Question

For doing some work Ganesh takes 10 days more than Gajanan.If both work together , they complete the work in 12 days. Find the number of days taken by Ganesh to complete the work , if he works alone.

Answer 1

The number of days taken by Ganesh to complete the work, if he works alone is 30 days.

Step-by-step explanation:

Let the amount of time taken by Gajanan to do the work be “x” days, then Ganesh will take “x+ 10” days to do the same work.

So,

In 1 day, Ganjanan will do = $\frac{1}{x}$ work

In 1 day, Ganesh will do = $\frac{1}{x+10}$ work

It is given that together they take 12 days to complete the work  

So, in 1 day, Ganesh + Gajanan will do = $\frac{1}{12}$ work

Therefore, we can write the eq. as

$\frac{1}{x} + \frac{1}{(x+10)} = \frac{1}{12}$

⇒ $\frac{x+10+x}{x(x+10)} = \frac{1}{12}$

⇒ 24x + 120 = x² + 10x

⇒ x² – 14x – 120 = 0

⇒ x² – 20x + 6x – 120 = 0

⇒ x(x-20) + 6(x-20) = 0

⇒ (x-20)(x+6) = 0

⇒ x = 20 days

Thus,

The number of days taken by Ganesh to complete the work alone is given by,

= x+10

= 20 + 10

= 30 days

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