`30%` of a is `40%` of 720 & `15%` of b is `25%` of 1080. If `40%` of (a + b) is equal to `80%` of c, then find `20%` of ( a + c- b)?

Options

A. A)54
B. B)216
C. C)108
D. D)224

Answer

To solve the problem step by step, let's break it down:

### Step 1: Find the value of 'a'
We know that:
\[ 30\% \text{ of } a = 40\% \text{ of } 720 \]

Calculating \( 40\% \text{ of } 720 \):
\[ 40\% \text{ of } 720 = \frac{40}{100} \times 720 = 288 \]

So, we have:
\[ 30\% \text{ of } a = 288 \]

Now, to find 'a':
\[ 30\% \text{ of } a = \frac{30}{100} \times a = 288 \]
\[ a = \frac{288 \times 100}{30} = 960 \]

### Step 2: Find the value of 'b'
Next, we know that:
\[ 15\% \text{ of } b = 25\% \text{ of } 1080 \]

Calculating \( 25\% \text{ of } 1080 \):
\[ 25\% \text{ of } 1080 = \frac{25}{100} \times 1080 = 270 \]

So, we have:
\[ 15\% \text{ of } b = 270 \]

Now, to find 'b':
\[ 15\% \text{ of } b = \frac{15}{100} \times b = 270 \]
\[ b = \frac{270 \times 100}{15} = 1800 \]

### Step 3: Find the value of 'c'
Now we need to find 'c' using the equation:
\[ 40\% \text{ of } (a + b) = 80\% \text{ of } c \]

First, calculate \( a + b \):
\[ a + b = 960 + 1800 = 2760 \]

Now calculate \( 40\% \text{ of } (a + b) \):
\[ 40\% \text{ of } 2760 = \frac{40}{100} \times 2760 = 1104 \]

Now we set this equal to \( 80\% \text{ of } c \):
\[ 80\% \text{ of } c = 1104 \]
\[ \frac{80}{100} \times c = 1104 \]
\[ c = \frac{1104 \times 100}{80} = 1380 \]

### Step 4: Find \( 20\% \text{ of } (a + c - b) \)
Now we need to calculate \( a + c - b \):
\[ a + c - b = 960 + 1380 - 1800 = 540 \]

Now calculate \( 20\% \text{ of } (a + c - b) \):
\[ 20\% \text{ of } 540 = \frac{20}{100} \times 540 = 108 \]

### Final Answer
Thus, the final answer is:
\[ \boxed{108} \]