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When faced with mixture problems, many students spend extra time juggling percentages and ratios. Yet, there is a simple, elegant shortcut called the rule of alligation. This method allows you to instantly determine the required ratio when two different qualities are mixed to achieve a particular resultant quality. The principle is straightforward: place the two given qualities on either side, write the resultant value in the middle, and take differences diagonally. These differences directly give the ratio of the two quantities. For example, if the two values are 2 and 10, and the result is 7, the differences are 5 and 3, giving the ratio as 3:5. Such clarity in approach helps avoid careless mistakes, especially under exam pressure. Building these skills through an efficient GMAT preparation course and applying them in a thorough GMAT test series makes you quicker, sharper, and more confident in handling mixture and alligation questions.
Alligation is an efficient tools in arithmetic. It is especially useful in cases where two different values are combined to form a given result, and the task is to find the mixing ratio.
Question: Two qualities of sugar – $2 per lbs and $10 per lbs – are mixed to form a new quality of $7 per lbs. Find the ratio of the two qualities used.
Consider the values $2 and $10, with a resultant of $7. Write 2 and 10 on either side, and place 7 in between.
Now, place these values opposite the original numbers. The ratio between the two quantities becomes 3:5.
Rather than calculating weighted averages and adjusting through trial and error, alligation gives the ratio almost instantly. In fact, with some practice, such a problem can be solved in under 30 seconds.
Mastering such methods not only helps in mixture problems but also strengthens logical thinking and efficiency, both of which are central to success on the GMAT. Regular practice, particularly through structured GMAT mock, ensures that this concept becomes second nature during the exam.
Alligation is a quiet lesson in balance. Begin with what you have, name what you need, and let the differences guide your mix. The same habit steadies choices beyond the test: weigh tradeoffs, allocate time where the gap is widest, and move with intent. When numbers and priorities pull in different directions, sketch the frame, breathe, and trust the structure. With practice, clarity replaces noise. Seek MBA admissions help if and when you need perspective; a companion can align effort and outcomes.
