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The average of 12 number is 70. The average of the first four numbers is 60 while the average of the last five number is \(33\frac{1}{3}\%\) more than the average of the first four numbers. The 6th number is 20 more than the 5th number while the 7th number is 10 more than the 6th number. By what percent is the 6th number more than the 5th number?

The average of 12 number is 70. The average of the first four numbers is 60 while the average of the last five number is \(33\frac{1}{3}\%\) more than the average of the first four numbers. The 6th number is 20 more than the 5th number while the 7th number is 10 more than the 6th number. By what percent is the 6th number more than the 5th number? Correct Answer 40%

The average of 12 numbers = 70

The sum of 12 numbers = 70 × 12 = 840

The average of the first 4 numbers = 60

Sum of the first 4 numbers = 60 × 4 = 240

Average of the last 5 numbers = 60 × = 80

Sum of the last 5 numbers = 80 × 5 = 400

⇒ Sum of 5th, 6th and 7th numbers = 840 – 400 – 240 = 200

Let the 5th number be x.

6th number will be = x + 20

7th number will be = x + 20 + 10 = x + 30

According to the question

⇒ x + x + 20 + x + 30 = 200

⇒ x = 50

6th number = x = 50 + 20 = 70

7th number = x + 30 = 80

∴ Required percentage = × 100 = 40%

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