If a/b = 1/4 , b/c =1/8 and a=2 then the value of c is-
A. 8
B. 16
C. 32
D. 64

Options

A. C
B. A
C. D
D. B

Answer

To solve the problem step by step, we need to use the given ratios and the value of \( a \).

### Step 1: Understand the given ratios
We have:
1. \( \frac{a}{b} = \frac{1}{4} \)
2. \( \frac{b}{c} = \frac{1}{8} \)

### Step 2: Substitute the value of \( a \)
We are given that \( a = 2 \). We can substitute this value into the first ratio:
\[ \frac{2}{b} = \frac{1}{4} \]

### Step 3: Solve for \( b \)
To find \( b \), we can cross-multiply:
\[ 2 \cdot 4 = 1 \cdot b \implies 8 = b \]
So, \( b = 8 \).

### Step 4: Use the value of \( b \) to find \( c \)
Now we can use the value of \( b \) in the second ratio:
\[ \frac{b}{c} = \frac{1}{8} \]
Substituting \( b = 8 \):
\[ \frac{8}{c} = \frac{1}{8} \]

### Step 5: Solve for \( c \)
Again, we cross-multiply:
\[ 8 \cdot 8 = 1 \cdot c \implies 64 = c \]
So, \( c = 64 \).

### Final Answer
The value of \( c \) is \( 64 \).

### Options
The correct option is D. 64.

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