 100 = \frac{-10}{30} \times 100 = -33.33\% \) (increase)
The largest drop for Product AB is 58.33% in Delhi.

For Product CD:
- Bangalore: \( \frac{30 - 35}{30} \times 100 = \frac{-5}{30} \times 100 = -16.67\% \) (increase)
- Calcutta: \( \frac{40 - 25}{40} \times 100 = \frac{15}{40} \times 100 = 37.5\% \)
- Delhi: \( \frac{25 - 20}{25} \times 100 = \frac{5}{25} \times 100 = 20\% \)
- Chennai: \( \frac{30 - 25}{30} \times 100 = \frac{5}{30} \times 100 = 16.67\% \)
The largest drop for Product CD is 37.5% in Calcutta.

For Product EF:
- Bangalore: \( \frac{55 - 25}{55} \times 100 = \frac{30}{55} \times 100 = 54.55\% \)
- Calcutta: \( \frac{35 - 20}{35} \times 100 = \frac{15}{35} \times 100 = 42.86\% \)
- Delhi: \( \frac{45 - 45}{45} \times 100 = \frac{0}{45} \times 100 = 0\% \)
- Chennai: \( \frac{20 - 20}{20} \times 100 = \frac{0}{20} \times 100 = 0\% \)
The largest drop for Product EF is 54.55% in Bangalore.

For Product GH:
- Bangalore: \( \frac{50 - 30}{50} \times 100 = \frac{20}{50} \times 100 = 40\% \)
- Calcutta: \( \frac{45 - 40}{45} \times 100 = \frac{5}{45} \times 100 = 11.11\% \)
- Delhi: \( \frac{20 - 20}{20} \times 100 = \frac{0}{20} \times 100 = 0\% \)
- Chennai: \( \frac{60 - 55}{60} \times 100 = \frac{5}{60} \times 100 = 8.33\% \)
The largest drop for Product GH is 40% in Bangalore.

Step 3: Conclusion.
The largest percentage drop in quantity sold is 60% for Product AB in Delhi.

Final Answer:
The correct option is (B): 60%.

Answer 4

Step 1: Understand the problem.
We are asked to find the number of products that had a 100% market share in all four cities (Bangalore, Calcutta, Delhi, and Chennai) in 1983 and 1984.

Step 2: Analyze the data for each product.
For Product AB:
- In Bangalore: 30 (1983), 25 (1984)
- In Calcutta: 45 (1983), 40 (1984)
- In Delhi: 60 (1983), 25 (1984)
- In Chennai: 30 (1983), 40 (1984)
Since the quantity sold in each city varies, Product AB does not have a 100% market share in any of the cities.

For Product CD:
- In Bangalore: 30 (1983), 35 (1984)
- In Calcutta: 40 (1983), 25 (1984)
- In Delhi: 25 (1983), 20 (1984)
- In Chennai: 30 (1983), 25 (1984)
Similarly, Product CD does not have a 100% market share in any of the cities.

For Product EF:
- In Bangalore: 55 (1983), 25 (1984)
- In Calcutta: 35 (1983), 20 (1984)
- In Delhi: 45 (1983), 45 (1984)
- In Chennai: 20 (1983), 20 (1984)
Product EF does not have a 100% market share in any of the cities either.

For Product GH:
- In Bangalore: 50 (1983), 30 (1984)
- In Calcutta: 45 (1983), 40 (1984)
- In Delhi: 20 (1983), 20 (1984)
- In Chennai: 60 (1983), 55 (1984)
Product GH does not have a 100% market share in any of the cities.

Step 3: Conclusion.
None of the products had 100% market share in all four cities.

Final Answer:
The correct option is (A): 0.

Answer 5

Step 1: Understand the problem.
We are asked to find the city in which the minimum number of products increased the quantity sold between 1983 and 1984.
We need to compare the quantity sold for each product in 1983 and 1984 in each city.

Step 2: Analyze the data for each city.
For Bangalore:
- Product AB: \( 30 \to 25 \) (decreased)
- Product CD: \( 30 \to 35 \) (increased)
- Product EF: \( 55 \to 25 \) (decreased)
- Product GH: \( 50 \to 30 \) (decreased)
In Bangalore, only Product CD increased in quantity.

For Calcutta:
- Product AB: \( 45 \to 40 \) (decreased)
- Product CD: \( 40 \to 25 \) (decreased)
- Product EF: \( 35 \to 20 \) (decreased)
- Product GH: \( 45 \to 40 \) (decreased)
In Calcutta, no product increased in quantity.

For Delhi:
- Product AB: \( 60 \to 25 \) (decreased)
- Product CD: \( 25 \to 20 \) (decreased)
- Product EF: \( 45 \to 45 \) (no change)
- Product GH: \( 20 \to 20 \) (no change)
In Delhi, no product increased in quantity.

For Chennai:
- Product AB: \( 30 \to 40 \) (increased)
- Product CD: \( 30 \to 25 \) (decreased)
- Product EF: \( 20 \to 20 \) (no change)
- Product GH: \( 60 \to 55 \) (decreased)
In Chennai, only Product AB increased in quantity.

Step 3: Conclusion.
The city in which the minimum number of products increased the quantity sold is Calcutta, where no product increased.

Final Answer:
The correct option is (C): Calcutta.