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Three diggers dug a ditch of 324 m deep in six days working simultaneously. During one shift, the third digger digs as many metres more than the second as the second digs more than the first. The third digger’s work in 10 days is equal to the first digger’s work in 14 days. How many metres does the first digger dig per shift?
  • a)
    15 m
  • b)
    18 m
  • c)
    21 m
  • d)
    27 m
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Three diggers dug a ditch of 324 m deep in six days working simultaneo...
The per day digging of all three combined is 54 meters. Hence, their average should be 18. This
means that the first should be 18 – x, the second, 18 & the third 18 + x.
The required conditions are met if we take the values as 15,18,21 meters for the first, second and
third diggers respectively. Hence, (a) is the correct answer.
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Most Upvoted Answer
Three diggers dug a ditch of 324 m deep in six days working simultaneo...
Let's solve the problem step by step:

Let's assume that the first digger digs x meters per shift.
According to the given conditions:
- The second digger digs x + y meters per shift, where y is the additional meters the third digger digs more than the second.
- The third digger digs (x + y) + y = x + 2y meters per shift.

Digger's work in 6 days:
In six days, the first digger completes 6x meters of work.
The second digger completes 6(x + y) = 6x + 6y meters of work.
The third digger completes 6(x + 2y) = 6x + 12y meters of work.

Given that the total depth of the ditch is 324 meters, we have the equation:
6x + 6y + 6x + 12y = 324
12x + 18y = 324
2x + 3y = 54

Digger's work in 14 days:
In 14 days, the first digger completes 14x meters of work.
The third digger completes 14(x + 2y) = 14x + 28y meters of work.

Given that the third digger's work in 10 days is equal to the first digger's work in 14 days, we have the equation:
14x + 28y = 10(14x)
14x + 28y = 140x
28y = 126x
y = 126x/28
y = 9x/2

Substituting the value of y in the equation 2x + 3y = 54:
2x + 3(9x/2) = 54
2x + 27x/2 = 54
4x + 27x = 108
31x = 108
x = 108/31

x ≈ 3.48

Therefore, the first digger digs approximately 3.48 meters per shift, which can be rounded to 3.5 meters per shift or 15 meters in 6 days.

Hence, the correct answer is option A) 15 m.
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Three diggers dug a ditch of 324 m deep in six days working simultaneously. During one shift, the third digger digs as many metres more than the second as the second digs more than the first. The third digger’s work in 10 days is equal to the first digger’s work in 14 days. How many metres does the first digger dig per shift?a)15 mb)18 mc)21 md)27 mCorrect answer is option 'A'. Can you explain this answer?
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