1.

If `p : q = 5 : 7 " and " p - q = - 4`, then find the value of ` (3p + 4q)`.

Answer» We have , ` p : q = 5 : 7 " or, " p/q = 5/7 = (5k)/(7k) [k ne 0]`
` :. ` Let ` [ = 5k " and " q = 7k`.
Also, ` p - q = - 4 " or, " 5k - 7k = - 4 " or, " - 2k = - 4 " or, " k = (-4)/(-2) = 2`.
` :. P = 5k = 5 xx 2 = 10 " and " q = 7k = 7 xx 2 = 14`.
` :. 3p + 4q = 3 xx 10 + 4 xx 14 = 30 + 56 = 86`.
Hence the required value = 86.


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