Question

Pintu takes 6 days more than those of Nishu to complete certain work. If they work together they finish it in 4 days. How many days would it take to complete the work if they work alone. 

Answer 1

Let Nishu take x days to complete the work alone.

∴ Total work done by Nishu in 1 day = `1/x` Also, Pintu takes (x + 6) days to complete the work alone.

∴ Total work done by Pintu in 1 day = `1/(x + 6)`

∴ Total work done by both in 1 day = `(1/x + 1/(x + 6))`

But, both take 4 days to complete the work together.

∴ Total work done by both in 1 day = `1/4`

According to the given condition,

`1/x + 1/(x+6) = 1/4`

∴ `(x + (6+x))/(x(x+6)) = 1/4`

∴ `(2x + 6)/(x(x+6)) = 1/4`

∴ 4(2x + 6) = x(x + 6)

∴ 8x + 24 = x² + 6x

∴ x² + 6x – 8x – 24 = 0

∴ x² – 2x – 24 = 0

∴ x² – 6x + 4x – 24 = 0

∴ x(x – 6) + 4(x – 6) = 0

∴ (x – 6)(x + 4) = 0

By using the property, if the product of two numbers is zero, then at least one of them is zero, we get,

∴ x – 6 = 0 or x + 4 = 0

∴ x = 6 or x = –4

But, the number of days cannot be negative,

∴ x = 6 and x + 6 = 6 + 6 = 12

∴ The number of days taken by Nishu and Pintu to complete the work alone is 6 days and 12 days respectively.