Solving for the Unknown Number
The problem asks us to find a specific number based on a relationship involving percentages.
1. Define the Unknown
Let the unknown number be represented by the variable $x$.
2. Translate the Statement into an Equation
The statement "20% of a number is more than 20% of 620 by 210" can be written as:
$ (20\% \text{ of } x) = (20\% \text{ of } 620) + 210 $
Converting percentages to decimals:
$ 0.20x = (0.20 \times 620) + 210 $
3. Calculate the Known Percentage
First, calculate 20% of 620:
$ 0.20 \times 620 = 124 $
4. Simplify the Equation
Substitute the calculated value back into the equation:
$ 0.20x = 124 + 210 $
$ 0.20x = 334 $
5. Solve for the Number ($x$)
To find $x$, divide both sides by 0.20:
$ x = \frac{334}{0.20} $
Since $0.20 = \frac{20}{100} = \frac{1}{5}$, dividing by 0.20 is the same as multiplying by 5:
$ x = 334 \times 5 $
$ x = 1670 $
6. Conclusion
The number is 1670.
Important Questions from Percentage (Notes)
- Girish scored 572 marks in an examination and was 30 marks short of 28% of maximum marks. In the same examination, his friend scored 473 marks. What is the percentage of marks scored by his friend?
- Anubhav spent 14% of his income on electricity bills, 28% on rent and 18% on shopping. If $\frac{1}{4}$ th of the remaining amount is ₹5120, how much did he spend on electricity bills ?
- The total population of a town is 50,000. The number of males and females increases by 10% and 15% respectively and consequently the population of the town becomes 56,000. What was the number of males in the town?
- Gokul donates $17\%$ of his savings to old age home, $17\%$ of the savings to orphanage and $17\%$ of his savings to foundations for medical help. The remaining amount of Rs.$9800$ of savings is been deposited in bank. Find the salary of Gokul, if $50\%$ of the salary is his savings amount. (In Rs.)
- Which of the following multipliers will increase a given number by 25.3 % ?
