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**Hint:**We need to find the cost price of the item. We have been given the relationship between the gains when the article is sold at two different prices. Percentage gain is given by the formula $\text{gain=}\dfrac{\text{selling price-cost price}}{\text{cost price}}\times 100$ . We will use this formula and express the relationship between the two gains in the form of an equation. By solving that equation, we will get our answer.

**Complete step-by-step solution:**Let the cost of the article be x.

Therefore, we need to find the value of ‘x’ in this question.

We have been given that the gain is 5% more when the items are sold for Rs.350 than when it is sold for Rs.340.

Percentage gain is given by the formula:

$\text{gain=}\dfrac{\text{selling price-cost price}}{\text{cost price}}\times 100$

Hence, cost price =x

When the selling price is Rs.350, the percentage gain is given as :

$\%gain=\left( \dfrac{350-x}{x}\times 100 \right)\%$ .....(1)

When the selling price is Rs.340, the percentage gain is given as:

$\%gain=\left( \dfrac{340-x}{x}\times 100 \right)\%$

Now, we have been given that give is 5% more in the case when the selling price is Rs.350 than when it was for Rs.340

Thus, percentage gain where the selling price in Rs. 350 is given as:

$\%gain=\left( 5+\dfrac{340-x}{x}\times 100 \right)\%$ .....(2)

From equation (1) and (2) we have:

$\left( \dfrac{350-x}{x} \right)\times 100=5+\left( \dfrac{340-x}{x} \right)\times 100$

$\begin{align}

& \Rightarrow \left( \dfrac{350-x}{x} \right)\times 100-\left( \dfrac{340-x}{x} \right)\times 100=5 \\

& \Rightarrow \left( \dfrac{35000-100x}{x} \right)-\left( \dfrac{34000-100x}{x} \right)=5 \\

& \Rightarrow \dfrac{35000-100x-34000+100x}{x}=5 \\

& \Rightarrow \dfrac{1000}{x}=5 \\

& \Rightarrow 1000=5x \\

& \Rightarrow x=200 \\

\end{align}$

Therefore, the cost price of the article is Rs.200.

**Hence, option (C) is the correct option.**

**Note:**The relationship given in the question is based on the percentage of the gains obtained at two different cost prices. So, you have to be careful to form the equations in the form of percentage gain only not in the form of gain (which is equal to the difference between the selling price and cost price) otherwise the equations formed will not be correct.

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