Question

Jamila sold a table and a chair for ₹ 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 ₹ 1065. Find the cost price of each .

Answer 1

Let the CP of the table be Rs x and that of the chair be Rs y.
Case I: Profit on table = $\frac{10}{100}x$
We know SP − CP = Profit
⇒ SP = Profit + CP
⇒ SP = $\frac{10}{100}x$ + x = $\frac{110}{100}x=\frac{11}{10}x$
Profit on chair = $\frac{25}{100}y$
SP = $\frac{25}{100}y$ + y = $\frac{125}{100}y$
Total SP = $\frac{110}{100}x+\frac{125}{100}y=1050$
110x + 125y = 105000 .....(i)
Case II: Profit on table = $\frac{25}{100}x$
⇒ SP = Profit + CP
⇒ SP = $\frac{25}{100}x$ + x = $\frac{125}{100}x$
Profit on chair = $\frac{10}{100}y$
SP = $\frac{10}{100}y$ + y = $\frac{110}{100}y$
Total SP = $\frac{125}{100}x$ + $\frac{110}{100}y$ = 1065
125x + 110y = 106500 .....(ii)
From (i) and (ii), we have
235(x + y) = 211500
⇒ x + y = 900 .....(iii)
Subtracting (i) from (ii), we have
15(x − y) = 1500
⇒ x − y = 100 .....(iv)
Solving (iii) and (iv), we get
x = 500 and y = 400
Thus, CP of table = Rs 500 and CP of chair = Rs 400.