The length of a rubber cord is `l_(1)` m when the tension is 4 N and `l_(2)` m when the tension is 6 N.The length when the tension is 9 N, is

Explanation

Let l be the original length and `l_3` be the length of the wire when the tension is 9N.
` rArr (l_1 - l) prop 4......(1), (l_2-l) prop 5........(2)`
`(l_3 - l) prop 9...........(3)`
From (1) and (2) `(l_1 - l)/(l_2 - l) = 4/5 rArr 5l_1 - 5l = 4l_2 - 4l`
`l = 5l_1 - 4l_2` ...(4)
From (1) and (3) `(l_1 - l)/(l_3 - l) = 4/9 rArr (l_1 - (5l_2 - 4l_2))/(l_3 - (5l_1 - 4l_2)) = 4/9`
`rArr (l_2 - 5l_1 + 4l_2)/(l_3 - 5l_1 + 4l_2) = 4/9 rArr (4l_2 - 4l_1)/(l_3 - 5l_1 + 4l_2) = 4/9`
` rArr 36l_2 - 36l_1 = 4l_3 = 20l_2 + 16l_2`
` 20l_2 - 16l_1 = 4l_3 `
`l_3 = 5l_2 - 4l_1`