The ratio of A to B is 4 : 5 and that of B to C is `2 : 3`. If A equals 800, C equals

Options

A. 1000
B. 1200
C. 1500
D. 2000

Answer

To solve the problem step by step, we will use the given ratios and the value of A to find the value of C.

### Step 1: Understand the Ratios
We are given two ratios:
1. The ratio of A to B is 4:5.
2. The ratio of B to C is 2:3.

### Step 2: Express B in terms of A
From the ratio of A to B (4:5), we can express B in terms of A:
\[ \frac{A}{B} = \frac{4}{5} \implies B = \frac{5}{4} A \]

### Step 3: Express C in terms of B
From the ratio of B to C (2:3), we can express B in terms of C:
\[ \frac{B}{C} = \frac{2}{3} \implies B = \frac{2}{3} C \]

### Step 4: Substitute the value of B
Now, we have two expressions for B:
1. \( B = \frac{5}{4} A \)
2. \( B = \frac{2}{3} C \)

We can set these equal to each other:
\[ \frac{5}{4} A = \frac{2}{3} C \]

### Step 5: Substitute the value of A
We know that \( A = 800 \). Now, we can substitute this value into the equation:
\[ \frac{5}{4} \times 800 = \frac{2}{3} C \]

### Step 6: Calculate B
Calculating the left side:
\[ \frac{5 \times 800}{4} = \frac{4000}{4} = 1000 \]
So, we have:
\[ 1000 = \frac{2}{3} C \]

### Step 7: Solve for C
To find C, we will rearrange the equation:
\[ C = \frac{1000 \times 3}{2} \]
Calculating the right side:
\[ C = \frac{3000}{2} = 1500 \]

### Final Answer
Thus, the value of C is:
\[ \boxed{1500} \]