Question

Riyan and Taksh can build a tank in 12 days while Taksh and Hiren in 15 days and Riyan and Hiren in 20 days how long would each take todo the same work?​

Answer 1

Answer:

Riyan, Taksh and Hiren individually take 30 days, 20 days and 60 days

Step-by-step explanation:

Let Riyan be r, Taksh be t and Hiren be h for representation.

Riyan and Taksh in 1 day will build 1/12 part  => 1/r + 1/t = 1/12.

Taksh and hiren in 1 day will build 1/15 part => 1/t + 1/h = 1/15

Riyan and Hiren in 1 day will build 1/20 part => 1/r + 1/h = 1/20.

Now add all the three equations.

1/r + 1/t  + 1/t + 1/h + 1/r + 1/h = 1/12+1/15+1/20

2[1/r + 1/t +1/h] =   5 + 4 + 3 / 60 = 12/60 = 1/5

=> 1/r + 1/t + 1/h = 1/10.

which is nothing but Riyan, Taksh and Hiren can together build the tank in 10 days.  

Now for individual days taken.

1/r + 1/t + 1/h = 1/10

1/12 + 1/h = 1/10 = > 1/h = 1/10 - 1/12 = 6 - 5/60 = 1/60 => h = 60 days

1/r + 1/15 = 1/10  =>  1/r = 1/10 - 1/15 = 3-2/30  = 1/30   => r = 30 days.

1/t + 1/20 = 1/10 => 1/t = 1/10 - 1/20 = 2-1/20 = 1/20     => t = 20 days.

So Riyan, Taksh and Hiren individually take 30 days, 20 days and 60 days respectively.