Question

The number of days in which A, B and C can do a work are in arithmetic progression. if they can finish the work together in 13 days they individually require to complete the work if they work at same rate?​

Answer 1

Answer:

In CAT, Time and Work questions have become important, as a result of the rise in the number of questions from arithmetic. There are many shortcut formulas and tricks, which are frequently used to solve CAT Time and Work questions in quick time. Alternatively, Time and Work problems can easily be solved by the concept of the LCM method.

Questions from Pipes and Cisterns also fall under Time and Work as the concept requires to solve such questions is the same as the concepts used to solve Time and Work Questions.

To apply the concepts to solve CAT problems on Time and Work, an aspirant must be good at Ratio & Proportion and Percentages. As the level of difficulty of the questions varies a lot, it is advisable to follow the below tips to construct a proper approach to Time and Work questions for CAT exam.

Answer 2

Given: The number of days in which A, B and C can do a work are in arithmetic progression. if they can finish the work together in 13 days

To find: They individually require to complete the work if they work at same rate.

Solution:

Let the three consecutive terms in the arithmetic progression be a-d, a and a+d. These terms are the number of days taken by A, B and C to do the work individually. Here, a is the first term and d is the common difference of the arithmetic progression. Now, the following equation can be written.

$a-d +a+a+d = 13$

$3a = 13$

$a = \frac{13}{3}$

Hence, the number of days taken by A, B and c can be written as follows.

$A = \frac{13}{3} - d$

$B = \frac{13}{3}$

$C = \frac{13}{3} + d$

Therefore, they individually require 13/3-d, 13/3 and 13/3+d to complete the work if they work at same rate.