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If 4 boys or 5 women can reap a field in 20 days. Then what will be the time taken by 6 boys and 8 women to reap the field.
- a)200/33 days
- b)200/31 days
- c)200/35 days
- d)200/37 days
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If 4 boys or 5 women can reap a field in 20 days. Then what will be th...
work done by one boy in one day = 1/(4*20) Similarly for women = 1/(5*20) Now the time taken by 6 boys and 8 women to reap the field = 6/80 + 8/100 = 1/d (d = 200/31 will be the answer)
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If 4 boys or 5 women can reap a field in 20 days. Then what will be th...
Given data:
4 boys or 5 women can reap a field in 20 days.
Let's assume that the efficiency of 1 boy in reaping the field is 'x' and the efficiency of 1 woman in reaping the field is 'y'. Then we can write:
Efficiency of 4 boys = 4x
Efficiency of 5 women = 5y
According to the question, these two groups can reap the field in 20 days. So, we can write:
4x * 20 = 5y * 20
=> 4x = 5y
=> x/y = 5/4
Now, we need to find the time taken by 6 boys and 8 women to reap the field. Let's assume that it takes 't' days for them to do so. Then we can write:
Efficiency of 6 boys = 6x
Efficiency of 8 women = 8y
Total efficiency of the group = 6x + 8y
According to the question, this group can reap the field in 't' days. So, we can write:
(6x + 8y) * t = 1
=> 6xt + 8yt = 1
=> 6xt + 8xt*(5/4) = 1 (Substituting x/y = 5/4)
=> 6xt + 10xt = 1
=> 16xt = 1
=> t = 1/16
Therefore, the time taken by 6 boys and 8 women to reap the field is 1/16 days, which is equal to 200/16 = 25/2 = 12.5 days.
Hence, option B (200/31 days) is the correct answer.
4 boys or 5 women can reap a field in 20 days.
Let's assume that the efficiency of 1 boy in reaping the field is 'x' and the efficiency of 1 woman in reaping the field is 'y'. Then we can write:
Efficiency of 4 boys = 4x
Efficiency of 5 women = 5y
According to the question, these two groups can reap the field in 20 days. So, we can write:
4x * 20 = 5y * 20
=> 4x = 5y
=> x/y = 5/4
Now, we need to find the time taken by 6 boys and 8 women to reap the field. Let's assume that it takes 't' days for them to do so. Then we can write:
Efficiency of 6 boys = 6x
Efficiency of 8 women = 8y
Total efficiency of the group = 6x + 8y
According to the question, this group can reap the field in 't' days. So, we can write:
(6x + 8y) * t = 1
=> 6xt + 8yt = 1
=> 6xt + 8xt*(5/4) = 1 (Substituting x/y = 5/4)
=> 6xt + 10xt = 1
=> 16xt = 1
=> t = 1/16
Therefore, the time taken by 6 boys and 8 women to reap the field is 1/16 days, which is equal to 200/16 = 25/2 = 12.5 days.
Hence, option B (200/31 days) is the correct answer.
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