Three solutions A, B, and C contain alcohol in the proportions 30%, 50%, and 80%, respectively. They are mixed to form a new solution containing 55% alcohol. If solutions A and B are taken in equal quantities, find the ratio of the combined quantity of (A + B) to the quantity of C.
5 : 3
Equal quantities of A (30%) and B (50%) give a combined strength of (30 + 50)/2 = 40% alcohol.
Alligation between the (A + B) mix at 40% and C at 80% to get 55%:
(A + B) : C = (80 – 55) : (55 – 40)
= 25 : 15
= 5 : 3
Check: 5 L at 40% + 3 L at 80% = 2 + 2.4 = 4.4 L alcohol in 8 L, and 4.4 ÷ 8 = 55%.
Hence, 5 : 3.
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