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If x:y=8:3, then (xтИТy):(x+y)=?
2:5
5:11
5:2
11:5
5:11
Substitute x=8 and y=3 directly into the expression (xтИТy):(x+y) to get (8тИТ3):(8+3)=5:11.
x : y = 8 : 3
x+yxтИТyтАЛ
Substitute x=8 and y=3 directly into the expression (xтИТy):(x+y) to get (8тИТ3):(8+3)=5:11.
Students might confuse (xтИТy):(x+y) with (x+y):(xтИТy) or perform subtraction incorrectly.
Step 1: Write the given ratio
From the question, we are given the ratio of x to y as x:y=8:3. We can assume x=8k and y=3k where k is a constant.
x=8k,y=3k
Step 2: Substitute into the required expression
We need to find the ratio (xтИТy):(x+y). Substitute x=8 and y=3 directly into the expression.
(xтИТy):(x+y)=(8тИТ3):(8+3)
Step 3: Simplify the expression
Calculate the difference and the sum: 8тИТ3=5 and 8+3=11.
5:11
B is correct because substituting x=8 and y=3 into (xтИТy):(x+y) yields (8тИТ3):(8+3)=5:11.
Proportion properties like componendo and dividendo are extremely useful in advanced algebraic ratio problems.
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