The expenses of a family on rice, vegetables and cooking oil are in the ratio 9 : 11 : 5. If the prices of these items increases by 10%, 20% and 30%, respectively, then the total expenses of the family on these items will increase by:

18.4%

Rice : Vegetable : Cooking oil

 9    :    11         :      5

⇒ 9 x 110% : 11 x 120% : 5 x 130%

⇒ 9.9 : 13.2 : 6.5

⇒ Sum of initial ratio = 9 + 11 + 5 = 25

⇒ Sum of final ratio = 9.9 + 13.2 + 6.5 = 29.6

⇒ % increase in expense = \(\frac{29.6 - 25}{25}\) x 100 =  \(\frac{4.6}{25}\) x 100 =  18.4%.