Let A = number of gallons on Mixture A in 15 gallon mixture

B = number of gallons on Mixture B in 15 gallon mixture

(20/100)A + (50/100)B= (30/100)(A+B) --1

A+B=15 -- 2

On solving equations 1 and 2 , we get

A=10

B=5

Answer D 10 gallons

Alternatively , a quicker method to solve this will be weighted average .

We are mixing A , which has 20 % alcohol with

B which has 50 % alcohol

to get resultant mixture with 30 % alcohol

20 --30----50

30 is 10 away from 20 and 20 away from 50 . So the volumes of the mix A and B will be in inverse proportion - 2:1 .

V1/V2=(50-30)/(30-20)=2/1

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