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
In an examination, 25% of the candidates failed in Mathematics and 12% failed in English. If 10% of the candidates failed in both the subjects and 292 candidates passed in both the subjects, which one of the following is the number of total candidates appeared in the examination?
What is the value of 9% of 5500 + 2.4% of 1100 - 40% of 1600?
Population of a village is 7960 in which 4660 are female. If in that village 60% are literate in which 70% female are literate, then what is the number of literate male ?
The numbers of students of three classes of a school are in the ratio 4 : 5 : 6. If numbers of students in these classes increase by 25%, 20% and 25% respectively, then ratio of numbers of students will become:
In an examination, Ram obtained 20 % more than Ashok but 10% less than Rajesh. If the marks obtained by Ashok is 1080. Then the Percentage marks obtained by Rajesh if the full marks is 2000 ;
