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Let there be v1 ounces of drink A, which contains D% alcohol.


Let there be v2 ounces of drink B, which contains E% alcohol.

Mixing both, we get v1 + v2 ounces which contains F% alcohol

Given that v1 + v2 = 1000 ounces, therefore v2 = 1000 - v1

By Rule of Alligations (Refer to the Diagram below)

\(\frac{v1}{F - E}\) = \(\frac{1000 - v1}{D - F}\)

\(\frac{1000 - v1}{v1}\) = \(\frac{D - F}{F - E}\)

\(\frac{1000}{v1}\) - 1 = \(\frac{D - F}{F - E}\)

\(\frac{1000}{v1}\) = \(\frac{D - F}{F - E}\) + 1

\(\frac{1000}{v1}\) = \(\frac{D - F + F - E}{F - E}\)

\(\frac{1000}{v1}\) = \(\frac{D - E}{F - E}\)

v1 = \(\frac{1000(F - E) }{ (D - E)}\)

Option B

Arun Kumar
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