If ` a : b = 3 : 2 " and " b : c = 3 : 2 `, then find the value of the ratio `(a + b) : (b + c)`.

Explanation

` a : b = 3 : 2 rArr a/b = 3/2`.
`:. " Let " a = 3k_(1) " and " b = 2k_(1) [k_(1) ne 0]`
Also, ` b : c = 3 : 2 rArr b/c = 3/2`.
` :. " Let " b = 3k_(2) " and " c = 2k_(2) [k_(2) ne 0]`
Now, ` (a + b) : (b +c) = (a + b)/(b + c) = (3k_(1) + 2k_(1))/(3k_(2) = 2k_(2))`
` = (5k_(1))/(5k_(2)) = k_(1)/k_(2) ` .............. (1)
Also, ` a/b = 3/2 rArr (3k_(1))/(3k_(2)) = 3/2 rArr k_(1)/k_(2) = 3/2`.
` :. " from (1) we get , " (a + b)/(b + c) = 3/2` .
Hence ` (a +b) : (b + c) = 3 : 2`