4% of the selling price of an articie 5% of itsc ost price. Again 20% ofthes elling price is Rs. 120 more than 22% ofits cost price. he ratio of cost price & selling price is

Options

A. `2:3`
B. `3:2`
C. `4:5`
D. `5:4`

Answer

To solve the problem step by step, we will break down the information given in the question and derive the required ratio of the cost price (CP) and selling price (SP).

### Step 1: Set up the equations based on the information given.

We know from the question that:
1. \( 4\% \) of the selling price (SP) is equal to \( 5\% \) of the cost price (CP).
2. \( 20\% \) of the selling price is Rs. 120 more than \( 22\% \) of the cost price.

From the first statement, we can write the equation:
\[ 0.04 \times SP = 0.05 \times CP \]

### Step 2: Rearranging the first equation.

We can rearrange the equation to express the relationship between SP and CP:
\[ 4SP = 5CP \]
Dividing both sides by 4 and 5 gives us:
\[ \frac{SP}{CP} = \frac{5}{4} \]

### Step 3: Find the ratio of CP to SP.

To find the ratio of cost price to selling price (CP:SP), we take the reciprocal of the above ratio:
\[ \frac{CP}{SP} = \frac{4}{5} \]
This means that the ratio of CP to SP is 4:5.

### Step 4: Analyze the second statement.

Now, let's analyze the second statement:
\[ 0.20 \times SP = 0.22 \times CP + 120 \]

### Step 5: Substitute SP in terms of CP.

From the first equation, we can express SP in terms of CP:
\[ SP = \frac{5}{4} CP \]
Substituting this into the second equation gives:
\[ 0.20 \times \left(\frac{5}{4} CP\right) = 0.22 \times CP + 120 \]

### Step 6: Simplify the equation.

Now, simplifying the left side:
\[ 0.20 \times \frac{5}{4} CP = \frac{1}{4} CP \]
So we have:
\[ \frac{1}{4} CP = 0.22 CP + 120 \]

### Step 7: Rearrange to isolate CP.

Rearranging gives:
\[ \frac{1}{4} CP - 0.22 CP = 120 \]
Finding a common denominator (4):
\[ \frac{1}{4} CP - \frac{0.88}{4} CP = 120 \]
This simplifies to:
\[ \frac{1 - 0.88}{4} CP = 120 \]
\[ \frac{0.12}{4} CP = 120 \]
Multiplying both sides by 4:
\[ 0.12 CP = 480 \]
Dividing by 0.12:
\[ CP = \frac{480}{0.12} = 4000 \]

### Step 8: Calculate SP.

Now, substituting back to find SP:
\[ SP = \frac{5}{4} \times 4000 = 5000 \]

### Conclusion: Final Ratio

Now we have:
- Cost Price (CP) = 4000
- Selling Price (SP) = 5000

Thus, the ratio of Cost Price to Selling Price (CP:SP) is:
\[ CP:SP = 4000:5000 = 4:5 \]

### Final Answer
The ratio of cost price to selling price is **4:5**.