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In a class of 72 children, children are seated in rows and columns in such a way that the number of children in each row is 12.5% more than the number of children in each column. How many children are there in each row ?
- a)9
- b)8
- c)18
- d)12
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
In a class of 72 children, children are seated in rows and columns in ...
let the number of children in each column be x.Thus, the number of children in each row is 1.125
given, total number of children=72=x(1.125x)
∴x=8.
thus, number of children in a row=1.125x=9
Most Upvoted Answer
In a class of 72 children, children are seated in rows and columns in ...
Given:
- Total number of children = 72
- Number of children in each row is 12.5% more than the number of children in each column
To find:
- How many children are there in each row?
Solution:
Let's assume the number of children in each column is x.
Step 1: Calculate the number of children in each row
- As per the given condition, the number of children in each row is 12.5% more than the number of children in each column.
- 12.5% of x = 0.125x
- Number of children in each row = x + 0.125x = 1.125x
Step 2: Calculate the total number of children
- Total number of children = Number of rows × Number of columns
- 72 = (Total number of children) = (Number of rows) × (Number of columns)
Step 3: Substitute the value of Number of children in each row from Step 1 into the equation from Step 2
- 72 = (1.125x) × (x)
Step 4: Solve the equation
- 72 = 1.125x^2
- Divide both sides by 1.125: (72/1.125) = (1.125x^2/1.125)
- 64 = x^2
- Take the square root of both sides: √64 = √(x^2)
- 8 = x
Hence, there are 8 children in each column.
To find the number of children in each row, we substitute the value of x into the equation from Step 1:
Number of children in each row = 1.125x = 1.125 × 8 = 9
Therefore, there are 9 children in each row.
- Total number of children = 72
- Number of children in each row is 12.5% more than the number of children in each column
To find:
- How many children are there in each row?
Solution:
Let's assume the number of children in each column is x.
Step 1: Calculate the number of children in each row
- As per the given condition, the number of children in each row is 12.5% more than the number of children in each column.
- 12.5% of x = 0.125x
- Number of children in each row = x + 0.125x = 1.125x
Step 2: Calculate the total number of children
- Total number of children = Number of rows × Number of columns
- 72 = (Total number of children) = (Number of rows) × (Number of columns)
Step 3: Substitute the value of Number of children in each row from Step 1 into the equation from Step 2
- 72 = (1.125x) × (x)
Step 4: Solve the equation
- 72 = 1.125x^2
- Divide both sides by 1.125: (72/1.125) = (1.125x^2/1.125)
- 64 = x^2
- Take the square root of both sides: √64 = √(x^2)
- 8 = x
Hence, there are 8 children in each column.
To find the number of children in each row, we substitute the value of x into the equation from Step 1:
Number of children in each row = 1.125x = 1.125 × 8 = 9
Therefore, there are 9 children in each row.
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In a class of 72 children, children are seated in rows and columns in such a way that the number of children in each row is 12.5% more than the number of children in each column. How many children are there in each row ?a)9b)8c)18d)12Correct answer is option 'A'. Can you explain this answer?
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