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.
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Let Vinay will take time to complete the job himself = x days .
a/c to question,
Vinay by himself can complete the job in 5 days less than Praveen .
so, Praveen will take time to complete the job himself = (x + 5) days
now, if they are working together,
then, time taken by them = x × (x + 5)/{x + (x + 5)}
6 days = x(x + 5)/(2x + 5)
=> 6(2x + 5) =x² + 5x
=> 12x + 30 = x² + 5x
=> x² - 7x - 30 = 0
=> x² - 10x + 3x - 30 = 0
=> x(x - 10) + 3(x - 10) = 0
=> (x + 3)(x - 10) = 0
x = 10 and -3 but x ≠ -3
so, Vinay takes 10 days to complete the job himself
a/c to question,
Vinay by himself can complete the job in 5 days less than Praveen .
so, Praveen will take time to complete the job himself = (x + 5) days
now, if they are working together,
then, time taken by them = x × (x + 5)/{x + (x + 5)}
6 days = x(x + 5)/(2x + 5)
=> 6(2x + 5) =x² + 5x
=> 12x + 30 = x² + 5x
=> x² - 7x - 30 = 0
=> x² - 10x + 3x - 30 = 0
=> x(x - 10) + 3(x - 10) = 0
=> (x + 3)(x - 10) = 0
x = 10 and -3 but x ≠ -3
so, Vinay takes 10 days to complete the job himself
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