CAT Quantitative Aptitude Questions on Ratios

Let us begin with some easy problems on the topic of ratios. You will need to pay attention as the steps shown in these problems will come really handy once you graduate to solving the CAT level problems on various topics, including this one.

Problem 1:

In the figure above, it is given that. What is the ratio  ?

[1]  1/2(x+y)

[2]  (x+y)

[3]  1/2

[4]  1

Solution:
The trick here is to recognize that both the triangles ABC and ADC have the same altitude AD.

Therefore, the area of Δ ABC is 1/2×y×AD and for Δ ADC, the area is 1/2×x×AD  .

The required ratio, therefore, is x/y

But since , the ratio comes out to be 1; hence the correct choice is [4].

Problem 2:   
The weight of a glass jar is 20% of the weight of the jar fully filled with coffee beans. After some of the beans have been removed, the weight of the jar and the remaining beans is 60% of the original total weight. What is the ratio of the weight of coffee beans remaining in the jar to the weight of the coffee beans when the jar was fully filled?

[1] 1/5

[2] 1/3

[3] 2/5

[4] 1/2

Solution:
Here we can use actual numbers instead of the putting the solutions in the form of algebraic unknowns.

If the total weight of the jar and its contents is, say, 10 kg, then the jar alone weighs 20% of this, then the weight of the jar is 2 kg; and the coffee beans weigh 8 kg.

Now if we remove some beans so that the combined weight of the jar and remaining coffee beans is 6 kg, then out of this 6 kg the jar weighs 2 kg and the coffee beans weigh 4 kg.
 
So we have 4 kg of coffee beans remaining out of the original 8 kg when the jar is fully filled with coffee beans.
Therefore, the ratio of coffee beans remaining now to the coffee beans earlier = 4/8 = 1/2. Hence, the correct choice is [4].

Problem 3: 

The sum of three numbers is 98. The ratio of the first to the second is , and the ratio of the second to the third is . The second number is:

[1] 20

[2] 30

[3] 32

[4] 33

Solution:

Let the second number be x.

Therefore, first number 2/3x  and the third number = 8/5x

Therefore, 2/3x+x+8/5x=98

Solving the above equation we get . The correct choice is [2].

You can also work backwards from options to solve such problems.