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

Options

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

Answer

To solve the problem step by step, we will follow the ratios given and find the value of C based on the information provided.

### 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: Set Up the Ratios
From the ratio of A to B (4:5), we can express B in terms of A:
\[ \frac{A}{B} = \frac{4}{5} \]
Given that A = 800, we can substitute this value into the equation:
\[ \frac{800}{B} = \frac{4}{5} \]

### Step 3: Cross-Multiply to Solve for B
Cross-multiplying gives us:
\[ 4B = 800 \times 5 \]
Calculating the right side:
\[ 4B = 4000 \]
Now, divide both sides by 4 to find B:
\[ B = \frac{4000}{4} = 1000 \]

### Step 4: Set Up the Second Ratio
Now we have B = 1000. We will use the second ratio (B to C = 2:3) to find C:
\[ \frac{B}{C} = \frac{2}{3} \]
Substituting B = 1000 into the equation:
\[ \frac{1000}{C} = \frac{2}{3} \]

### Step 5: Cross-Multiply to Solve for C
Cross-multiplying gives us:
\[ 2C = 1000 \times 3 \]
Calculating the right side:
\[ 2C = 3000 \]
Now, divide both sides by 2 to find C:
\[ C = \frac{3000}{2} = 1500 \]

### Final Answer
Thus, the value of C is 1500.

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