The ratio of A to B is `4:5` and that ofB to C is `2 :3`. IfA equals 1600, then what is the value of C?

Options

A. 1000
B. 1200
C. 3000
D. 2000

Answer

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

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

### Step 2: Express A, B, and C in terms of a common variable
Let’s denote the common variable as \(k\).
From the ratio of A to B:
- \(A = 4k\)
- \(B = 5k\)

From the ratio of B to C:
- \(B = 2m\)
- \(C = 3m\)

### Step 3: Make B the same in both ratios
To find a common value for B, we can express B in terms of a single variable. We know:
- From \(A\) to \(B\), \(B = 5k\)
- From \(B\) to \(C\), \(B = 2m\)

To make these equal, we can set \(5k = 2m\).

### Step 4: Solve for m in terms of k
From the equation \(5k = 2m\), we can solve for \(m\):
\[ m = \frac{5k}{2} \]

### Step 5: Substitute m back to find C in terms of k
Now, substitute \(m\) into the expression for \(C\):
\[ C = 3m = 3 \left(\frac{5k}{2}\right) = \frac{15k}{2} \]

### Step 6: Use the value of A to find k
We are given that \(A = 1600\):
\[ A = 4k = 1600 \]
Now, solve for \(k\):
\[ k = \frac{1600}{4} = 400 \]

### Step 7: Find the value of C
Now that we have \(k\), we can find \(C\):
\[ C = \frac{15k}{2} = \frac{15 \times 400}{2} = \frac{6000}{2} = 3000 \]

### Final Answer
Thus, the value of C is \(3000\).

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