KnowledgeBoat Logo
|

Mathematics

A can do a piece of work in 5 days and B can do the same work in (x + 5) days. The total number of days taken by A and B, working together, 3133\dfrac{1}{3}. The value of x is :

  1. 5

  2. 10

  3. 15

  4. 2122\dfrac{1}{2}

Quadratic Equations

20 Likes

Answer

A can do a piece of work in 5 days.

So, in 1 day

A will do 15\dfrac{1}{5} th of the work.

B can do a piece of work in (x + 5) days.

So, in 1 day

B will do 1x+5\dfrac{1}{x + 5} of the work.

Work done by A and B in 1 day = 15+1x+5\dfrac{1}{5} + \dfrac{1}{x + 5}

Days taken to complete work = 1Work done by A and B in 1 day\dfrac{1}{\text{Work done by A and B in 1 day}}

⇒313=115+1x+5⇒103=1x+5+55(x+5)⇒103=5(x+5)x+10⇒103=5x+25x+10⇒10(x+10)=3(5x+25)⇒10x+100=15x+75⇒15x−10x=100−75⇒5x=25⇒x=255=5.\Rightarrow 3\dfrac{1}{3} = \dfrac{1}{\dfrac{1}{5} + \dfrac{1}{x + 5}} \\[1em] \Rightarrow \dfrac{10}{3} = \dfrac{1}{\dfrac{x + 5 + 5}{5(x + 5)}} \\[1em] \Rightarrow \dfrac{10}{3} = \dfrac{5(x + 5)}{x + 10} \\[1em] \Rightarrow \dfrac{10}{3} = \dfrac{5x + 25}{x + 10} \\[1em] \Rightarrow 10(x + 10) = 3(5x + 25) \\[1em] \Rightarrow 10x + 100 = 15x + 75 \\[1em] \Rightarrow 15x - 10x = 100 -75 \\[1em] \Rightarrow 5x = 25 \\[1em] \Rightarrow x = \dfrac{25}{5} = 5.

Hence, Option 1 is the correct option.

Answered By

3 Likes

Related Questions