Question 61082
Suppose that 'x' liters of 80% base solution is taken.

Then quantity of 30% base solution = (150 - x)liters [as the total is 150L)

Strength of 150L solution = 62%

The equation becomes,
x*0.8  + (150-x)*0.3 = 150*0.62
==> 0.8x + 45 - 0.3x = 93
==> 0.5x + 45 = 93
==> 0.5x = 93 - 45 [adding -45 to both the sides]
==> 0.5x = 48
==> 0.5x/0.5 = 48/0.5
==> x = 96

so 150-x = 150-96
         = 54

Thus 96L of 80% base is to be added to 54L of 30% base to get 150L  of 62% base.