Question

The ratio of the prices of the two houses A and B was \[4:5\] last year. This year the price of A increased by 25% and B by \[{\rm{Rs }}50,000\]. If their prices are now in the ratio of\[9:10\], then the price of A last year was
A.\[{\rm{Rs}}\;3,{\rm{ }}60,000\]
B.\[{\rm{Rs}}\;4,{\rm{ }}50,000\]
C.\[{\rm{Rs}}\;4,{\rm{ }}80,000\]
D.\[{\rm{Rs}}\;5,{\rm{ }}00,000\]

Answer 1

Hint: Here, it is given that the price of both houses is increased to some extent this year, so firstly assume the prices according to the ratio then add the increased price to it and equate the both prices with the ratios of the current prices.

Complete step-by-step answer:
Given:
The price ratio of the house A and B last year is\[4:5\].
Let us assume the price in of the house A last year is,
 $ A = 4x $
Assuming the price in Rs of the house B last year is,
\[B = 5x\;\]
The price of the A is increased by 25% this year, and then the price of the house A in this year will be,
\[{A_1} = 4x + (0.25 \times 4x)\]
The price of the B is increased by 50,000 this year, then the price of the house B in this year will be,
\[{B_1} = 5x + 50,000\]
The price ratio of the houses A and B this year after increasing is 9:10.
We know that the equation to find the value of the x is,
\[\dfrac{{{A_1}}}{{{B_1}}} = \dfrac{9}{{10}}\]
Substitute the values in the above equation.
\[\begin{array}{c}
\dfrac{{{A_1}}}{{{B_1}}} = \dfrac{9}{{10}}\\
\dfrac{{4x + (0.25 \times 4x)}}{{5x + 50,000}} = \dfrac{9}{{10}}\\
10 \times 5x = 9\left( {5x + 50,000} \right)\\
50x = 45x + 4,50,000\,{\rm{Rs}}
\end{array}\]
On further solving the above equation.
\[\begin{array}{c}
5x = 450000\\
x = 90000
\end{array}\]
The equation to find the price of the houses A last year is,
 $ A = 4x $
Substitute the values in the above equation.
\[\begin{array}{c}
A = 4x\\
 = 4 \times 90000\\
 = 3,60,000
\end{array}\]
Therefore, the price of the house A last year is Rs. 3,60,000 that means option (a) is correct.
So, the correct answer is “Option A”.

Note: While equating the ratios of the current prices to the last year prices be sure the values are correctly taken and after finding the value of the x, substitute it in the last year ratio 4x to find its last year price. Increase of the house A price is given as percentage, to convert it from percentage make sure it is divided by 100.