To solve the problem of finding the ratio of the decrease in prices, follow these steps:
1. Determine the Old and New Prices:
- Old Price (\(P_{\text{old}}\)) = Rs. 1600
- New Price (\(P_{\text{new}}\)) = Rs. 1200
2. Calculate the Decrease in Price:
The decrease in price (\(D\)) is found by subtracting the new price from the old price:
[tex]\[
D = P_{\text{old}} - P_{\text{new}}
\][/tex]
Substituting the given values:
[tex]\[
D = 1600 - 1200 = 400
\][/tex]
3. Calculate the Ratio of the Decrease to the Original Price:
The ratio of the decrease in price to the original price (\(R\)) is calculated by dividing the decrease by the old price:
[tex]\[
R = \frac{D}{P_{\text{old}}}
\][/tex]
Substituting the known values:
[tex]\[
R = \frac{400}{1600}
\][/tex]
4. Simplify the Ratio:
[tex]\[
R = 0.25
\][/tex]
So, the decrease in price is Rs. 400, and the ratio of the decrease to the original price is 0.25 or 25%.
