Quantitative Aptitude – Arithmetic – Time and Work – A person can complete

Quantitative Aptitude – Arithmetic – Time and Work

Question

A person can complete a job in 120 days. He works alone on Day 1.
On Day 2, he is joined by another person who also can complete the job in exactly 120 days.
On Day 3, they are joined by another person of equal efficiency.
Like this, everyday a new person with the same efficiency joins the work. How many days are required to complete the job?

Answer

15

Solution

As per the question from CAT 2017 – Quantitative Aptitude – Arithmetic – Time and Work, we can see that,
On Day 1, the person works alone. So, work done on Day 1 = 1/120
Next day, another person joins him, Work done on Day 2 = 2/120
And so on, until the final day
So, sum total of work done = 1/120 + 2/120 +………+ n/120 = 1
(1/120) (1 + 2+3+……+n) = 1
(1/120) [n(n+1)/2] = 1 (Sum of n positive integers)
On solving, we get n = 15.

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Quantitative Aptitude – Arithmetic

Quantitative Aptitude – Arithmetic – Mixtures – Q1 : Consider three mixtures – the first having water and liquid A in the ratio 1 : 2, the second having water and liquid B in the ratio 1 : 3, and the third having water and liquid C in the ratio 1 : 4.
Quantitative Aptitude – Arithmetic – Mixtures – Q2: Bottle 1 contains a mixture of milk and water in 7 : 2 ratio and Bottle 2 contains a mixture of milk and water in 9 : 4 ratio.
Quantitative Aptitude – Arithmetic – Time and Work – Ques: Amal can complete a job in 10 days and Bimal can complete it in 8 days. Amal, Bimal and Kamal together complete the job in 4 days and are paid a total amount of Rs 1000 as remuneration.
Quantitative Aptitude – Arithmetic – Time, Speed and Distance
Quantitative Aptitude – Arithmetic – Percentages
Quantitative Aptitude – Arithmetic – Profit and Loss
Quantitative Aptitude – Arithmetic – Pipes and Cisterns – Ques: A tank has an inlet pipe and an outlet pipe. If the outlet pipe is closed then the inlet pipe fills the empty tank in 8 hours.
Quantitative Aptitude – Arithmetic – Averages
Quantitative Aptitude – Arithmetic – Ratios

Other posts related to Quantitative Aptitude – Arithmetic

Learn the Basics of Time, Speed & Distance for CAT 2017
Time Speed Distance – Motion of Two Bodies in a Straight Line
Simple Interest and Compound Interest – Basic Concepts and Tricks for solving CAT Questions
Installments – Various Cases and Questions including Simple and Compound Interest
Profit and Loss – Basic Concepts for CAT Preparation
How to solve Time and Work problems in CAT 2017
Alligations and Mixtures Concepts for CAT Exam Preparation
Clocks -Fundamental Principles
Percentage concepts, questions and shortcut tricks for the CAT exam

---

---