Question

A house and a garden together cost Rs. 8,40,000. The price of the garden is $ \dfrac{5}{7} $ times the price of the house. Find the house of the price and the garden.

Answer 1

Hint: Start by letting the cost of the house to be Rs. x and the cost of the garden to be Rs. y. Now use the statement that the price of the garden is $ \dfrac{5}{7} $ times the price of the house to get the relation between x and y. Also, the other relation is that the sum of x and y is the total cost , i.e., Rs. 8,40,000. So, use the two relations to find the value of x and y.

Complete step-by-step answer:
Let us start the solution to the above question by letting the cost of the house to be Rs. x and the cost of the garden to be Rs. y.
Now as it is given that the price of the garden is $ \dfrac{5}{7} $ times the price of the house, we can say that:
 $ \dfrac{5}{7}x=y.....(i) $
Also, the other relation is that the sum of x and y is the total cost , i.e., Rs. 8,40,000. So, use the two relations to find the value of x and y. If we represent this mathematically, we get
 $ x+y=8,40,000 $
Now, we will substitute y from equation (i) in this equation. On doing so, we get
 $ x+\dfrac{5}{7}x=8,40,000 $
Now, we will take the LCM of the LHS to be 7.
 $ \dfrac{7x+5x}{7}=8,40,000 $
 $ \Rightarrow \dfrac{12x}{7}=8,40,000 $
 $ \Rightarrow x=\dfrac{8,40,000\times 7}{12}=4,90,000 $
Now, we will substitute the value of x in equation (i). On doing so, we get
 $ \dfrac{5}{7}\times 490000=y $
 $ \Rightarrow 3,50,000=y $
Therefore, the cost of the house is Rs. 4,90,000 and the cost of the garden is Rs. 3,50,000.

Note: Don’t get confused and take $ \dfrac{5}{7} $ of the total cost to be the cost of the garden, as it is given that the cost of the garden is $ \dfrac{5}{7} $ the cost of the house. Also, be very careful about x and y, as you need to be exact whether x is the cost of the house or the cost of the garden, so always read the assumption line before you form an equation in x and y.