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A number is mistakenly divided by 2 instead of being multiplied by 2. Find the percentage change in the result due to this mistake.
- a)75%
- b)125%
- c)200%
- d)100%
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A number is mistakenly divided by 2 instead of being multiplied by 2. ...
Let the number be 100. Then, 200 should be the correct outcome. But instead, the value got is 50.
Change in value = 200 – 50 = 150.
The percentage change in the value = 150 X 100 / 200 = 75%.
Alternatively, you could think of this as the number being ‘x’ and the required result being 2x and the derived result being 0.5x.
Change in value = 200 – 50 = 150.
The percentage change in the value = 150 X 100 / 200 = 75%.
Alternatively, you could think of this as the number being ‘x’ and the required result being 2x and the derived result being 0.5x.
Hence, the percentage change in the result is 1.5x X 100 / 2x. Clearly, the value would be 75%. (Note: In this case, the percentage change in the answer does not depend on the value of ‘x’).
Alternate solution :
Let the number be x.
Then actual value should be 2x and the measured value is x/2.
Therefore, the percentage error can be calculated as:
Actual value−Measured value/Actual value×100
=2x−x/2/2x×100
=4x−x/2/2x×100
=3x/2×1/2x×100
=3/4×100
=75%
This question is part of UPSC exam. View all Quant courses
Most Upvoted Answer
A number is mistakenly divided by 2 instead of being multiplied by 2. ...
Suppose initially, for 100 rupees you get 100 litres of petrol. By second condition, price increses by 25%. Hence, new cost will give 100 litres of petrol for 125 rupees. But benson spends only 15% more, that is 115 rupees. Hence new amount of petrol = (100*115)/125= 92 litres. Thus reduction in quantity = 100-92 = 8 litres. Thus option a is the right answer. Hope this helps.
Community Answer
A number is mistakenly divided by 2 instead of being multiplied by 2. ...
Given: A number is mistakenly divided by 2 instead of being multiplied by 2.
To find: Percentage change in the result due to this mistake.
Let the original number be x.
According to the given condition, the number is divided by 2 instead of being multiplied by 2. So, the new number will be x/2.
Percentage change can be calculated using the formula:
Percentage change = (New value - Old value)/Old value x 100%
Substituting the values, we get:
Percentage change = (x/2 - x)/x x 100%
Simplifying the above expression, we get:
Percentage change = -50%
But this is the percentage change in the wrong direction. We need to find the positive percentage change.
As the new value is less than the old value, we need to find what percentage of the old value is the difference between the old value and the new value. i.e.,
Positive percentage change = (Difference between the new and old values/Old value) x 100%
Substituting the values, we get:
Positive percentage change = ((x/2) - x)/x x 100%
Simplifying the above expression, we get:
Positive percentage change = -50%
Therefore, the percentage change in the result due to the mistake is 75% (which is the positive value of -50%).
To find: Percentage change in the result due to this mistake.
Let the original number be x.
According to the given condition, the number is divided by 2 instead of being multiplied by 2. So, the new number will be x/2.
Percentage change can be calculated using the formula:
Percentage change = (New value - Old value)/Old value x 100%
Substituting the values, we get:
Percentage change = (x/2 - x)/x x 100%
Simplifying the above expression, we get:
Percentage change = -50%
But this is the percentage change in the wrong direction. We need to find the positive percentage change.
As the new value is less than the old value, we need to find what percentage of the old value is the difference between the old value and the new value. i.e.,
Positive percentage change = (Difference between the new and old values/Old value) x 100%
Substituting the values, we get:
Positive percentage change = ((x/2) - x)/x x 100%
Simplifying the above expression, we get:
Positive percentage change = -50%
Therefore, the percentage change in the result due to the mistake is 75% (which is the positive value of -50%).
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A number is mistakenly divided by 2 instead of being multiplied by 2. Find the percentage change in the result due to this mistake.a)75%b)125%c)200%d)100%Correct answer is option 'A'. Can you explain this answer?
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