Question: The total cost of 4kg of apples and 6 kg of oranges is Rs. 570. If the cost of 3 kg of apples is  the same as the cost of 5 kg of oranges, find the rate of cost of apples and oranges.

Solution:

Let the cost of 1kg of apple be Rs'x' and the cost of 1kg of orange be Rs'y'.

According to the question,

Condition I,
The total cost of 4kg of apples and 6 kg of oranges is Rs. 570.
$or, 4x + 6y = 570$
$or, 4x = 570-6y$
$or, x = \frac{570-6y}{4}$ - (i)

Condition II,
The cost of 3kg of apples is the same as the cost of 5kg of oranges.
$or, 3x = 5y$ - (ii)

Now,
Put the value of x from equation (i) into equation (ii), we get,

$or, 3\left ( \dfrac{570-6y}{4} \right ) = 5y$

$or, \dfrac{3(570-6y)}{4} = 5y$

$or, 1710 - 18y = 5y × 4$

$or, 1710 = 20y + 18y$

$or, 1710 = 38y$

$or, y = \dfrac{1710}{38}$

$\therefore y = 45$


Again,
Put the value of y in equation (i), we get,

$or, x = \dfrac{570 - 6×45}{4}$

$or, x = \dfrac{300}{4}$

$\therefore x = 75$

So, (x,y) = (75,45)

Therefore, the required rate of cost of apples is Rs 75 and the rate of cost of oranges is Rs 45.