Ratio of salt solution strengths

Let the strengths of A, B, C be $a, b, c$ respectively.

From first mixture (ratio 1 : 2 : 3, total 6 parts): $\frac{a + 2b + 3c}{6} = 20 \implies a + 2b + 3c = 120$

From second mixture (ratio 3 : 2 : 1, total 6 parts): $\frac{3a + 2b + c}{6} = 30 \implies 3a + 2b + c = 180$

Subtracting first equation from second: $2a - 2c = 60 \implies a - c = 30 \implies c = a - 30$

Substitute $c = a - 30$ into first equation: $a + 2b + 3(a - 30) = 120$ $4a + 2b - 90 = 120 \implies 4a + 2b = 210 \implies 2b = 210 - 4a$

Strength of solution D (mixing B and C in ratio 2 : 7): $d = \frac{2b + 7c}{9} = \frac{(210 - 4a) + 7(a - 30)}{9} = \frac{210 - 4a + 7a - 210}{9} = \frac{3a}{9} = \frac{a}{3}$

Ratio of strength of D to A is $\frac{d}{a} = \frac{a/3}{a} = \frac{1}{3} = 1 : 3$.