Question

A bartender has two casks full of mixture of vodka and tomato juice. the ratio of vodka and tomato juice in the first and second cask is 3:10 and 8:15 respectively. in what proportion should the mixtures be mixed to satisfy a customer who likes vodka and tomato juice in the ratio 7:16

Answer 1

Let the ratio of mixtures from two casks be mixed in ration X:Y to get final ratio 7:16
Quantiy of Vodka/ Qunatity of Juice in mixture =
= [3x/13 +8y/23] / [10x /13 +15y/23] = 7/16
by taking L.c.m and solving it we get :
69x+104y/230x +195y
= 7/16
=16[69x+104y]=7[230x +195y]
=1104x+1664y=1610x+1365y
506x=299y
x:y= 299:506 =13:22

∴ In proportion 13:22  the mixtures should be mixed to satisfy a customer who likes vodka and tomato juice in the ratio 7:16