Question

If a man sells the chair at 7% loss and table at 17% profit then he earns 296 as total profit but he sells the chair at 7% and table at 12% profit then he earns 400 as total profit. find the cost of table​

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Answer:

Let the Price of Chair be 100x and Price of Table be 100y

$\underline{\bigstar\:\textsf{According to the given Question :}}$

$\underline{\bf Statement\:\textit{1 :}}$

$:\implies\sf 7\%\:loss\:on\:chair+17\%\:profit\:on\:table=Rs.\:296\\\\\\:\implies\sf - (7\% \times 100x) + (17\% \times 100y) = 296\\\\\\:\implies\sf -7x + 17y = 296 \qquad eq. - 1$

$\underline{\bf Statement\:\textit{2 :}}$

$:\implies\sf 7\%\:profit\:on\:chair+12\%\:profit\:on\:table=Rs.\:400\\\\\\:\implies\sf (7\% \times 100x) + (12\% \times 100y) = 400\\\\\\:\implies\sf 7x + 12y = 400 \qquad eq. - 2$

⠀

$\underline{\bigstar\:\textsf{Adding eq. 1 and eq. 2 :}}$

$:\implies\sf-7x + 17y = 296\\\\:\implies\sf \:\:\:7x + 12y = 400 \\ \frac{ \qquad \qquad \qquad \qquad \qquad \quad}{} \\:\implies\sf (17y + 12y) = 296 + 400\\\\\\:\implies\sf 29y = 696\\\\\\:\implies\sf y = \dfrac{696}{29}\\\\\\:\implies\sf y = 24$

$\rule{180}{1.5}$

$\underline{\bigstar\:\textsf{Cost of the Table :}}$

$\dashrightarrow\sf Table=100y\\\\\\\dashrightarrow\sf Table=100 \times 24 \\\\\\\dashrightarrow\underline{\boxed{\sf Table=Rs.\:2400}}$

⠀

$\therefore\:\underline{\textsf{Hence, Cost of the table is \textbf{Rs. 2400}}}.$