X alone can build a castle in 5 days. Y can do the same in 10 days. Z destroys that castle in few days. If they all start working at the same time, the castle is built in 8 days. How many days (integral value) does Z take to destroy the castle? (e.g., take 1.2 days as 2 days)a)3b)5c)6d)7Correct answer is option 'C'. Can you explain this answer?

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X alone can build a castle in 5 days. Y can do the same in 10 days. Z destroys that castle in few days. If they all start working at the same time, the castle is built in 8 days. How many days (integral value) does Z take to destroy the castle? (e.g., take 1.2 days as 2 days)

a)
3
b)
5
c)
6
d)
7

Correct answer is option 'C'. Can you explain this answer?

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X alone can build a castle in 5 days. Y can do the same in 10 days. Z ...

Let Z take z days to destroy the castle.

Z takes 6 days to destroy the castle. Hence, option 3.

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X alone can build a castle in 5 days. Y can do the same in 10 days. Z ...

Let's assume that the work done by X, Y, and Z in one day is represented by the fractions 1/5, 1/10, and -1/d, respectively. Here, d represents the number of days it takes for Z to destroy the castle.

Work done by X, Y, and Z in 8 days:
X = 8 * 1/5 = 8/5
Y = 8 * 1/10 = 4/5
Z = 8 * (-1/d) = -8/d

Since the castle is built in 8 days, the total work done by X, Y, and Z should add up to 1:
8/5 + 4/5 - 8/d = 1

Now, let's simplify the equation:
(8d + 4d - 40) / (5d) = 1
12d - 40 = 5d
7d = 40
d = 40/7

As we need to find an integral value for d, we round up 40/7 to the nearest whole number, which is 6.

Therefore, Z takes 6 days to destroy the castle. Hence, the correct answer is option C.

Answered by Wizius Careers · View profile

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