CAT Quantitative Aptitude Questions | CAT Ratios, Mixtures, Alligations and Averages Questions

The question is from CAT Ratio, Mixtures and Averages. It is different from other questions. Instead of finding out the average, we are finding how many days it took to cut those trees. CAT exam is known to test on basics rather than high funda ideas. A range of CAT questions can be asked from Ratios and Proportions, Mixtures, Alligations and Averages. Make sure you master the topics. 2IIMs CAT questions bank provides you with CAT questions that can help you gear for CAT Exam CAT 2023.

Question 41: A group of people decided to cut 128 trees in a certain number of days. For the first 4 days, they were able to achieve their planned per day target. However, for the remaining days, the group was able to cut 4 more trees daily than planned. In this way, the group had cut 164 trees one day before the planned finish date. What was the number of trees the group was planning to cut per day?

1. 16
2. 32
3. 8
4. 64

Explanatory Answer

Method of solving this CAT Question from Ratio, Mixtures and Averages: How the individual data points affect the average?

Let the original target be x trees/day and the number of planned days be y.
=> y = \\frac{128}{x}\\)
Also, as per the question
(y-4-1) * (x+4) + 4x = 164
(y-5) * (x+4) + 4x = 164
xy – 5x + 4y – 20 + 4x = 164
x * \\frac{128}{x}\\) + 4 * \\frac{128}{x}\\) - x = 184
128 + \\frac{512}{x}\\) - x = 184
\\frac{512}{x}\\) - x = 56
Taking LCM, we get, \\frac{512 - x^2}{x}\\) = 56
=> 512 - x² = 56x
=> x² + 56x - 512 = 0
Solving for x, we get x = -64 or x = 8
x cannot be -64, so, x is 8.

The question is "What was the number of trees the group was planning to cut per day?"

Hence, the answer is "8".

Choice C is the correct answer.