Working at their normal constant rates, 20 diggers can dig a 100-meter long trench in hard soil in 3 days. A constructio

[M7MBA]

Working at their normal constant rates, 20 diggers can dig a 100-meter long trench in hard soil in 3 days. A construction company ordered the diggers to dig a 180-meter long trench in soft soil. If diggers can work 20% faster in soft soil than in hard soil, how many diggers are required to complete this task in 3 days?

A. 25
B. 28
C. 29
D. 30
E. 32

Answer: D

Source: GMAT Club Tests

[Scott@TargetTestPrep]

Working at their normal constant rates, 20 diggers can dig a 100-meter long trench in hard soil in 3 days. A construction company ordered the diggers to dig a 180-meter long trench in soft soil. If diggers can work 20% faster in soft soil than in hard soil, how many diggers are required to complete this task in 3 days?

A. 25
B. 28
C. 29
D. 30
E. 32

Answer: D

Source: GMAT Club Tests

Solution:

Since 20 diggers can dig a 100-meter long trench in hard soil in 3 days, 1 digger can dig a 100/20 = 5 meter trench in 3 days. So the rate of 1 digger is 5/3 meters per day in hard soil. Since digging in soft soil is 20% faster, the rate of 1 digger is 5/3 x 1.2 = 6/3 = 2 meters per day in soft soil. So 1 digger can dig 2 x 3 = 6 meters in 3 days in soft soil. Since a 180-meter long trench in soft soil needs to be dug,the company needs 180/6 = 30 diggers to do the job in 3 days.

Answer: D