A and B can dig a trench in 6 days. If A alone can do it in 10 days, how long would B alone take to do it?
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Question:
A and B can dig a trench in 6 days. If A alone can do it in 10 days , how long would B alone take to do it ?
Answer:
15 days
Solution:
Let the time taken by B to dig the trench alone be x days.
Thus,
One day work of B = 1/x work
Also,
It is given that ,
The time taken by A to dig the trench alone is 10 days.
Thus,
One day work of B = 1/10 work
Also,
It is said that,
A and B can dig the trench in 6 days.
Thus,
=> One day work of A and B together
= 1/6
=> One day work of A
+ One day work of B = 1/6
=> 1/10 + 1/x = 1/6
=> (x + 10)/10x = 1/6
=> 6(x + 10) = 10x
=> 6x + 60 = 10x
=> 10x - 6x = 60
=> 4x = 60
=> x = 60/4
=> x = 15
Hence,
B can dig the trench alone in 15 days.
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