Question

Arpit can fence a garden in 3hrs ,Ankur can do it in 5hrs and Akash takes 6hrs m to do the same. If they work together, in how many hours can they fence the garden ( in Inverse variations)​

Answer 1

Ans . Arpit takes 3hrs to fence a garden.

Ankur takes 5hrs to fence a garden.

Aakash takes 6hrs to fence a garden.

a

First we have to take LCM of 3,5,6 which is 30.

So in 30hrs Arpit fence 30/3 = 10 gardens

Like that in 30hrs Ankur fence 30/5= 6 gardens

And Aakash in 30hrs fence 30/6= 5 gardens

Total Garden = 10+ 6+5 = 21

Total Hours = 30+ 30+ 30 = 90

21 garden takes 90hrs if they work together .

So They together fence that 1 garden in 90/21 = 4.28 hrs

So Ans is 4.28 hrs .

Answer 2

Answer:

If Arpit, Ankur, and Akash can fence a garden in 3 hrs, 5 hrs, 6hrs respectively. Then they can complete the work together in 1.42 hours

Step-by-step explanation:

Let W be the total amount of work required to fence the garden

Given

Time Arpit requires to fence the garden = 3hrs

Amount of work done by Arpit in 1 hour = $\frac{1}{3}$ of total work= $\frac{1}{3}W$

Time Ankur requires to fence the garden = 5hrs

Amount of work done by Ankur in 1 hour = $\frac{1}{5}$ of total work= $\frac{1}{5}W$

Time Akash requires to fence the garden = 6hrs

Amount of work done by Akash in 1 hour = $\frac{1}{6}$ of total work = $\frac{1}{6}W$

Amount of work done by Arpit, Ankur, and Akash in 1 hour

$=\frac{1}{3}+\frac{1}{5}+\frac{1}{6} \\\\=\frac{1*10}{3*10} +\frac{1*6}{5*6} +\frac{1*5}{6*5} \\\\=\frac{10}{30} +\frac{6}{30} +\frac{5}{30} \\\\=\frac{21}{30} \\\\=\frac{7}{10}W$

So 7/10 of total work is done in 1 hour

So total work W is done in $\frac{1}{\frac{7}{10} } \\\\=\frac{10}{7} \\\\= 1.42$

So, Arpit, Ankur, and Akash can complete the work together in 1.42 hours