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A number is decreased by 10% and then increased by 10%. The number so obtained is 10 less than the original number. What was the original number ?
- a)1200
- b)1000
- c)100
- d)200
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A number is decreased by 10% and then increased by 10%. The number so ...
Given:
Let the original number be x.
The number is decreased by 10% and then increased by 10%.
The number so obtained is 10 less than the original number.
To find: What was the original number?
Solution:
Let's solve the problem step by step:
Step 1: Decrease the original number by 10%
The number is decreased by 10%, which means that we subtract 10% of x from x.
10% of x = (10/100) * x = 0.1x
The number after decreasing by 10% = x - 0.1x = 0.9x
Step 2: Increase the number obtained in step 1 by 10%
The number obtained in step 1 is 0.9x.
We need to increase this number by 10%, which means that we add 10% of 0.9x to 0.9x.
10% of 0.9x = (10/100) * 0.9x = 0.09x
The number after increasing by 10% = 0.9x + 0.09x = 0.99x
Step 3: The number obtained in step 2 is 10 less than the original number
According to the question, the number obtained in step 2 is 10 less than the original number.
0.99x = x - 10
Solving for x, we get:
0.99x - x = -10
-0.01x = -10
x = (-10)/(-0.01) = 1000
Therefore, the original number is 1000.
Answer: Option B (1000)
Let the original number be x.
The number is decreased by 10% and then increased by 10%.
The number so obtained is 10 less than the original number.
To find: What was the original number?
Solution:
Let's solve the problem step by step:
Step 1: Decrease the original number by 10%
The number is decreased by 10%, which means that we subtract 10% of x from x.
10% of x = (10/100) * x = 0.1x
The number after decreasing by 10% = x - 0.1x = 0.9x
Step 2: Increase the number obtained in step 1 by 10%
The number obtained in step 1 is 0.9x.
We need to increase this number by 10%, which means that we add 10% of 0.9x to 0.9x.
10% of 0.9x = (10/100) * 0.9x = 0.09x
The number after increasing by 10% = 0.9x + 0.09x = 0.99x
Step 3: The number obtained in step 2 is 10 less than the original number
According to the question, the number obtained in step 2 is 10 less than the original number.
0.99x = x - 10
Solving for x, we get:
0.99x - x = -10
-0.01x = -10
x = (-10)/(-0.01) = 1000
Therefore, the original number is 1000.
Answer: Option B (1000)
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Community Answer
A number is decreased by 10% and then increased by 10%. The number so ...
Let the original number be x.
If number is decreased by 10% and then increased by 10%, then Final number obtained = 110% of (90% of x)
= (110/100 * 90/100 * x)
= (99/100)x.
By the given data, number so obtained is 10 less than the original number,
Therefore x- (99/100)x=10 or x =1000
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A number is decreased by 10% and then increased by 10%. The number so obtained is 10 less than the original number. What was the original number ?a)1200b)1000c)100d)200Correct answer is option 'B'. Can you explain this answer?
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