The set is from Word Problems. The revenues and the growth rates of five companies are given in length paragraph through comparison. Our task is to determine the revenue of some companies which is asked in the follow up questions. With simple arithmetic calculations, you can ace this topic. Word problems in CAT is an important topic for CAT Exam, and we can expect a set like this in the CAT Data Interpretation and Logical Reasoning section in the CAT Exam
Five Companies A, B, C, D and E saw growth rates ranging from 10% to 50% in the year 2015. The company A with the least revenues of Rs. 600 crores in 2015 saw the maximum growth rate of 50% and the Company D with the highest revenue saw the least growth rate of 10%. Company B’s revenues in 2016 was equal to that of Company D in 2015, while Company C’s 2016 revenue was equal to that of Company B’s in 2015, Company A’s 2016 revenue was equal to that of Company E in 2015.
John, an accountant observes that one of the companies has twice the growth rate of another. Mathew, his colleague corrects him and says that this is the case in two different instances.
Company E has a revenue equal to the average seen in Company A and D, and growth rate equal to the average growth rate of A and D.
Ram, known for his cryptic-speak mentioned that if company C had grown at the rate seen by company A in 2015 would have reached the revenues seen by Company B in 2016.
Question 1: What is the overall average growth rate seen by all 5 companies put together?
We are going to construct and fill a table with details that we can infer from the statements. Company A has Revenues of Rs. 600 crores and sees a growth rate of 50%. Let Company D’s revenue in 2015 be X. The revenue of Company B in 2016 should also be X. Let revenue of Company B in 2015 be Y, this should be equal to revenue of Company C in 2016. Let us capture this in a table:
Company A’s 2016 revenue was equal to that of Company E in 2015.
The next statement that is very useful is “Company E has a revenue equal to the average seen in Company A and D, and growth rate equal to the average growth rate of A and D.”. So, Company E should have seen a growth rate of 30%. Revenue of Company D should be Rs. 1200 crores:
Or, if Company C had grown by 50%, it would have reached a revenue of X. Or, Company C had a revenue of 2/3 X in 2015.
Now, we move to these two statements – “John, an accountant observes that one of the companies has twice the growth rate of another. Mathew, his colleague corrects him and says that this is the case in two different instances.” Among the three % growths we already have, none is twice any other. So, the other two growth rates seen in B and C should somehow incorporate this.
So, the growth rates seen in B and C should be from either 2 * growth rates of A, D or E or ½ of growth rates seen in A, D or E. But since the growth rates should be between 10% and 50%, the only possibilities we have are 15%, 20% and 25%.
From the numbers, we can see that Company C should have grown by 25% and Company B by 20%
One more way of doing this - While we are taking growth rate for C as 25% , it is just an assumption. It can be 20% also. In this case, C will grow by 20%. We have -
Then revenue of C in 2016 will be 960 which is equivalent to revenue of B in 2015. Now growth rate of B is 25% (960 + 25% of 960 is equal to 1200)
Solution to Question 1
We can calculate the overall rate by adding the revenues for 2015 and 2016.
The question is "What is the overall average growth rate seen by all 5 companies put together?"
Choice B is the correct answer.
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