Ratios and Percentages

Ratios and percentages represent some of the easiest questions in the IPAT. Having a calculator handy – which the IPAT allows – is always useful. While the questions themselves are easy, it is important to familiarize yourself with the type and rhythm of such questions. Here are some IPAT like ratio and proportion questions –

Q) If a:b = 1:3, b:c = 4:5, c:d = 1:7 what is a:d?


We observe, a:d = a:b x b:c x c:d = 1:3 x 4:5 x 1:7 = 4:105

Q) If there are 16 girls in a class of 24 students. How many more boys need to be admitted to the class to have the number of boys represent half the class size?


Let’s assume number of boys to be added to be ‘b’.

Number of boys currently in the class =24-16 = 8

(b+8)/(24+b) = 50%

b + 8 = 12 + 0.5b

0.5b = 4

b =8

hence 8 boys need to be admitted to the class

Q) An office table contains a few large, medium and small envelopes. The number of large envelopes is 3 plus 50% of the number of medium envelopes. The number of small envelopes is 3 times, 20% of the number of large envelopes. There are a total of 66 envelopes on the table . How many small, medium and large envelopes are there on the table?


Let s,m,l denote the number of small, medium and large envelopes.

L = 3 + 0.5M

S = 3×0.2xL

S+M+L = 66

Converting all equations into standard form

L – 0.5M = 3

0.6L – S = 0

L + M + S = 66

Solving the above equations,

S = 12 M = 34 L = 20 envelopes

As you will notice, the questions are not unreasonably hard. In our experience, what makes this section of the test hard is the 2.15 minutes cutoff per question. We have developed full length practice sets to mimic the sharp cutoff you will face in the IPAT. These sets will also expose you to the entire breadth of questions you will face in the IPAT so that nothing surprises you in the real test. You can get the practice sets here. For the next lesson on IPAT work and time click next.

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