(Q4)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:

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
x
+
6
x + 5
=1

6(
1
x
+
1
x + 5
)=1

6(
x + 5 + x
x(x + 5)
)=1

6(2x + 5) = x2 + 5x

x2 -7x - = 0

x2 - x + 3x - = 0

x(x - ) + 3(x - ) = 0

(x - )(x + 3) = 0

x - = 0 or x + 3 = 0

x = or x = -3

∴x = (∵ x can't be negative)

∴ Time taken by Vinay = x = 10 days

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