Two friends, Aman and Vivek started a project together. They worked together for the first 6 days, but only 30% of the project was completed. Therefore, both Aman and Vivek increased their respective efficiencies by 40% each, and the project was completed on time. If they had not increased their respective efficiencies, then the work would have been delayed by how many days?

Let, efficiencies of Aman and Vivek be 'x' units/day and 'y' units/day, respectively. So, total work = (6x + 6y) × (10/3) = (20x + 20y) units Work done in first 6 days = (6x + 6y) units Remaining work = 20x + 20y − 6x − 6y = (14x + 14y) units Increased efficiencies of Aman and Vivek are 1.4x units/day and 1.4y units/day, respectively. So, '14x + 14y' units of work will be done in = (14x + 14y)/(1.4x + 1.4y) = 10 days Total time taken to complete the work = 6 + 10 = 16 days And, if efficiencies were not increased then total work will be done in (20x + 20y)/(x + y) = 20 days Required number of days = 20 − 16 = 4 days