Question

Xamion can dig a trench in 20 days. After he has done half the job, Yakov begins to fill the dugout trench and Xamion goes on digging the trench. The trench is dug out in 30 more days. How many days would Yakov take to fill in the dugout the trench?

Answer 1

Given : Xamion can dig a trench in 20 days.

After he has done half the job, Yakov begins to fill the dugout trench and Xamion goes on digging the trench.

The trench is dug out in 30 more days.

To Find : How many days would Yakov take to fill in the dugout the trench?

Solution:

Xamion can dig a trench in 20 days

=> Xamion can dig half a trench in 20/2 = 10 days

hence half job is done in 10 days

30 more days are taken  Hence  

Xamion dig for 40 days  = 2 x 20 days

= 2 (  trench)

And  Yakov fill the trench = 2 - 1  = 1   in 30 days ( as 2 are digged and finally 1 is digged hence filled = 2 - 1 = 1)

Hence Yakov take 30 days to fill in the dugout the trench

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Answer 2

Given :-

• Xamion can dig a trench in 20 days.
• After he has done half the job, Yakov begins to fill the dugout trench and Xamion goes on digging the trench.
• The trench is dug out in 30 more days.

To Find :-

• How many days would Yakov take to fill in the dugout the trench ?

Solution :-

Let us assume that, total work is 40 units.

so,

→ Efficiency of Xamion = Total work / days = 40 / 20 = 2 unit / day .

then,

→ Xamion completes half work in = Half work / efficiency (20/2) = 10 days.

now, let us assume that, efficiency of Yakov filling the trench is x unit / day.

then,

→ Days taken * Efficiency of (Xamion - Yakov) = Remaining work .

→ 30(2 - x) = 20

→ 2 - x = 2/3

→ x = (2 - 2/3)

→ x = (4/3) units / day.

therefore,

= Yakov takes time to fill in the dugout the trench = (Total work) / Efficiency = 40 / (4/3) = 40 * (3/4) = 30 days. (Ans.)

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