Question

A merchant daily buys orange for $1200$ rupees and mango for $1200$ rupees. One day the price of orange and mango were $40$ rupees each per kilogram. How many kilogram of orange and mango did he got on that day? On another day, the price of one kilogram of mango was $10$ rupees less than that of orange. Hence he got $20$ kilogram more mango than orange. Then what was the price of one kilogram of orange on that day?

Answer 1

Cost of oranges and mangoes, each per kg$=$Rs.$40$
Amount paid daily for mangoes and oranges each $=$Rs.$1200$
$\Rightarrow \frac{1200}{40}=30kg$
Thus, the merchant got $30kg$ of oranges and mangoes each that day.
Let the price of mango be Rs.$x$ next day.
$\Rightarrow$ Price of orange next day $=$ Rs.$(x+10$
From the information given in the problem, we have
$\frac{1200}{x}-\frac{1200}{x+10}=20$
$\Rightarrow \frac{60}{x}-\frac{60}{x+10}=1$
$60x+600-60x=x(x-10)$
$\Rightarrow 600=x^2+10x$
$\Rightarrow x^2+10x-600=0$
$\Rightarrow x^2+30x-20x-600=0$
$\Rightarrow x(x+30)-20(x+30)=0$
$\Rightarrow (x+30)(x-20)=0$
$\Rightarrow x=-30,20$
$-30$ is inadmissible , hence $x=20$
$\Rightarrow x+10=20+10=30$
Thus, price of oranges $=$Rs.$30$/kg on that day.