Understanding the Income and Expenditure Relationship
This question involves calculating a person's total income based on their savings percentage and expenditure amount. We know that income is split between savings and expenditure.
- The person saves 40% of their income.
- The expenditure is given as ₹480.
Calculating Expenditure Percentage
If the person saves 40% of their income, the remaining portion must be their expenditure. We can calculate this as:
Expenditure Percentage = Total Income Percentage - Savings Percentage
Expenditure Percentage = $100\% - 40\% = 60\%$
So, the expenditure of ₹480 represents 60% of the person's total income.
Solving for Total Income
Let the total income be represented by '$I$'. We can set up the equation based on the expenditure:
60% of Income = Expenditure
Using LaTeX notation:
$$ 60\% \times I = 480 $$To solve for '$I$', we first convert the percentage to a decimal or fraction:
$$ \frac{60}{100} \times I = 480 $$ $$ 0.60 \times I = 480 $$Now, we isolate '$I$' by dividing both sides by 0.60:
$$ I = \frac{480}{0.60} $$To simplify the division, we can multiply the numerator and denominator by 100:
$$ I = \frac{480 \times 100}{60} $$ $$ I = \frac{48000}{60} $$Performing the division:
$$ I = \frac{4800}{6} $$ $$ I = 800 $$Therefore, the person's total income is ₹800.
Final Answer Verification
Let's check if the calculated income matches the given information:
- Income = ₹800
- Savings = 40% of ₹800 = $0.40 \times 800 = ₹320$
- Expenditure = 60% of ₹800 = $0.60 \times 800 = ₹480$
- Total = Savings + Expenditure = $320 + 480 = ₹800$. This matches the calculated income.
The expenditure matches the given amount of ₹480.
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:
