A is `25%` less than B , B is `30%` less than C, and C is `50%` more than D . If the difference between A and C is 285 ,then `33(1)/(3)%` of B is equal to :

Options

A. 140
B. 150
C. 120
D. 105

Answer

To solve the problem step by step, we will define the relationships between A, B, C, and D based on the given percentages and then find the required value.

### Step 1: Define the variables
Let D = x.

### Step 2: Calculate C
C is 50% more than D. Therefore,
\[ C = D + 0.5D = 1.5D = 1.5x. \]

### Step 3: Calculate B
B is 30% less than C. Therefore,
\[ B = C - 0.3C = 0.7C = 0.7 \times 1.5x = 1.05x. \]

### Step 4: Calculate A
A is 25% less than B. Therefore,
\[ A = B - 0.25B = 0.75B = 0.75 \times 1.05x = 0.7875x. \]

### Step 5: Set up the equation for the difference between A and C
We know the difference between A and C is 285. Therefore,
\[ C - A = 285. \]
Substituting the values of A and C:
\[ 1.5x - 0.7875x = 285. \]

### Step 6: Simplify the equation
Combine like terms:
\[ (1.5 - 0.7875)x = 285, \]
\[ 0.7125x = 285. \]

### Step 7: Solve for x
To find x, divide both sides by 0.7125:
\[ x = \frac{285}{0.7125} = 400. \]

### Step 8: Calculate B
Now that we have the value of x, we can find B:
\[ B = 1.05x = 1.05 \times 400 = 420. \]

### Step 9: Calculate \( 33\frac{1}{3}\% \) of B
To find \( 33\frac{1}{3}\% \) of B, we can convert \( 33\frac{1}{3}\% \) to a fraction:
\[ 33\frac{1}{3}\% = \frac{100}{3}\%. \]
Now calculate:
\[ \frac{100}{3}\% \text{ of } B = \frac{100}{3} \times \frac{420}{100} = \frac{420}{3} = 140. \]

### Final Answer
Thus, \( 33\frac{1}{3}\% \) of B is equal to **140**.

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