Question

Two 1 litre jugs are each filled with a mixture of olive oil and vinegar. The first jug has 3 times as much as oil as vinegar and the second jug has 4 times as much as oil as vinegar. They are poured into a larger jug. In this jug the volume of oil will be?

Answer 1

`The\ first\ jug:\\\\(oil)/(vinegar) = (3)/(1) \ \ \ \Rightarrow\ \ \ the\ volume\ of\ the\ oil= (3)/(4) \ of\ the\ jug\\\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \Rightarrow\ \ \ the\ volume\ of\ oil\ =(3)/(4) \ litre\\\\The\ second\ jug:\\\\(oil)/(vinegar) = (4)/(1) \ \ \ \Rightarrow\ \ \ the\ volume\ of\ the\ oil= (4)/(5) \ of\ the\ jug\\\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \Rightarrow\ \ \ the\ volume\ of\ oil\ =(4)/(5) \ litre\\\\`


`The\ larger\ jug:\\\\ (3)/(4) \ litre+ (4)/(5)\ litre=0.75+0.8\ [litre]=1.55\ [litre]\\\\Ans.\ the\ volume\ of\ the\ oil\ is\ 1.55\ litres.`

Answer 2

`In\ the\ first\ jug\ is\ (3)/(4)l\ olive\ oil.\\\\In\ the\ second\ jug\ is\ (4)/(5)l\ olive\ oil\\\\(3)/(4)l+(4)/(5)l\\\\(3)/(4)\to the\ denominator\ is\ 4\\\\list\ the\ multiples\ of\ 4:\ 0;\ 4;\ 8;\ 12;\ 16;\ \fbox{20};\ 24;\ 28;...\\\\(4)/(5)\to the\ denominator\ is\ 5\\\\list\ the\ multiples\ of\ 5:\ 0;\ 5;\ 10;\ 15;\ \fbox{20};\ 25;\ 30;...\\\\Least\ Cammon\ Denominator\ of\ (3)/(4)\ and\ (4)/(5)\ is\ 20`


`(3)/(4)=(3\cdot5)/(4\cdot5)=(15)/(20)\\\\(4)/(5)=(4\cdot4)/(5\cdot4)=(16)/(20)\\-----------------\\\\(3)/(4)l+(4)/(5)l=(15)/(20)l+(16)/(20)l=(15+16)/(20)l=(31)/(20)l=1(11)/(20)l=1.55l\leftarrow solution`