The ratio of the incomes of A and B is 1:2 and that of their expenditure is 2:3. If 80% of B's expenditure is equal the income of A, then what is the ratio of the savings of B to the savings of A ?

Options

A. `2:9`
B. `9:2`
C. `7:3`
D. `3:7`

Answer

To solve the problem step by step, we will follow the given information and calculate the required ratio of the savings of B to the savings of A.

### Step 1: Define the incomes of A and B
Given the ratio of incomes of A and B is 1:2, we can represent their incomes as:
- Income of A = \( x \)
- Income of B = \( 2x \)

### Step 2: Define the expenditures of A and B
Given the ratio of expenditures of A and B is 2:3, we can represent their expenditures as:
- Expenditure of A = \( 2y \)
- Expenditure of B = \( 3y \)

### Step 3: Set up the equation based on the given condition
It is given that 80% of B's expenditure is equal to A's income. Therefore, we can write:
\[ 0.8 \times (3y) = x \]
This simplifies to:
\[ 2.4y = x \]

### Step 4: Calculate the savings of A and B
Savings can be calculated as:
- Savings of A = Income of A - Expenditure of A
\[ \text{Savings of A} = x - 2y \]
Substituting \( x = 2.4y \):
\[ \text{Savings of A} = 2.4y - 2y = 0.4y \]

- Savings of B = Income of B - Expenditure of B
\[ \text{Savings of B} = 2x - 3y \]
Substituting \( x = 2.4y \):
\[ \text{Savings of B} = 2(2.4y) - 3y = 4.8y - 3y = 1.8y \]

### Step 5: Calculate the ratio of savings of B to savings of A
Now we can find the ratio of the savings of B to the savings of A:
\[ \text{Ratio} = \frac{\text{Savings of B}}{\text{Savings of A}} = \frac{1.8y}{0.4y} \]
The \( y \) cancels out:
\[ \text{Ratio} = \frac{1.8}{0.4} = \frac{18}{4} = \frac{9}{2} \]

### Final Answer
The ratio of the savings of B to the savings of A is \( \frac{9}{2} \).

---