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
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.
