Income and Expenditure: Percentage Formulas and Questions

Income and Expenditure questions use percentages to compare earnings, spending and savings. The main relationships are savings = income − expenditure, expenditure percentage = expenditure divided by income × 100, and savings percentage = savings divided by income × 100. These questions also involve changes in income, changes in expenditure, ratios and the effect on monthly savings.

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What is Income and Expenditure?

Income is the money received by a person, while expenditure is the money spent. The amount left after expenditure is called savings: Savings = Income − Expenditure.

If income is I and expenditure is E, then savings S = I − E. Expenditure as a percentage of income is (E/I) × 100, and savings as a percentage of income is (S/I) × 100. Since income is divided into expenditure and savings, expenditure percentage + savings percentage = 100%. For example, if income is ₹20,000 and expenditure is ₹15,000, savings are ₹5,000, expenditure is 75% of income and savings are 25% of income.

Income and Expenditure Formula & Tricks

Important Formulas

Savings
S = I − E

Savings are obtained by subtracting expenditure from income.

Expenditure percentage
Expenditure percentage = (E/I) × 100

This gives expenditure as a percentage of total income.

Savings percentage
Savings percentage = (S/I) × 100

This gives savings as a percentage of total income.

Income from savings percentage
If savings are p% of income, then E = (100 − p)% of I

When savings form p% of income, expenditure forms the remaining (100 − p)%.

Change in savings
New savings = I(1 + x/100) − E(1 + y/100)

If income increases by x% and expenditure increases by y%, substitute the original income I and expenditure E in this formula.

Income, expenditure and savings ratio
If E:S = a:b, then I:E:S = (a + b):a:b

Income equals expenditure plus savings, so the income part is the sum of the two ratio parts.

Quick Tricks

Assume income as 100

When only percentages are given, take total income as 100 units. The percentage values then directly represent expenditure and savings.

Example: If expenditure is 72% of income, assume income = 100 units. Expenditure = 72 units and savings = 28 units.
Use the remaining percentage

Expenditure percentage and savings percentage always add to 100% of income.

Example: If a person saves 18% of income, expenditure is 100 − 18 = 82% of income.
Compare changes in actual amounts

A percentage increase applies to the original quantity, not to the new quantity. Calculate the changed income and changed expenditure separately before finding new savings.

Example: For income ₹30,000 increasing by 10%, new income is ₹33,000. It is not ₹30,000 + 10.

Income and Expenditure Concepts

Income, Expenditure and Savings Relationship

Savings equal income minus expenditure: S = I − E.

The three quantities are related by I = E + S. Therefore, if any two quantities are known, the third can be calculated. If expenditure exceeds income, the result is a deficit rather than positive savings.

Example: For income ₹45,000 and expenditure ₹32,000, savings = ₹45,000 − ₹32,000 = ₹13,000.

Percentage of Income Spent or Saved

To find a percentage of income, divide the required amount by income and multiply by 100.

Expenditure percentage is (E/I) × 100, while savings percentage is (S/I) × 100. These two percentages total 100% because expenditure and savings together equal income.

Example: If income is ₹25,000 and savings are ₹7,500, savings percentage = (7,500/25,000) × 100 = 30%. Expenditure percentage is 70%.

Finding Income or Expenditure from a Percentage

If an amount is p% of income, divide that amount by p/100 to find the income.

If savings S are p% of income, then I = S × 100/p. If expenditure is q% of income, then I = E × 100/q. After finding income, the other component can be obtained using I = E + S.

Example: If savings are ₹6,000 and equal 20% of income, income = 6,000 × 100/20 = ₹30,000. Expenditure = ₹30,000 − ₹6,000 = ₹24,000.

Effect of Changes in Income and Expenditure

New savings are found by subtracting new expenditure from new income.

If income changes by x% and expenditure changes by y%, use new income = I(1 ± x/100) and new expenditure = E(1 ± y/100), choosing plus for an increase and minus for a decrease. Then subtract the new expenditure from the new income.

Example: Income ₹40,000 rises by 10% and expenditure ₹30,000 rises by 5%. New income = ₹44,000 and new expenditure = ₹31,500, so new savings = ₹12,500.

Ratio of Income, Expenditure and Savings

If expenditure and savings are in the ratio a:b, income is represented by a+b parts.

Since income = expenditure + savings, E:S = a:b gives I:E:S = (a+b):a:b. If the total income is known, divide it by a+b to find the value of one part.

Example: If expenditure:savings = 5:3 and income is ₹32,000, total parts = 8. One part = ₹4,000, so expenditure = ₹20,000 and savings = ₹12,000.

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Practice Income and Expenditure Questions

Practise published questions related to this topic.

1210 chips and 294 toffees are to be distributed among maximum number of boys. Each boy gets the same number of chips. Each boy get the same number of toffees. How many chips does each boy get?→ 2The selling price of an iPhone is ₹3,300, after allowing two successive discounts of 36% and 25%. Find the marked price of the iPhone.→ 3The HCF of 1/2, 3/4, 27/16 and 81/64 is:→ 4An article is sold for a loss Rs. 69. Loss percentage is 30 percent. What is the selling price of the article?→ 5How many numbers up to 200 are divisible by 4 and 3 both?→ 6A man sells a mobile phone for ₹600 and loses something. If he had sold it for ₹1190, his gain would have been 4-times the former loss. The cost price (in ₹) of the mobile phone is ________.→ 7What is the Least Common Multiple of 4/7, 8/14 and 12/21?→ 8By selling an article for ₹117, a man loses 35%. At what price (in ₹) should he sell the same article to gain 50%?→ 9The profit earned on selling an article for Rs. 1600 is 19 times of the loss incurred on selling the same article for Rs. 1200. What will be the selling price of the article to earn a profit of 30 percent?→ 10A shopkeeper sold a pen for ₹150 and made a profit of ₹30. Find the cost price of the pen.→

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Quick Revision Notes

Income and Expenditure Revision Points

Use these relationships to solve percentage applications involving income, expenditure and savings.

  • Savings = Income − Expenditure.
  • Income = Expenditure + Savings.
  • Expenditure percentage = (Expenditure/Income) × 100.
  • Savings percentage = (Savings/Income) × 100.
  • Expenditure percentage + savings percentage = 100%.
  • If savings are p% of income, expenditure is (100 − p)% of income.
  • For changed values, calculate new income and new expenditure separately, then subtract.
  • If E:S = a:b, then I:E:S = (a+b):a:b.

Income and Expenditure FAQs

What is the formula for savings percentage?

Savings percentage = (Savings/Income) × 100. For example, savings of ₹4,000 from an income of ₹20,000 equal (4,000/20,000) × 100 = 20%.

If expenditure is 65% of income, what percentage is saved?

Savings percentage = 100% − 65% = 35% of income.

A person's income is ₹50,000 and expenditure is 80% of income. What are the savings?

Expenditure = 80% of ₹50,000 = ₹40,000. Savings = ₹50,000 − ₹40,000 = ₹10,000.

How is new savings calculated when income and expenditure both change?

Use New savings = New income − New expenditure. For an x% income increase and y% expenditure increase, this becomes I(1 + x/100) − E(1 + y/100).

If income increases by 20% while expenditure remains unchanged, does savings increase by 20%?

Not necessarily. Savings increase by 20% of the original income, but the percentage increase in savings is calculated relative to the original savings.

If expenditure:savings is 7:3, what is the ratio of income to expenditure?

Income has 7 + 3 = 10 parts. Therefore, income:expenditure = 10:7.

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