A trader sells his table at a profit of 15 % | vedclass

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(B) Let the cost price of the table be $Rs. t$ and that of the chair be $Rs. c.$According to the first condition:$0.15t - 0.075c = 50$Multiplying by $

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$\frac{4000}{9}$

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(B) Let the cost price of the table be $Rs. t$ and that of the chair be $Rs. c.$According to the first condition:$0.15t - 0.075c = 50$Multiplying by $100$ to simplify:$15t - 7.5c = 5000$$15t - \frac{15}{2}c = 5000$$30t - 15c = 10000$ $...(1)$According to the second condition:$-7.5t + 15c = 0$$15c = 7.5t$$c = \frac{7.5}{15}t = 0.5t = \frac{t}{2}$ $...(2)$Substituting $(2)$ into $(1)$:$30t - 15(\frac{t}{2}) = 10000$$60t - 15t = 20000$$45t = 20000$$t = \frac{20000}{45} = \frac{4000}{9}$Thus,the cost price of the table is $Rs. \frac{4000}{9}$.

$A$ trader sells his table at a profit of $15 \%$ and the chair at a loss of $7 \frac{1}{2} \%,$ but on the whole he gains $Rs. 50.$ If he sells the table at a loss of $7 \frac{1}{2} \%,$ and the chair at a profit of $15 \%,$ then he neither gains nor loses. Find the cost price of the table.

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