Question

X alone takes 14 days to build a water tank. Y working alone takes 21 days to build
tank is built by X alone for half the time and the remaining half time by X and Y together then determine
time taken to build the tank.​

Answer 1

If the tank is built by X alone for half the time and the remaining half time by X and Y together then time taken to build the tank is 10.5 days.

Step-by-step explanation:

Time taken by X alone to build a water tank = 14 days

So, X’s 1-day work = $\frac{1}{14}$

Time taken by Y alone to build the water tank = 21 days  

So, Y’s 1-day work = $\frac{1}{21}$

∴ The amount of work done by X & Y together =  [$\frac{1}{14}$ + $\frac{1}{21}$ ]

It is given that X alone does the work for half the time and for the remaining half time the work is done by X & Y together.

Therefore, we can write the eq. as,

= [½ * $\frac{1}{14}$ ] + [½ * {$\frac{1}{14}$ + $\frac{1}{21}$}]  

= $\frac{1}{28}$ + [½ * {$\frac{3+2}{42}$ }]

= $\frac{1}{28}$ + $\frac{5}{84}$

= $\frac{84+140}{28*84}$

= $\frac{224}{28*84}$

= $\frac{2}{21}$

= $\frac{1}{10.5}$

Thus, the time taken to build the water tank is 10.5 days.

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