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8 girls and 12 boys can finish work in 10 days while 6 girls and 8 boys can finish it in 14 days. Find the time taken by the one girl alone that by one boy alone to finish the work.
- a)120, 130
- b)140,280
- c)240,280
- d)100,120
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
8 girls and 12 boys can finish work in 10 days while 6 girls and 8 boy...
Work done by 1 girl and 1 boy in x and y days respectively.
work done by 1 girl and 1 boy in 1 day is (1/x) and (1/y).
so, work done by 8 girls and 12 boys in 1 day is (8/x) + (12/y) = 1/10
let (1/x) = a and (1/y) = b
so, 8a + 12b = 1/10
→ 80a + 120b = 1 ---- (1)
work done by 6 girls and 8 boys in 1 day is (6/x) + (8/y) = 1/14
6a + 80 = 1/14
→ 84a + 112b = 1 ---- (2)
By elimination method, Multiple equation 1 by 21 on both sides, we get
1680a + 2520b = 21 ---- (3)
Multiply equation 2 by 20 on both sides, we get
1680a + 2240b = 20 ---- (4)
On solving equation 3 and 4, we get
2520 b - 2240b = 21 - 20
→ 280 b = 1
→ b = 1/280
b =1/y
→ 1/280 = 1/y
→ y = 280
80a + 120 x (1/280) = 1 (From 1)
→ 80a + (3/7) = 1
→ 80a = 1 - (3/7)
→ 80a = (7 - 3)/7
→ 80a = 4/7
→ a = 4/(7 × 80)
→ a = 1/140
→ a = 1/x
→ 1/140 = 1/x
→ x = 140
1 girl and 1 boy alone take 140 days and 280 days to complete a work.
Most Upvoted Answer
8 girls and 12 boys can finish work in 10 days while 6 girls and 8 boy...
Given data:
- 8 girls and 12 boys can finish work in 10 days.
- 6 girls and 8 boys can finish it in 14 days.
Let's assume that the work requires a certain amount of effort, which we can measure in terms of "work units".
Let the total work be represented by W. Then,
- In the first case, 8 girls and 12 boys complete the work in 10 days. So, their combined rate of work is:
Rate of work of 1 girl + Rate of work of 1 boy = W / (8 x 10) + W / (12 x 10)
- In the second case, 6 girls and 8 boys complete the same work in 14 days. So, their combined rate of work is:
Rate of work of 1 girl + Rate of work of 1 boy = W / (6 x 14) + W / (8 x 14)
Since the amount of work is the same in both cases, we can equate the two expressions for the combined rate of work:
W / (8 x 10) + W / (12 x 10) = W / (6 x 14) + W / (8 x 14)
Simplifying this equation, we get:
3W / 240 + 2W / 240 = W / 168 + W / 224
Multiplying both sides by the LCM of the denominators (which is 1680), we get:
21W + 14W = 10W + 12W
25W = 22W
W = 0
This implies that the work cannot be completed at all, which is clearly not possible. Therefore, there must be an error in the data given.
However, let's assume that there is a typo in the question, and the second case should be "4 girls and 8 boys can finish it in 14 days". Then, we can proceed as follows:
- In the first case, the combined rate of work of 8 girls and 12 boys is:
Rate of work of 1 girl + Rate of work of 1 boy = W / (8 x 10) + W / (12 x 10)
Simplifying this, we get:
Rate of work of 1 girl + Rate of work of 1 boy = W / 80
- In the second case, the combined rate of work of 4 girls and 8 boys is:
Rate of work of 1 girl + Rate of work of 1 boy = W / (4 x 14) + W / (8 x 14)
Simplifying this, we get:
Rate of work of 1 girl + Rate of work of 1 boy = W / 56
Now, we can set up two equations:
- For the rate of work of girls:
8 x (Rate of work of 1 girl + Rate of work of 1 boy) = 6 x (Rate of work of 1 girl + Rate of work of 1 boy)
Simplifying this, we get:
2(Rate of work of 1 girl + Rate of work of 1 boy) = Rate of work
- 8 girls and 12 boys can finish work in 10 days.
- 6 girls and 8 boys can finish it in 14 days.
Let's assume that the work requires a certain amount of effort, which we can measure in terms of "work units".
Let the total work be represented by W. Then,
- In the first case, 8 girls and 12 boys complete the work in 10 days. So, their combined rate of work is:
Rate of work of 1 girl + Rate of work of 1 boy = W / (8 x 10) + W / (12 x 10)
- In the second case, 6 girls and 8 boys complete the same work in 14 days. So, their combined rate of work is:
Rate of work of 1 girl + Rate of work of 1 boy = W / (6 x 14) + W / (8 x 14)
Since the amount of work is the same in both cases, we can equate the two expressions for the combined rate of work:
W / (8 x 10) + W / (12 x 10) = W / (6 x 14) + W / (8 x 14)
Simplifying this equation, we get:
3W / 240 + 2W / 240 = W / 168 + W / 224
Multiplying both sides by the LCM of the denominators (which is 1680), we get:
21W + 14W = 10W + 12W
25W = 22W
W = 0
This implies that the work cannot be completed at all, which is clearly not possible. Therefore, there must be an error in the data given.
However, let's assume that there is a typo in the question, and the second case should be "4 girls and 8 boys can finish it in 14 days". Then, we can proceed as follows:
- In the first case, the combined rate of work of 8 girls and 12 boys is:
Rate of work of 1 girl + Rate of work of 1 boy = W / (8 x 10) + W / (12 x 10)
Simplifying this, we get:
Rate of work of 1 girl + Rate of work of 1 boy = W / 80
- In the second case, the combined rate of work of 4 girls and 8 boys is:
Rate of work of 1 girl + Rate of work of 1 boy = W / (4 x 14) + W / (8 x 14)
Simplifying this, we get:
Rate of work of 1 girl + Rate of work of 1 boy = W / 56
Now, we can set up two equations:
- For the rate of work of girls:
8 x (Rate of work of 1 girl + Rate of work of 1 boy) = 6 x (Rate of work of 1 girl + Rate of work of 1 boy)
Simplifying this, we get:
2(Rate of work of 1 girl + Rate of work of 1 boy) = Rate of work
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8 girls and 12 boys can finish work in 10 days while 6 girls and 8 boys can finish it in 14 days. Find the time taken by the one girl alone that by one boy alone to finish the work.a)120, 130b)140,280c)240,280d)100,120Correct answer is option 'B'. Can you explain this answer?
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