Tip #2: You can directly perform multiplication/ division operations on ratio elements
Question: Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?
Ratio after proposal = 5/20 * T * 1.4 : 7/20 * T * 1.5 : 8/20 * T * 1.75
As a quick shortcut, we can also directly multiply the ratio elements to determine the new ratio.
Ratio after proposal (shortcut) = 5 * 1.4 : 7 * 1.5 : 8 * 1.75
= 2 : 3 : 4
Tip #3: Ensure that the units for the numerator and denominator match across the equation
Question: Ken can walk 40 dogs in 8 hours. How many dogs can Ken walk in 12 hours?
We assume that the number of dogs walked and the time taken are directly proportional.
Number of dogs walked αTime taken
Number of dogs walked = k * Time taken (k is some constant)
Number of dogs walked / Time taken = k
40 / 8 = x / 12 where x is count of dogs walked in 12 hours
In the above equation, numerator unit is dogs walked and denominator unit is time taken. Ensure that units match to avoid errors.
=> x = 60 dogs walked
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Ratios and Proportions
Aptitude Test on Ratios & Proportions: Tips and Aptitude Questions