3 TIPS on cracking Aptitude Questions on Ratios and Proportions

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Tip #1: Express each element in the ratio as a fraction of the total for easy calculations

Question: A sum of money is to be distributed among A, B, C, D in the proportion of 2: 5: 4: 3. If C gets Rs.2000 more than D, what is B's share?

Solution:

A = 2/14 * T

B = 5/14 * T

C = 4/14 * T

D = 3/14 * T

C – D = 2000

4/14 * T – 3/14 * T = 2000

T = 28000

=> B = 5/14 * T = Rs.10000

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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?

Solution:

                       

Ratio after proposal   = 5/20 * T * 1.4 : 7/20 * T * 1.5 : 8/20 * T * 1.75

                                   = 5/20 * 1.4 : 7/20 * 1.5 : 8/20 * 1.75    {dividing by T}

                                   = 5 * 1.4 : 7 * 1.5 : 8 * 1.75    {multiplying by 20}

                                   = 7 : 10.5 : 14   

                                   = 2 : 3 : 4    {dividing by 3.5}

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?

Solution:

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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