if 20% of a and 40% of b is 230 and 40% of a and 20% of b is 190 ,then b is what percentage more or less than a ?

Options

A. 0.8
B. 0.6
C. 0.5
D. 0.4

Explanation

To solve the problem step by step, we need to set up the equations based on the information given and then solve for the values of A and B.

### Step 1: Set up the equations
We are given two equations based on the problem statement:
1. \( 20\% \text{ of } A + 40\% \text{ of } B = 230 \)
2. \( 40\% \text{ of } A + 20\% \text{ of } B = 190 \)

We can express these equations in terms of A and B:
1. \( 0.2A + 0.4B = 230 \) (Equation 1)
2. \( 0.4A + 0.2B = 190 \) (Equation 2)

### Step 2: Multiply the equations to eliminate decimals
To make calculations easier, we can multiply both equations by 100:
1. \( 20A + 40B = 23000 \) (Equation 1)
2. \( 40A + 20B = 19000 \) (Equation 2)

### Step 3: Rearranging the equations
Now we can rearrange these equations:
1. \( 20A + 40B = 23000 \) (Equation 1)
2. \( 40A + 20B = 19000 \) (Equation 2)

### Step 4: Solve for one variable
We can multiply Equation 1 by 2 to align the coefficients of A:
- \( 40A + 80B = 46000 \) (Equation 3)

Now we can subtract Equation 2 from Equation 3:
\[ (40A + 80B) - (40A + 20B) = 46000 - 19000 \]
This simplifies to:
\[ 60B = 27000 \]
Now, divide by 60 to find B:
\[ B = \frac{27000}{60} = 450 \]

### Step 5: Substitute B back to find A
Now that we have B, we can substitute it back into one of the original equations to find A. Let's use Equation 1:
\[ 20A + 40(450) = 23000 \]
This simplifies to:
\[ 20A + 18000 = 23000 \]
Subtract 18000 from both sides:
\[ 20A = 5000 \]
Now, divide by 20:
\[ A = \frac{5000}{20} = 250 \]

### Step 6: Calculate the percentage difference
Now we have A = 250 and B = 450. We need to find out how much percentage B is more than A:
\[ \text{Percentage difference} = \frac{B - A}{A} \times 100 \]
Substituting the values:
\[ \text{Percentage difference} = \frac{450 - 250}{250} \times 100 = \frac{200}{250} \times 100 = 80\% \]

### Conclusion
B is 80% more than A.