Jamila sold a table and a chair for Rs., 1050 | vedclass

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(C) Let the cost price of the table be $Rs.\, x$ and the cost price of the chair be $Rs.\, y$.The selling price of the table at $10\%$ profit is $x +

Vedclass · Accepted Answer

$500, 400$

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(C) Let the cost price of the table be $Rs.\, x$ and the cost price of the chair be $Rs.\, y$.The selling price of the table at $10\%$ profit is $x + 0.10x = 1.10x$.The selling price of the chair at $25\%$ profit is $y + 0.25y = 1.25y$.Given,$1.10x + 1.25y = 1050$. Multiplying by $100$,we get $110x + 125y = 105000$ ....$(1)$If the table is sold at $25\%$ profit and the chair at $10\%$ profit,the selling price is $1.25x + 1.10y = 1065$.Multiplying by $100$,we get $125x + 110y = 106500$ ....$(2)$Adding $(1)$ and $(2)$:$235x + 235y = 211500 \implies x + y = 900$ ....$(3)$Subtracting $(2)$ from $(1)$:$-15x + 15y = -1500 \implies x - y = 100$ ....$(4)$Adding $(3)$ and $(4)$:$2x = 1000 \implies x = 500$.Substituting $x = 500$ in $(3)$:$500 + y = 900 \implies y = 400$.Thus,the cost price of the table is $Rs.\, 500$ and the cost price of the chair is $Rs.\, 400$.

Jamila sold a table and a chair for $Rs.\, 1050,$ thereby making a profit of $10\%$ on the table and $25\%$ on the chair. If she had taken a profit of $25\%$ on the table and $10\%$ on the chair,she would have got $Rs.\, 1065.$ Find the cost price of each (in $Rs.$).

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