Question

A man sold a chair and a table together for ​₹1,520, thereby making a profit of 25% on chair and 10% on table. By selling them together for ​₹1,535, he would would have made a profit of 10% on the chair and 25% on the table. Find the cost of each.

Answer 1

Let the cost price of the chair and table be ₹x and ₹y respectively.
Then as per the question
Selling price of chair + Selling price of table = 1520
$$\begin{gathered} \frac{100+25}{100}\times x+\frac{100+10}{100}\times y=1520 \\ \Rightarrow \frac{125}{100}x+\frac{110}{100}y=1520 \\ \Rightarrow 25x+22y-30400=0.....\left(i\right) \end{gathered}$$
When the profit on chair and table are 10% and 25% respectively, then

$$\begin{gathered} \frac{100+10}{100}\times x+\frac{100+25}{100}\times y=1535 \\ \Rightarrow \frac{110}{100}x+\frac{125}{100}y=1535 \\ \Rightarrow 22x+25y-30700=0.....\left(ii\right) \end{gathered}$$
Solving (i) and (ii) by cross multiplication, we get
$$\begin{gathered} \frac{x}{\left(22\right)\left(-30700\right)-\left(25\right)\left(-30400\right)}=\frac{y}{\left(-30400\right)\left(22\right)-\left(-30700\right)\left(25\right)}=\frac{1}{\left(25\right)\left(25\right)-\left(22\right)\left(22\right)} \\ \Rightarrow \frac{x}{7600-6754}=\frac{y}{7675-6688}=\frac{100}{3\times 47} \\ \Rightarrow \frac{x}{846}=\frac{y}{987}=\frac{100}{3\times 47} \\ \Rightarrow x=\frac{100\times 846}{3\times 47},y=\frac{100\times 987}{3\times 47} \end{gathered}$$
$\Rightarrow x=600,y=700$
Hence, the cost of chair and table are ​₹600 and ​₹700 respectively.