Word Problem 18
Problem 18: A mixture of a certain quantity of milk with 16 liters of water is worth 90 paisas per liter . If pure milk be worth Rs 1.09 per liter, the quantity of milk in the mixture is ;
a) 16 liters b) 80 liters c) 15 liters d) 2 liters
( there are 100 paisas in a rupee !)
Solution:
Given data is ;
water = 16 liters
Mixture = 90 paisas per liter
milk = Rs 1,09 per liter
Quantity of milk in the mixture =?
The data can be arranged as under;
Quantity | Price/liter (Rs) | Total cost | |
Milk | Y | 1.08 | 1.08Y |
Water | 16 | 0 (assuming water is free of cost) |
0 |
Mixture | Y+16 | 0.90 | 0.90(Y+16) |
Price of Mixture = Price of milk + Price of water
We get;
\[ 0.90(Y+16)=1.08Y+0 \]
This gives;
\[ 0.90Y+0.90\times16=1.08Y \]
This gives;
\[ 0.90\times 16= 1.08Y-0.90Y = 0.18Y \]
Finally we get;
\[ Y=\frac{0.90\times16}{0.18}=80 liters \]
So, the pure milk quantity is 80 liters
