Let [tex]\( CP \)[/tex] be the cost price of the table.
1. When the table is sold at a loss of [tex]\( 10\% \)[/tex]:
The selling price (SP_loss) at [tex]\( 10\% \)[/tex] loss is calculated as:
[tex]\[
SP_{\text{loss}} = CP - \left( \frac{10}{100} \times CP \right) = CP - 0.1CP = 0.9CP
\][/tex]
2. When the table is sold at a gain of [tex]\( 10\% \)[/tex]:
The selling price (SP_gain) at [tex]\( 10\% \)[/tex] gain is calculated as:
[tex]\[
SP_{\text{gain}} = CP + \left( \frac{10}{100} \times CP \right) = CP + 0.1CP = 1.1CP
\][/tex]
3. According to the problem, the difference in selling prices when sold at a gain of [tex]\( 10\% \)[/tex] instead of a loss of [tex]\( 10\% \)[/tex] is ₹ 660. Thus:
[tex]\[
SP_{\text{gain}} - SP_{\text{loss}} = 660
\][/tex]
Substituting the values of [tex]\( SP_{\text{gain}} \)[/tex] and [tex]\( SP_{\text{loss}} \)[/tex] into the equation:
[tex]\[
1.1CP - 0.9CP = 660
\][/tex]
4. Simplifying the equation:
[tex]\[
0.2CP = 660
\][/tex]
5. Solving for [tex]\( CP \)[/tex]:
[tex]\[
CP = \frac{660}{0.2} = 3300
\][/tex]
Therefore, the cost price of the table is ₹ 3300.
