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

Answer:

Step-by-step explanation:

Consider the provided information.

Let Gajanan takes x days.

Ganesh takes 10 days more than Gajanan: x+10

Together they complete the work in 12 days.

This can be written as:

\frac{1}{x} +\frac{1}{x+10}=\frac{1}{12}

x

1

+

x+10

1

=

12

1

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

x(x+10)

x+10+x

=

12

1

\frac{10+2x}{x^2+10x}=\frac{1}{12}

x

2

+10x

10+2x

=

12

1

120+24x=x^2+10x120+24x=x

2

+10x

x^2-14x-120=0x

2

−14x−120=0

x^2-20x+6x-120=0x

2

−20x+6x−120=0

x(x-20)+6(x-20)=0x(x−20)+6(x−20)=0

(x-20)(x-6)=0(x−20)(x−6)=0

x=20\ or\ x=-6x=20 or x=−6

Number of days can't be a negative number so the value of x is 20.

Thus, Gajanan takes 20 days.

Ganesh takes 10 days more than Gajanan i.e 30 days