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
- A student's marks in Mathematics were 20% more than in Physics. If he scored 72 in Physics, how many marks did he score in Mathematics?
- An employee contributes 20% of their salary to charity. From the remaining amount, 40% is allocated to investments. The rest is divided for education and travel in the ratio 7: 5. If the expense on travel is ₹6000, what is the employee's total salary?
- A number was mistakenly increased by 25% instead of decreased by 20%. By what percent is the final result more than the CORRECT value?
- A person spends 80% of his income and saves ₹2000. What is his income?
- The population of a village increases by 8% annually. If the current population is 58,320, what was it two years ago (approx)?
- A man spends 80% of his income. His income has increased by 25%, but his expenditure remains the same. By what percent have his savings increased?
- Out of her total monthly income, a woman spends 60% on household expenses and 15% on savings. The remaining is spent on other items. What percentage of her income is spent on these other items?
- A's salary is 40% more than B's. If B's salary increases by 20% and A's increases by x%, then A's new salary becomes 25% more than B's new salary. What is the value of x?
- The value of a machine depreciates 10% in the first year, 20% in the second year, and 30% in the third year. If the initial value was Rs. 10,000, what is its value at the end of 3 years?
- A reduction of 20% in the price of sugar enables a person to buy 5 kg more for Rs. 200. What is the original price per kg?
Important Questions from Percentage
A number p increased by p% of 99 equals 99 increased by 99% of p. What is (p + 51)% of 928 + 72?
Amina saves 16% of her income. Now her income is increased by 20% but she still saves the same amount as before. What is the percentage increase in her expenditure?
What is 12% of 4% of 7% of 2 × 10 6 ?
Vignesh spends 42% of his monthly salary on food, 16% on house rent, 11% on entertainment and 7% on conveyance. But due to some family function, he has to borrow Rs. 12,000 from a money leader to meet the expenses of Rs. 18,000 What is his monthly salary?
If X is 12.25% more than Y. then Y is approximately_____ less than X.
