CAT Quantitative Aptitude Questions | CAT Percentages Problems - Integers

The question is from CAT Percentages. 2IIMs CAT question bank provides you with CAT questions that can help you gear for CAT Exam CAT 2023. This question is from the topic percentages using integers. In this question, Two workers are planting trees. Later another worker is added and overall efficiency is increased. So, we need to find the no of trees planted by the second worker as a percentage of the number of trees planted by first worker.

Question 32 : In a field, two workers are planting trees. After sometime, a third worker is added and the number of trees planted becomes half as large. How many trees can the second worker plant as a percentage of the number of trees planted by first worker if it is given that efficiency of second worker is 1/3 of 1^st and 3^rd worker combined.

1. 65%
2. 60%
3. 70%
4. 75%

Explanatory Answer

Method of solving this CAT Question from Percentages: Going by options might help at times.

Half as large means an increase of 50%.
=> 3^rd worker = \\frac{1st Worker + 2nd worker}{2}\\) --------Equation (1)
Also given, number of trees planted by 1^st + 3^rd = 3 * 2^nd --------Equation (2)

This problem can be solved easily using options:
a) If trees planted by 2nd worker = 65 1^st worker = 100 3^rd worker = 82.5 (from Equation(1))
Putting in Equation (2) => 182.5 = 3 * 65 = 185 (Not satisfied)

b) If trees planted by 2^nd worker = 60
1^st worker = 100
3^rd worker = 80 (from Equation(1))
Putting in Equation(2) => 180 = 3 * 60 = 180 (Satisfied)

The question is "How many trees can the second worker plant as a percentage of the number of trees planted by first worker if it is given that efficiency of second worker is 1/3 of 1st and 3rd worker combined. "
The second worker can plant 60% of the number of trees planted by first worker

Hence, the answer is 60%

Choice B is the correct answer.