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The length and breadth of a rectangle are 2.4 units and 3.6 units respectively. If A is the area obtained by first multiplying the dimensions and then rounding the product to the nearest integer, and A* is the area obtained by first rounding each dimension to the nearest integer and then multiplying them, by what percentage is A* lesser or greater than A?
  • a)
    2.5%
  • b)
    4.1%
  • c)
    9.1%
  • d)
    11.1%
  • e)
    12.5%
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The length and breadth of a rectangle are 2.4 units and 3.6 units resp...
Given:
  • Length of rectangle = 2.4 units
  • Breadth of rectangle = 3.6 units
  • A = Result of rounding 2.4*3.6 to nearest integer
  • A* = Product of (2.4 rounded to nearest integer) and (3.6 rounded to nearest integer)
To Find: By what percentage is A* less or greater than A?
Approach:
  1. Let A* be p percentage greater than A. So, we can write
 
d. So, to find the value of p, we need to find the value of A*/A
e. (Note: if upon calculation, the value of p comes to be negative, this will mean that A* is less than A by p percentage)

2. To find the value of A*/A, we’ll calculate the values of A* and A.
Working out :
 
  • Finding the value of A*
    • The result of rounding 2.4 to the nearest integer is 2
    • The result of rounding 3.6 to the nearest integer is 4
    • So, A* = 2*4 = 8
  • Finding the value of A
    • 2.4*3.6 = 8.64
    • So, A = Result of rounding 8.64 to nearest integer
    • That is, A = 9
Looking at the answer choices, we see that the correct answer is Option D
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Most Upvoted Answer
The length and breadth of a rectangle are 2.4 units and 3.6 units resp...
Given:
Length of rectangle = 2.4 units
Breadth of rectangle = 3.6 units

To find:
Percentage difference between A* and A

Solution:
Step 1: Calculate the area using the given dimensions:
A = 2.4 * 3.6 = 8.64

Step 2: Round the product obtained in Step 1 to the nearest integer:
A ≈ 9

Step 3: Round each dimension to the nearest integer:
Length ≈ 2
Breadth ≈ 4

Step 4: Calculate the area using the rounded dimensions:
A* = 2 * 4 = 8

Step 5: Find the percentage difference between A* and A:
Percentage difference = [(A* - A) / A] * 100

Substituting the values:
Percentage difference = [(8 - 9) / 9] * 100
Percentage difference = (-1 / 9) * 100
Percentage difference ≈ -11.1%

Answer:
The area A* is approximately 11.1% lesser than the area A. Option D is the correct answer.
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The length and breadth of a rectangle are 2.4 units and 3.6 units respectively. If A is the area obtained by first multiplying the dimensions and then rounding the product to the nearest integer, and A* is the area obtained by first rounding each dimension to the nearest integer and then multiplying them, by what percentage is A* lesser or greater than A?a)2.5%b)4.1%c)9.1%d)11.1%e)12.5%Correct answer is option 'D'. Can you explain this answer?
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