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Let x ml of alcohol is mixed with the solution,
initially 15% in 400 = (15×400)/100 = 60 ml
now,after mixing x ml it becomes 32% and the volume of solution becomes (400+x)ml
32% of (400 +x) is (60+x)
⇒32×(400+x)/100 = (60+x)
⇒12800 + 32x =6000 +100x
⇒68x =6800
⇒x =100 ml
so 100 ml of pure alcohol is to be mixed to make it 32% alcohol solution.