Question

Vinay and Praveen working together can paint the exterior of a house in 6 days. Vinay by himself can complete the job in 5 days less than Praveen. How long will it take Vinay to complete the job by himself?

Answer 1

Let the time taken by Vinay to complete the job = x days 

Then the time taken by Praveen to complete the job = x + 5 days 

Both worked for 6 days to complete a job. 

∴ Total Work done by them is

⇒ 6(2x + 5) = x² + 5x 

⇒ x² – 7x – 30 = 0 

⇒ x² – 10x + 3x – 30 = 0 

⇒ x(x – 10) + 3(x – 10) = 0

⇒ (x – 10) (x + 3) = 0 

⇒ x – 10 = 0 (or) x + 3 = 0 

⇒ x = 10 (or) x = -3 

∴ x = 10 (∵ x can’t be negative) 

∴ Time taken by Vinay = x = 10 days 

Time taken by Praveen = x + 5 = 15 days.