John walks to a library which is x km away from his home. On his way back home, he stops at a shop that is `(1)/(4)` of the distance he had walked earlier. Find the distance of the shop from John's home.

Answer

To solve the problem step by step, we will follow the information given in the question and use basic algebraic operations.

### Step 1: Understand the distances involved
John walks from his home to the library, which is \( x \) km away. Therefore, the distance from John's home to the library is:
\[ \text{Distance from home to library} = x \text{ km} \]

### Step 2: Determine the distance John walks back
On his way back, he stops at a shop that is \( \frac{1}{4} \) of the distance he had walked earlier. Since he initially walked \( x \) km to the library, the distance from the library to the shop is:
\[ \text{Distance from library to shop} = \frac{1}{4} x \text{ km} \]

### Step 3: Calculate the distance from John's home to the shop
To find the distance from John's home to the shop, we need to subtract the distance from the library to the shop from the total distance from home to the library. Thus, the distance from John's home to the shop is:
\[ \text{Distance from home to shop} = \text{Distance from home to library} - \text{Distance from library to shop} \]
This can be expressed as:
\[ \text{Distance from home to shop} = x - \frac{1}{4} x \]

### Step 4: Simplify the expression
To simplify \( x - \frac{1}{4} x \), we need a common denominator. The common denominator for 1 and 4 is 4. Therefore, we rewrite \( x \) as \( \frac{4}{4} x \):
\[ \text{Distance from home to shop} = \frac{4}{4} x - \frac{1}{4} x \]
Now, we can subtract the fractions:
\[ \text{Distance from home to shop} = \frac{4x - 1x}{4} = \frac{3x}{4} \]

### Final Answer
Thus, the distance of the shop from John's home is:
\[ \frac{3x}{4} \text{ km} \]

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