In a new budget, the price of petrol rose by 25%. By how much percent must a person reduce his consumption so that his expenditure on it does not increase?
20%
To solve the problem of determining by how much percent a person must reduce his consumption of petrol to ensure his expenditure does not increase despite a price rise, let's go through the solution step-by-step.
Given:
- Initial price of petrol = \( P \)
- New price of petrol after a 25% increase = \( P + 0.25P = 1.25P \)
Let the initial consumption be \( C \) (liters). Therefore, the initial expenditure is given by:
\(E_{\text{initial}} = P \times C\)
For the expenditure to remain unchanged after the price hike, the new expenditure should be equal to the initial expenditure:
\(E_{\text{new}} = 1.25P \times C_{\text{new}} = P \times C\)
Solving the above equation for \( C_{\text{new}} \):
\(C_{\text{new}} = \frac{P \times C}{1.25P} = \frac{C}{1.25}\)
This can be written as:
\(C_{\text{new}} = 0.8C\)
Thus, the consumption must be reduced to 80% of the original.
The percentage reduction in consumption is calculated as:
\(\text{Percentage Reduction} = \frac{C - C_{\text{new}}}{C} \times 100\)
Substituting the known values:
\(\text{Percentage Reduction} = \frac{C - 0.8C}{C} \times 100 = \frac{0.2C}{C} \times 100 = 20\%\)
Therefore, the person must reduce his consumption by 20% to maintain the same expenditure.
Given options: 10%, 15%, 20%, 25%
Correct Answer: 20%
This ties with the given solution and answers the question accurately. Thus, 20% is the correct and justified choice.
Similar Questions
If the price of sugar increases by 25%, determine the percentage by which its consumption be reduced so as not to increase the expenditure on it?
The length of the side of a square (5.0 cm × 5.0 cm) is increased by 1%. By what percentage (%) the area of the square increases?
If 60% of (a − b) = 40% of (a + b), then what percent of a is b?
Manoj's commission is 10% on all sales up to Rs. 10,000 and 5% on all sales exceeding this. He remits Rs. 75,500 to his company after deducting his commission. The total sales will come out to be:
If x and y are two positive numbers and x is 25% greater than y, what is the value of the ratio y/x?
5% of the inhabitants of a village having died of malaria, a panic set in. During this, 20% of the remaining inhabitants left the village. The population is then reduced to 4750. Find the number of original inhabitants?
In a class, 20% of the boys have blue eyes and 10% of the girls have blue eyes. If the ratio of boys to girls in the class is 4:3, then what is the portion of the students in the class having blue eyes?
During one year, the population of a town increased by 5% and during the next year, the population decreased by 5%. If the total population is 29925 at the end of the second year, then what was the population size in the beginning of the first year?
If income of X is 20% more than that of Y and income of Y is 25% less than that of Z, then the total income of X, Y and Z are in which of the following ratios?
In a class, there are 60% female students and the remaining are male. 40% of the female students and 70% of the male students have opted for the research methodology course. If in all, 60 students have not opted for the research methdology course, which of the following is the total number of students in the class?
Important Questions from Percentage
- By how much is 50% of 60 greater than 30% of 40?
- A fruit seller had some apples. He sells 40% of those apples and still has 240 apples. How many apples did he originally have?
- In an election between two candidates, 75% of the voters cast their votes. 2% of the votes cast were declared invalid. A candidate got 9261 votes which were 75% of the total valid votes. The total number of voters enrolled in that election was:
- The population of a district is 328000, out of which 164000 are males. 24% of the population is literate. If 34% males are literate, then what percentage of females are literate?
- A number, when decreased by 6%, gives 3760. The number is:
