Question

Ayush and Rahul together complete a work in half of time of veer,while Ayush and veer together can complete same work in 1/3rd time of Rahul .if they together complete a piece of work in 30days.then in how many days Rahul can alone complete the work.​

Answer 1

Answer:

22.5 days

Step-by-step explanation:

let time required to do work by rahul is x

by ayush is y

by veer is z

given x+y=z/2

y+z=x/3..²

and x+y+z=30 days

from ²

x+x/3=30

4x/3=30

4x=90

x=90/4

x=22.5

hope my answer helps you

Answer 2

$\large\underline{\sf{Solution-}}$

Let

• Time taken by Ayush alone to finish the work be 'x' days.

• Time taken by Rahul alone to finish the work be 'y' days.

• Time taken by Veer alone to finish the work be 'z' days.

So,

$\rm :\longmapsto\: \: Ayush \: 1 \: day \: work \: = \dfrac{1}{x}$

$\rm :\longmapsto\: \: Rahul \: 1 \: day \: work = \dfrac{1}{y}$

$\rm :\longmapsto\: \: Veer \: 1 \: day \: work = \dfrac{1}{z}$

Now,

According to statement,

• Ayush and Rahul together complete a work in half of time of veer.

So, there 1 day work is

$\rm :\longmapsto\:\dfrac{1}{x} + \dfrac{1}{y} = \dfrac{2}{z} - - - (1)$

Also, given that

• Ayush and veer together can complete same work in 1/3rd time of Rahul.

So, there 1 day work is

$\rm :\longmapsto\:\dfrac{1}{x} + \dfrac{1}{z} = \dfrac{3}{y} - - - (2)$

Also, given that

• They together complete a piece of work in 30days.

So, there 1 day work is

$\rm :\longmapsto\:\dfrac{1}{x} + \dfrac{1}{y} + \dfrac{1}{z} = \dfrac{1}{30}$

$\rm :\longmapsto\:\dfrac{2}{z} + \dfrac{1}{z} = \dfrac{1}{30} \: \: \: \: \: \: \{using \: (1) \}$

$\rm :\longmapsto\:\dfrac{3}{z} = \dfrac{1}{30}$

$\bf\implies \:z \: = \: 90 - - - (4)$

Now,

On Subtracting equation (2) from equation (1), we get

$\rm :\longmapsto\:\dfrac{1}{y} - \dfrac{1}{z} = \dfrac{2}{z} - \dfrac{3}{y}$

$\rm :\longmapsto\:\dfrac{4}{y} = \dfrac{3}{z}$

$\rm :\longmapsto\:\dfrac{4}{y} = \dfrac{3}{90} \: \: \: \: \: \: \: \{ \because \: z = 90 \}$

$\rm :\longmapsto\:\dfrac{4}{y} = \dfrac{1}{30}$

$\bf\implies \:y = 120$

$\bf\implies \:Rahul \: alone \: take \: 120 \: days \: to \: finish \: the \: work.$