In what ratio must 25% alcohol be mixed with 50% alcohol to get a mixture of 40% alcohol?

This is a straight alligation problem. Take the stronger solution (50%) and find its distance from the target (50 - 40 = 10). Take the weaker solution (25%) and find its distance from the target (40 - 25 = 15). The quantity of the weaker solution to the stronger one is the inverse of these distances, so 25% : 50% = 10 : 15 = 2 : 3.

Check: 2 litres of 25% alcohol give 50 units of alcohol. 3 litres of 50% alcohol give 150 units. Total is 200 units in 5 litres, which is 40%.

• A) 2:1 gives (50 + 50)/3 = 33.3%, not 40%.
• B) 3:1 gives (75 + 50)/4 = 31.25%.
• D) 3:2 gives (75 + 100)/5 = 35%.

Core concept: alligation, the weighted-average rule where mixing ratios are inversely proportional to the distance of each component from the mean. It is useful in Prelims for CSAT-style quantitative questions and reappears in price-weighted average problems and data interpretation.

Trap: Aspirants match the ratio to the numbers in the order they appear, or pair each strength with the difference on its own side. Always pair each strength with the distance from the mean on the opposite side.