Finding the Number Using Percentage Difference
Let the unknown number be represented by the variable $x$.
The problem states that the difference between 20% of the number and 10% of the number is 120.
We can express this mathematically:
- 20% of the number is $0.20x$.
- 10% of the number is $0.10x$.
The difference is given as 120:
$0.20x - 0.10x = 120$
Solving the Equation
Combine the terms involving $x$:
$ (0.20 - 0.10)x = 120 $
$ 0.10x = 120 $
To find the value of $x$, divide both sides of the equation by 0.10:
$ x = \frac{120}{0.10} $
$ x = 1200 $
Verification
Check the answer:
- 20% of 1200 is $0.20 \times 1200 = 240$.
- 10% of 1200 is $0.10 \times 1200 = 120$.
- The difference is $240 - 120 = 120$.
The calculated difference matches the value given in the problem.
Therefore, the number is 1200.
Similar Questions
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Important Questions from Percentage
Radha saves 25% of her income. If her expenditure increases by 20% and her income increases by 29%, then her savings increase by;
The income of A is 45% more than the income of B and the income of C is 60% less than the sum of the incomes of A and B. The income of D is 20% more than that of C. If the difference between the incomes of B and D is Rs. 13200, then the income (in Rs.) of C is:
The price of cooking oil increased by 25%. Find by how much percentage a family must reduce its consumption in order to maintain the same budget.
The population of a city increased by 30% in the first year and decreased by 15% in the next year. If the present population is 11,050 then population 2 years ago was:
The income of A is 30% less than the income of B and the income of B is 137.5% more than that of C. If the income of A is Rs. 28500 less than that of B, then the income (in Rs.) of C is:
