Two numbers A and B are such that the sum of 5 % of A and 4% of B is `2/3` rd of the sum of 6% of A and 8% of B. The ratio A:B in

Options

A. `4:3`
B. `3:4`
C. `1:1`
D. `2:3`

Answer

To solve the problem, we need to set up the equation based on the information provided in the question. Let's go through the solution step by step.

### Step 1: Write the equation based on the given information
We know that:
- The sum of 5% of A and 4% of B is equal to \( \frac{2}{3} \) of the sum of 6% of A and 8% of B.

This can be expressed mathematically as:
\[ 0.05A + 0.04B = \frac{2}{3}(0.06A + 0.08B) \]

### Step 2: Clear the percentages
To eliminate the decimals, we can multiply the entire equation by 100:
\[ 5A + 4B = \frac{2}{3}(6A + 8B) \]

### Step 3: Simplify the right-hand side
Now, we simplify the right-hand side:
\[ 5A + 4B = \frac{2}{3}(6A + 8B) \]
Multiplying both sides by 3 to get rid of the fraction:
\[ 3(5A + 4B) = 2(6A + 8B) \]
This gives us:
\[ 15A + 12B = 12A + 16B \]

### Step 4: Rearranging the equation
Now, we rearrange the equation to isolate terms involving A and B:
\[ 15A - 12A = 16B - 12B \]
This simplifies to:
\[ 3A = 4B \]

### Step 5: Finding the ratio A:B
Now, we can express the ratio of A to B:
\[ \frac{A}{B} = \frac{4}{3} \]
Thus, the ratio \( A:B \) is:
\[ A:B = 4:3 \]

### Final Answer
The ratio of A to B is \( 4:3 \).

---