Saves 40% of his income and B spends 30% of his income. If the expenditure

Quantitative Ability (20)

48872

General So...

(15)

Computer A... (15)

Sales Apti

... (10)

of A'is same as the savings 24887

(A) 4:5

(B) 8:7

(C) 7:6

(D) 9:8

To solve this problem, let's break it down step by step.

1. **Let the incomes of A and B be represented as $ I_A $ and $ I_B $** respectively.

2. **Given:**  
   - A saves 40% of his income, so his expenditure is 60% of his income.  
   - B spends 30% of his income, so his savings are 70% of his income.

3. **Let the expenditure of A be equal to the savings of B.**  
   - Expenditure of A = $ 0.60 \times I_A $  
   - Savings of B = $ 0.70 \times I_B $

   According to the problem:
   \[
   0.60 \times I_A = 0.70 \times I_B
   \]

4. **To find the ratio $ \frac{I_A}{I_B} $:**
   \[
   \frac{0.60 \times I_A}{0.70 \times I_B} = 1
   \]
   Simplifying the ratio:
   \[
   \frac{I_A}{I_B} = \frac{0.70}{0.60} = \frac{7}{6}
   \]

So, the ratio of the incomes of A to B is $ \boxed{7:6} $, which corresponds to option **(C) 7:6**.

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Do you want more details or have any questions? Here are some related problems:

1. If A's income is $7000, what is B's income?
2. If A's expenditure is $600, what is his total income?
3. What is B's savings if his income is $6000?
4. If B's income increases by 10%, how does the ratio change?
5. How does the ratio change if A saves 50% instead?

**Tip:** Always check if you're comparing percentages of the same base (income) when working with ratios.

Learn how to solve a problem involving income, savings, and expenditure. Understand the concept of percentages and ratio to find the ratio of incomes between A and B. Suitable for high school students.

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