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Average of 8 numbers is 40. The average of first three numbers is 46 and the average of next two numbers is 50. If the sixth number is 6 and 10 less than seventh and eighth number respectively, then what is the value of the eighth number?
- a)28
- b)22
- c)30
- d)32
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Average of 8 numbers is 40. The average of first three numbers is 46 a...
Sum of the 8 numbers = 8 × 40 = 320
Sum of first 3 numbers = 3 × 46 = 138
Sum of next two numbers = 2 × 50 = 100
Let the 6th number be ‘x
⇒ 7th number = x + 6
⇒ 8th number = x + 10
Hence,
⇒ 138 + 100 + x + x + 6 + x + 10 = 320
⇒ 3x = 320 – 254
⇒ x = 66/3 = 22
∴ The 8th number = 22 + 10 = 32
Sum of first 3 numbers = 3 × 46 = 138
Sum of next two numbers = 2 × 50 = 100
Let the 6th number be ‘x
⇒ 7th number = x + 6
⇒ 8th number = x + 10
Hence,
⇒ 138 + 100 + x + x + 6 + x + 10 = 320
⇒ 3x = 320 – 254
⇒ x = 66/3 = 22
∴ The 8th number = 22 + 10 = 32
Most Upvoted Answer
Average of 8 numbers is 40. The average of first three numbers is 46 a...
Given information:
- The average of 8 numbers is 40.
- The average of the first three numbers is 46.
- The average of the next two numbers is 50.
- The sixth number is 6 less than the seventh number.
- The sixth number is also 10 less than the eighth number.
Let's solve this step by step:
1. Average of 8 numbers is 40:
We can find the sum of the 8 numbers by multiplying the average by the total number of numbers. So, the sum of the 8 numbers is 8 * 40 = 320.
2. Average of the first three numbers is 46:
The sum of the first three numbers can be found by multiplying the average by the number of numbers. So, the sum of the first three numbers is 3 * 46 = 138.
3. Average of the next two numbers is 50:
The sum of the next two numbers can be found in a similar way. So, the sum of the next two numbers is 2 * 50 = 100.
4. The sixth number is 6 less than the seventh number:
Let's assume the seventh number is 'x'. Then, the sixth number will be 'x - 6'.
5. The sixth number is also 10 less than the eighth number:
Let's assume the eighth number is 'y'. Then, the sixth number will be 'y - 10'.
6. Equating the sum of the first three numbers, next two numbers, and the sixth number with the given sum:
138 + 100 + (x - 6) + (y - 10) = 320
7. Simplifying the equation:
238 + x + y - 16 = 320
x + y + 222 = 320
x + y = 320 - 222
x + y = 98
8. Solving the equation for 'x' and 'y':
From the equation x + y = 98, we can see that the values of x and y should add up to 98. Since we don't have any information about the exact values of x and y, there can be multiple solutions. However, we can find the value of y by assuming a value for x.
Let's assume x = 40. Then, y = 98 - 40 = 58.
Therefore, the value of the eighth number (y) is 58, which corresponds to option 'D'.
- The average of 8 numbers is 40.
- The average of the first three numbers is 46.
- The average of the next two numbers is 50.
- The sixth number is 6 less than the seventh number.
- The sixth number is also 10 less than the eighth number.
Let's solve this step by step:
1. Average of 8 numbers is 40:
We can find the sum of the 8 numbers by multiplying the average by the total number of numbers. So, the sum of the 8 numbers is 8 * 40 = 320.
2. Average of the first three numbers is 46:
The sum of the first three numbers can be found by multiplying the average by the number of numbers. So, the sum of the first three numbers is 3 * 46 = 138.
3. Average of the next two numbers is 50:
The sum of the next two numbers can be found in a similar way. So, the sum of the next two numbers is 2 * 50 = 100.
4. The sixth number is 6 less than the seventh number:
Let's assume the seventh number is 'x'. Then, the sixth number will be 'x - 6'.
5. The sixth number is also 10 less than the eighth number:
Let's assume the eighth number is 'y'. Then, the sixth number will be 'y - 10'.
6. Equating the sum of the first three numbers, next two numbers, and the sixth number with the given sum:
138 + 100 + (x - 6) + (y - 10) = 320
7. Simplifying the equation:
238 + x + y - 16 = 320
x + y + 222 = 320
x + y = 320 - 222
x + y = 98
8. Solving the equation for 'x' and 'y':
From the equation x + y = 98, we can see that the values of x and y should add up to 98. Since we don't have any information about the exact values of x and y, there can be multiple solutions. However, we can find the value of y by assuming a value for x.
Let's assume x = 40. Then, y = 98 - 40 = 58.
Therefore, the value of the eighth number (y) is 58, which corresponds to option 'D'.
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Average of 8 numbers is 40. The average of first three numbers is 46 and the average of next two numbers is 50. If the sixth number is 6 and 10 less than seventh and eighth number respectively, then what is the value of the eighth number?a)28b)22c)30d)32Correct answer is option 'D'. Can you explain this answer?
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Average of 8 numbers is 40. The average of first three numbers is 46 and the average of next two numbers is 50. If the sixth number is 6 and 10 less than seventh and eighth number respectively, then what is the value of the eighth number?a)28b)22c)30d)32Correct answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Average of 8 numbers is 40. The average of first three numbers is 46 and the average of next two numbers is 50. If the sixth number is 6 and 10 less than seventh and eighth number respectively, then what is the value of the eighth number?a)28b)22c)30d)32Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Average of 8 numbers is 40. The average of first three numbers is 46 and the average of next two numbers is 50. If the sixth number is 6 and 10 less than seventh and eighth number respectively, then what is the value of the eighth number?a)28b)22c)30d)32Correct answer is option 'D'. Can you explain this answer?.
Average of 8 numbers is 40. The average of first three numbers is 46 and the average of next two numbers is 50. If the sixth number is 6 and 10 less than seventh and eighth number respectively, then what is the value of the eighth number?a)28b)22c)30d)32Correct answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Average of 8 numbers is 40. The average of first three numbers is 46 and the average of next two numbers is 50. If the sixth number is 6 and 10 less than seventh and eighth number respectively, then what is the value of the eighth number?a)28b)22c)30d)32Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Average of 8 numbers is 40. The average of first three numbers is 46 and the average of next two numbers is 50. If the sixth number is 6 and 10 less than seventh and eighth number respectively, then what is the value of the eighth number?a)28b)22c)30d)32Correct answer is option 'D'. Can you explain this answer?.
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Average of 8 numbers is 40. The average of first three numbers is 46 and the average of next two numbers is 50. If the sixth number is 6 and 10 less than seventh and eighth number respectively, then what is the value of the eighth number?a)28b)22c)30d)32Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Average of 8 numbers is 40. The average of first three numbers is 46 and the average of next two numbers is 50. If the sixth number is 6 and 10 less than seventh and eighth number respectively, then what is the value of the eighth number?a)28b)22c)30d)32Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Average of 8 numbers is 40. The average of first three numbers is 46 and the average of next two numbers is 50. If the sixth number is 6 and 10 less than seventh and eighth number respectively, then what is the value of the eighth number?a)28b)22c)30d)32Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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