Question

The price of a house is decreased from Rupees Fifteen lakhs to Rupees Twelve lakhs. Find the percentage of decrease.

Answer 1

Hint: First find the decreased price of the house by the difference of the new and old prices. And use the formula for finding percentage decrease in the price, mentioned below;
$%decreases=\ \dfrac{Decrease\ in\ price}{Old\ price}\times 100$

Complete step-by-step answer:

We know that the value of decrease between two numbers can be given by taking differences between them and hence the percentage of decrease with respect to the given number is the fraction of decrease value and given number and hence multiply it by 100 to get the percentage.
Now, it is given that the price of a house has decreased from 15 lakhs rupees to 12 lakhs rupees. So, the decreased value can be calculated by taking the difference of it.
So, the decreased price of the house is equal to the old price minus new price. Hence, we get,
Decreased price = 1500000 – 1200000
= 300000 rupees
Now, we know that the percentage decrease of the price of a house can be given by taking a fraction of the decreased price with the older price and hence multiplying it by 100.
So, we can get percentage decrease by following formula:
$
 \Rightarrow Percentage\ decreases=\ \dfrac{Decreased\ value}{Old\ value}\times 100 \\
 \Rightarrow \dfrac{Decreased\ price}{Old\ price}\times 100 \\
$
Now, we know the decreased price and old price can be given as 15 lakhs rupees and 3 lakh rupees. Hence, we get percentage decrease of the price as;

$
 \Rightarrow Percentage\ Decrease=\dfrac{300000}{1500000}\times 100 \\
 \Rightarrow \dfrac{1}{5}\times 100=20% \\
$
Hence, percentage of decrease of the price is 20%, if the price of the house will decrease from fifteen lakh rupees to 12 lakh rupees.
Hence, the answer is 20%.

Note: Percentage decrease or any increase is measured as $\dfrac{change\ in\ quantity}{old\ quantity}$ i.e. we need to find % decrease or increase with respect to old value by which new value is increasing or decreasing. So, don’t put the new values in place of old to get the percentage increase or decrease.
So, one may go wrong with the question, if he/she finds a percentage as $\dfrac{3\ lakh}{12\ lakh}\times 100$ where he/she put a new price which is wrong. So, take care of it with these kinds of questions.
One may go wrong, if he/she divides the fraction $\dfrac{decrease\ in\ price}{old\ price}$ by 100. We need to multiply this fraction by 100. So, be careful with it as well.