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Question 2 - A is twice as efficient as B and can complete a job 30 days before B. In how much they
can complete the job together?
Solution - Let efficiency percentage as x
A's efficiency = 2x and B's efficiency = x
A is twice efficient and can complete the job 30 days before B. So,
A can complete the job in 30 days and B can complete the job in 60 days
A's efficiency = 1/30 = 3.33%
B's efficiency = 1/60 = 1.66%
Both can do 5% (3.33% + 1.66%) of the job in 1 day.
So the can complete the whole job in 20 days (100/5)
Question 3 - A tank can be filled in 20 minutes. There is a leakage which can empty it in 60 minutes.
In how many minutes tank can be filled?
Solution - Method 1
⇒ Efficiency of filling pipe = 20 minutes = 1/3 hour = 300%
⇒ Efficiency of leakage = 60 minutes = 100%
We need to deduct efficiency of leakage so final efficiency is 200%. We are taking 100% = 1 Hour as
base so answer is 30 minutes.
Method 2
⇒ Efficiency of filling pipe = 100/20 = 5%
⇒ Efficiency of leakage pipe = 100/60 = 1.66%
⇒ Net filling efficiency = 3.33%
So, tank can be filled in = 100/3.33% = 30 minutes
You can change the base to minutes or even seconds.
Question 4 - 4 men and 6 women working together can complete the work within 10 days. 3 men
and 7 women working together will complete the same work within 8 days. In how many days 10
women will complete this work?
Solution - Let number of men =x, number of women = y
⇒ Efficiency of 4 men and 6 women = 100/10 = 10%
⇒ So, 4x+6y = 10
Above equation means 4 men and 6 women can do 10% of a the job in one day.
⇒ Efficiency of 3 men and 7 women = 100/8 = 12.5%
So, 3x+7y = 12.5
By solving both equations we get, x = -0.5 and y = 2
⇒ Efficiency of 1 woman(y) = 2% per day
⇒ Efficiency of 10 women per day = 20%
So 10 women can complete the job in 100/20 = 5 days
Question 2 - A is twice as efficient as B and can complete a job 30 days before B. In how much they
can complete the job together?
Solution - Let efficiency percentage as x
A's efficiency = 2x and B's efficiency = x
A is twice efficient and can complete the job 30 days before B. So,
A can complete the job in 30 days and B can complete the job in 60 days
A's efficiency = 1/30 = 3.33%
B's efficiency = 1/60 = 1.66%
Both can do 5% (3.33% + 1.66%) of the job in 1 day.
So the can complete the whole job in 20 days (100/5)
Question 3 - A tank can be filled in 20 minutes. There is a leakage which can empty it in 60 minutes.
In how many minutes tank can be filled?
Solution - Method 1
⇒ Efficiency of filling pipe = 20 minutes = 1/3 hour = 300%
⇒ Efficiency of leakage = 60 minutes = 100%
We need to deduct efficiency of leakage so final efficiency is 200%. We are taking 100% = 1 Hour as
base so answer is 30 minutes.
Method 2
⇒ Efficiency of filling pipe = 100/20 = 5%
⇒ Efficiency of leakage pipe = 100/60 = 1.66%
⇒ Net filling efficiency = 3.33%
So, tank can be filled in = 100/3.33% = 30 minutes
You can change the base to minutes or even seconds.
Question 4 - 4 men and 6 women working together can complete the work within 10 days. 3 men
and 7 women working together will complete the same work within 8 days. In how many days 10
women will complete this work?
Solution - Let number of men =x, number of women = y
⇒ Efficiency of 4 men and 6 women = 100/10 = 10%
⇒ So, 4x+6y = 10
Above equation means 4 men and 6 women can do 10% of a the job in one day.
⇒ Efficiency of 3 men and 7 women = 100/8 = 12.5%
So, 3x+7y = 12.5
By solving both equations we get, x = -0.5 and y = 2
⇒ Efficiency of 1 woman(y) = 2% per day
⇒ Efficiency of 10 women per day = 20%
So 10 women can complete the job in 100/20 = 5 days
