Question

The price of a chair and a table together is 4500 rupees. The price of
the table is 1000 rupees more than that of the chair. What is the price
of each?

Answer 1

Solution :

$\bf{\red{\underline{\bf{Given\::}}}}$

The price of a chair and a table together is Rs.4500. The price of the table is Rs.1000 more than that of the chair.

$\bf{\red{\underline{\bf{To\:find\::}}}}$

The price of each table and chair.

$\bf{\red{\underline{\bf{Explanation\::}}}}$

Let the price of table be Rs.r

Let the price of chair be Rs.m

A/q

$\longrightarrow\sf{r+m=4500.................(1)}$

&

$\longrightarrow\sf{m=r+1000................(2)}$

Putting the value of m in equation (1), we get;

$\longrightarrow\sf{r+r+1000=4500}\\\\\longrightarrow\sf{2r+1000=4500}\\\\\longrightarrow\sf{2r=4500-1000}\\\\\longrightarrow\sf{2r=3500}\\\\\longrightarrow\sf{r=\cancel{\dfrac{3500}{2} }}\\\\\longrightarrow\sf{\pink{r=Rs.1750}}$

Putting the value of r in equation (2), we get;

$\longrightarrow\sf{m=1750+1000}\\\\\longrightarrow\sf{\pink{m=2750}}$

Thus;

$\underbrace{\sf{The\:cost\:of\:each\:table\:Rs.1750}}}}\\\underbrace{\sf{The\:cost\:of\:each\:chair\:Rs.2750}}}}$

Answer 2

${\green{\underline{\underline{\bf{\bigstar \:Solution : }}}}}$

${\red{\tt{\:\:\:\:\:\:\:}}}$

${\red{\tt{ Let, \:the\: price\: of \:chair\: be\: x}}}$

${\red{\tt{\:\:\:\:\:\:\:}}}$

${\orange{\tt{Price\:of\: chair\: and\:table together = Rs. 4500}}}$

${\orange{\tt{\implies x + 1000 + x = Rs. 4500 }}}$

${\orange{\tt{\implies x + x = Rs. 4500 - 1000}}}$

${\orange{\tt{\implies x + x = Rs. 3500 }}}$

${\orange{\tt{\implies 2x = Rs. 3500 }}}$

$\displaystyle{\orange{\tt{\implies x = \frac{Rs. 3500}{2} }}}$

$\displaystyle{\orange{\tt{\implies x = \frac{\cancel{Rs. 3500}}{\cancel{2}} }}}$

${\orange{\tt{\implies x = Rs. 1750 }}}$

${\red{\tt{\:\:\:\:\:\:\:}}}$

${\pink{\tt{ the\: price\: of \:chair = x}}}$

${\pink{\tt{\implies the\: price\: of \:chair = Rs. 1750}}}$

${\red{\tt{\:\:\:\:\:\:\:}}}$

${\blue{\tt{ the\: price\: of \: table = x + 1000}}}$

${\blue{\tt{\implies the\: price\: of \: table = x + 1000}}}$

${\blue{\tt{ \implies the\: price\: of \: table = Rs. 1750 + 1000}}}$

${\blue{\tt{ \implies the\: price\: of \: table = Rs. 2750 }}}$