A jeweller allows a discount of 16% to his customers and still gains 20%. Find the marked price of a ring which costs the jeweller Rs. 1190.

Answer

To find the marked price of the ring, we can follow these steps:

### Step 1: Understand the given information
- Cost Price (CP) of the ring = Rs. 1190
- Gain Percentage = 20%
- Discount Percentage = 16%

### Step 2: Calculate the Selling Price (SP)
The Selling Price can be calculated using the formula:
\[ SP = CP + \text{Gain} \]
Where Gain can be calculated as:
\[ \text{Gain} = \frac{\text{Gain Percentage}}{100} \times CP \]
Substituting the values:
\[ \text{Gain} = \frac{20}{100} \times 1190 = 238 \]
Now, substituting the gain back into the SP formula:
\[ SP = 1190 + 238 = 1428 \]

### Step 3: Relate Selling Price to Marked Price
The Selling Price is also related to the Marked Price (MP) and the discount:
\[ SP = MP - \text{Discount} \]
Where Discount can be calculated as:
\[ \text{Discount} = \frac{\text{Discount Percentage}}{100} \times MP \]
Substituting this into the SP equation gives:
\[ SP = MP - \left(\frac{16}{100} \times MP\right) \]
This simplifies to:
\[ SP = MP \left(1 - \frac{16}{100}\right) = MP \left(\frac{84}{100}\right) \]

### Step 4: Substitute SP into the equation
Now we know that SP = 1428, so we can set up the equation:
\[ 1428 = MP \left(\frac{84}{100}\right) \]

### Step 5: Solve for Marked Price (MP)
To find MP, rearrange the equation:
\[ MP = \frac{1428 \times 100}{84} \]
Calculating this gives:
\[ MP = \frac{142800}{84} = 1700 \]

### Conclusion
The marked price of the ring is Rs. 1700.

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