Question

X takes twice as much time as Y and Z together take to finish the job.X and Y working together finish the job in four days.Z alone can do the same job in four days.in how many days can Y alone do the same job.

Answer 1

Let time taken by Y and Z together to accomplish the work = a days

Time taken by X to Complete the work = 2 a Days

Let time taken by Y alone to complete the work = p Days

Time taken by Z alone to complete the work = q Days

Now writing the Statements of the question in equation form

1. $\frac{1}{p} +\frac{1}{q}=\frac{1}{a}$

2. $\frac{1}{q}=\frac{1}{4}$

3. $\frac{1}{2a} +\frac{1}{p}=\frac{1}{4}$

$\frac{1}{p}=\frac{1}{4}-\frac{1}{2a}$

Substituting the value of $\frac{1}{p} and \frac{1}{q} {\text{in equation 1}}$

equation 1 becomes

$\frac{1}{4}+\frac{1}{4}= \frac{1}{a} + \frac{1}{2a} \\\\ \frac{1}{2}=\frac{3}{2a}\\\\ a=3$

$\frac{1}{p} +\frac{1}{4}=\frac{1}{3}\\\\ \frac{1}{p}= \frac{1}{3} -\frac{1}{4} \\\\ \frac{1}{p}=\frac{1}{12}\\\\ p= 12$

Time taken by Y alone do the same job= 12 Days