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Average of four numbers is increased by 1 when a number is replaced by x and average of that four number is decreased by 1 when an another number is replaced with x. What is the difference of the both numbers?
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Average of four numbers is increased by 1 when a number is replaced by...
Given Information:
- Average of four numbers is increased by 1 when a number is replaced by x.
- Average of four numbers is decreased by 1 when another number is replaced with x.
To find:
- The difference between the two numbers that were replaced with x.
Solution:
Step 1: Setting up the equations
Let's assume the four numbers are a, b, c, and d.
The average of these four numbers is (a + b + c + d) / 4.
When one number is replaced by x:
New average = (a + b + c + x) / 4
According to the given information, this new average is increased by 1:
(a + b + c + x) / 4 = (a + b + c + d) / 4 + 1
When another number is replaced by x:
New average = (a + b + x + d) / 4
According to the given information, this new average is decreased by 1:
(a + b + x + d) / 4 = (a + b + c + d) / 4 - 1
Step 2: Solving the equations
Solving the above two equations, we get:
a + b + c + x = a + b + c + d + 4
a + b + x + d = a + b + c + d - 4
x = d + 4
x = c - 4
Step 3: Finding the difference
The difference between the two numbers that were replaced with x is:
(d + 4) - (c - 4)
= d + 4 - c + 4
= d - c + 8
Therefore, the difference between the two numbers that were replaced with x is 8.
- Average of four numbers is increased by 1 when a number is replaced by x.
- Average of four numbers is decreased by 1 when another number is replaced with x.
To find:
- The difference between the two numbers that were replaced with x.
Solution:
Step 1: Setting up the equations
Let's assume the four numbers are a, b, c, and d.
The average of these four numbers is (a + b + c + d) / 4.
When one number is replaced by x:
New average = (a + b + c + x) / 4
According to the given information, this new average is increased by 1:
(a + b + c + x) / 4 = (a + b + c + d) / 4 + 1
When another number is replaced by x:
New average = (a + b + x + d) / 4
According to the given information, this new average is decreased by 1:
(a + b + x + d) / 4 = (a + b + c + d) / 4 - 1
Step 2: Solving the equations
Solving the above two equations, we get:
a + b + c + x = a + b + c + d + 4
a + b + x + d = a + b + c + d - 4
x = d + 4
x = c - 4
Step 3: Finding the difference
The difference between the two numbers that were replaced with x is:
(d + 4) - (c - 4)
= d + 4 - c + 4
= d - c + 8
Therefore, the difference between the two numbers that were replaced with x is 8.
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Average of four numbers is increased by 1 when a number is replaced by x and average of that four number is decreased by 1 when an another number is replaced with x. What is the difference of the both numbers?
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Average of four numbers is increased by 1 when a number is replaced by x and average of that four number is decreased by 1 when an another number is replaced with x. What is the difference of the both numbers? for SSC CHSL 2025 is part of SSC CHSL preparation. The Question and answers have been prepared according to the SSC CHSL exam syllabus. Information about Average of four numbers is increased by 1 when a number is replaced by x and average of that four number is decreased by 1 when an another number is replaced with x. What is the difference of the both numbers? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Average of four numbers is increased by 1 when a number is replaced by x and average of that four number is decreased by 1 when an another number is replaced with x. What is the difference of the both numbers?.
Average of four numbers is increased by 1 when a number is replaced by x and average of that four number is decreased by 1 when an another number is replaced with x. What is the difference of the both numbers? for SSC CHSL 2025 is part of SSC CHSL preparation. The Question and answers have been prepared according to the SSC CHSL exam syllabus. Information about Average of four numbers is increased by 1 when a number is replaced by x and average of that four number is decreased by 1 when an another number is replaced with x. What is the difference of the both numbers? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Average of four numbers is increased by 1 when a number is replaced by x and average of that four number is decreased by 1 when an another number is replaced with x. What is the difference of the both numbers?.
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