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A and B working together can finish a piece of work in 12 days while B alone can finish it in 30 days. In how many days can A alone finish the work?
- a)18 days
- b)20 days
- c)24 days
- d)25 days
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A and B working together can finish a piece of work in 12 days while B...
Let total units of work = 60 units (LCM of 12 and 30)
∴ Efficiency of (A + B) = 60/12 = 5
And Efficiency of B = 60/30 = 2
∴ Efficiency of A = 5 – 2 = 3
∴ Time taken by A alone to finish the work = 60/3 = 20 days
∴ Efficiency of (A + B) = 60/12 = 5
And Efficiency of B = 60/30 = 2
∴ Efficiency of A = 5 – 2 = 3
∴ Time taken by A alone to finish the work = 60/3 = 20 days
Most Upvoted Answer
A and B working together can finish a piece of work in 12 days while B...
To solve this problem, we can use the concept of work rates. Let's denote the work rate of A as "a" (meaning A can complete "a" units of work per day) and the work rate of B as "b" (meaning B can complete "b" units of work per day).
We are given that A and B can finish the work together in 12 days, so their combined work rate is 1/12 of the work per day. This can be expressed as:
1/12 = a + b
We are also given that B alone can finish the work in 30 days, so B's work rate is 1/30 of the work per day. This can be expressed as:
1/30 = b
Now we have two equations with two unknowns (a and b). We can solve this system of equations to find the values of a and b.
Solving the second equation for b, we have:
b = 1/30
Substituting this value of b into the first equation, we have:
1/12 = a + 1/30
To simplify the equation, we can find a common denominator of 12 and 30, which is 60. Multiplying both sides of the equation by 60, we get:
5 = 60a + 2
Subtracting 2 from both sides of the equation, we have:
3 = 60a
Dividing both sides of the equation by 60, we get:
a = 3/60 = 1/20
Therefore, A's work rate is 1/20 of the work per day, meaning A can complete 1/20 of the work in one day. To find out how many days it will take for A to complete the work alone, we can invert A's work rate:
1 day = 1/20 of the work
20 days = 1 work
So, A alone can finish the work in 20 days. Therefore, the correct answer is option B.
We are given that A and B can finish the work together in 12 days, so their combined work rate is 1/12 of the work per day. This can be expressed as:
1/12 = a + b
We are also given that B alone can finish the work in 30 days, so B's work rate is 1/30 of the work per day. This can be expressed as:
1/30 = b
Now we have two equations with two unknowns (a and b). We can solve this system of equations to find the values of a and b.
Solving the second equation for b, we have:
b = 1/30
Substituting this value of b into the first equation, we have:
1/12 = a + 1/30
To simplify the equation, we can find a common denominator of 12 and 30, which is 60. Multiplying both sides of the equation by 60, we get:
5 = 60a + 2
Subtracting 2 from both sides of the equation, we have:
3 = 60a
Dividing both sides of the equation by 60, we get:
a = 3/60 = 1/20
Therefore, A's work rate is 1/20 of the work per day, meaning A can complete 1/20 of the work in one day. To find out how many days it will take for A to complete the work alone, we can invert A's work rate:
1 day = 1/20 of the work
20 days = 1 work
So, A alone can finish the work in 20 days. Therefore, the correct answer is option B.
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