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In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option. Quantity A: What is the difference between the average of the first 79 natural numbers and the average of the first 39 natural numbers? Quantity B: The average of 10 numbers is 20 and that of other 30 numbers is 40. What is the average of all the numbers?

In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option. Quantity A: What is the difference between the average of the first 79 natural numbers and the average of the first 39 natural numbers? Quantity B: The average of 10 numbers is 20 and that of other 30 numbers is 40. What is the average of all the numbers? Correct Answer Quantity A < Quantity B

Quantity A: 

∵ Sum of the first n natural numbers = n(n + 1)/2

⇒ Average of the first n natural numbers =

= (n + 1)/2

Hence,

Average of the first 79 natural numbers = (79 + 1)/2 = 80/2 = 40

Average of the first 39 natural numbers = (39 + 1)/2 = 40/2 = 20

∴ Required difference = 40 - 20 = 20

Quantity B:

The average of 10 numbers = 20

⇒ Sum of 10 numbers = 20 × 10 = 200

The average of other 30 numbers = 40

⇒ Sum of other 30 numbers = 40 × 30 = 1200

Sum of all 40 numbers = 200 + 1200 = 1400

∴ Average of all 40 numbers = 1400/40 = 35

Hence, Average of 40 numbers = 35

∴ Quantity A < Quantity B

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