The income of A is 80% of B's income, and the expenditure of A is 75% of B's expenditure. If A's income is 90% of B's expenditure, then the savings of A is.x% more than that of B. What is the value of x?
(a)25
(b)20
(c)15
(d)30

Options

A. 25
B. 20
C. 15
D. 30

Answer

To solve the problem step-by-step, we will define the incomes and expenditures of A and B based on the information given in the question.

### Step 1: Define Incomes
Let B's income be represented as \( B = 100 \) (for simplicity).
Then A's income, which is 80% of B's income, can be calculated as:
\[ A = 0.8 \times B = 0.8 \times 100 = 80 \]

### Step 2: Define Expenditures
Let B's expenditure be represented as \( E_B = 100 \) (again, for simplicity).
Then A's expenditure, which is 75% of B's expenditure, can be calculated as:
\[ E_A = 0.75 \times E_B = 0.75 \times 100 = 75 \]

### Step 3: Relate A's Income to B's Expenditure
According to the problem, A's income is also given as 90% of B's expenditure:
\[ A = 0.9 \times E_B \]
Substituting \( E_B = 100 \):
\[ A = 0.9 \times 100 = 90 \]

### Step 4: Set Up Equations
From the previous steps, we have two expressions for A's income:
1. \( A = 80 \) (from Step 1)
2. \( A = 90 \) (from Step 3)

Since both expressions must be equal, we can set them equal to each other:
\[ 80 = 0.9 \times E_B \]
From this, we can find \( E_B \):
\[ E_B = \frac{80}{0.9} \approx 88.89 \]

### Step 5: Calculate A's and B's Expenditures
Now we can find A's expenditure using the ratio established earlier:
\[ E_A = 0.75 \times E_B = 0.75 \times 88.89 \approx 66.67 \]

### Step 6: Calculate Savings
Now we can calculate the savings for both A and B:
- Savings of A:
\[ S_A = A - E_A = 80 - 66.67 \approx 13.33 \]
- Savings of B:
\[ S_B = B - E_B = 100 - 88.89 \approx 11.11 \]

### Step 7: Calculate the Difference in Savings
Now, we need to find how much more A's savings are compared to B's savings:
\[ \text{Difference} = S_A - S_B = 13.33 - 11.11 \approx 2.22 \]

### Step 8: Calculate Percentage Increase
To find the percentage increase of A's savings over B's savings:
\[ \text{Percentage Increase} = \left( \frac{S_A - S_B}{S_B} \right) \times 100 = \left( \frac{2.22}{11.11} \right) \times 100 \approx 20\% \]

### Conclusion
Thus, the value of \( x \) is 20.