Question
ERCISE 8.3 are in 10. The ratio of the income to the expenditure of a family is \( 10: 8 \). If the expenditure is \( ₹ 72,000 \), what is the income?
Ask by Powers Maxwell. in India
Feb 17,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The income is ₹90,000.
Solution
Given that the ratio of income to expenditure of a family is \( 10:8 \) and the expenditure is \( ₹72,000 \), we can find the income as follows:
Let the income be \( 10x \) and the expenditure be \( 8x \).
Since the expenditure is \( ₹72,000 \), we have:
\[ 8x = 72,000 \]
To find the income, we need to find the value of \( x \) first.
Let's solve for \( x \) using the equation \( 8x = 72,000 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(8x=72000\)
- step1: Divide both sides:
\(\frac{8x}{8}=\frac{72000}{8}\)
- step2: Divide the numbers:
\(x=9000\)
The value of \( x \) is \( 9000 \).
Now, we can find the income by substituting the value of \( x \) into the expression for income:
\[ \text{Income} = 10x = 10 \times 9000 = ₹90,000 \]
Therefore, the income of the family is \( ₹90,000 \).
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Simplify this solution Extra Insights
To find the income, we can set up a simple ratio calculation based on the given information. The ratio of income to expenditure is 10:8, which simplifies to 5:4. If the expenditure is ₹72,000, we can calculate the income by setting up a proportion. Let the income be \( I \). According to the ratio, we have: \[ \frac{I}{72,000} = \frac{5}{4} \] Cross-multiplying gives us: \[ I = 72,000 \times \frac{5}{4} = 72,000 \times 1.25 = ₹90,000 \] Thus, the income is ₹90,000.
