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Solve the following question.
A group of 8 men and 12 boys can complete a piece of work in 12 days. In how many days can a group of 40 men and 45 boys complete a piece of work three times as great, if 16 men can complete as much work in 8 hours as 12 boys can complete in 24 hours? (in days)
Correct answer is '8'. Can you explain this answer?
Verified Answer
Solve the following question.A group of 8 men and 12 boys can complete...
The work done by 16 men in 8 hours can be completed by 16 × 8 men in 1 hour. Similarly, the work done by 12 boys in 24 hours can be completed by 12 × 24 boys in 1 hour. Comparing these values, we realise that 4 men are equivalent to 9 boys.
Now, 8 men and 12 boys is equivalent to 30 boys who can complete the work in 12 days. Similarly, 40 men and 45 boys are equivalent to 135 boys. In n days, these 135 boys must complete a piece of work equivalent to the work done by 30 boys in 36 days. So, 135n = 30 * 36, which yields n = 8 days.
Most Upvoted Answer
Solve the following question.A group of 8 men and 12 boys can complete...
Given Information:
- A group of 8 men and 12 boys can complete a piece of work in 12 days.
- 16 men can complete as much work in 8 hours as 12 boys can complete in 24 hours.
- We need to find the number of days a group of 40 men and 45 boys can complete a piece of work three times as great.
Approach:
- Let's first find the work done by 1 man and 1 boy in 1 day using the first piece of information.
- Then, we can use the second piece of information to form an equation in terms of work done by 1 man and 1 boy.
- Using this equation, we can find the number of days required by 40 men and 45 boys to complete the given work.
Calculation:
- Let's assume that the work to be done is 1 unit.
- From the first piece of information, we can say that:
- 8 men and 12 boys can complete 1 unit of work in 12 days.
- So, in 1 day, 8 men and 12 boys can complete 1/12 units of work.
- We can divide both sides of the equation by 8 to get the work done by 1 man and 1 boy in 1 day.
- 1 man can complete 1/96 units of work in 1 day.
- 1 boy can complete 1/144 units of work in 1 day.
- From the second piece of information, we can say that:
- 16 men can complete as much work in 1 day as 12 boys can complete in 24 hours.
- So, 16 men can complete 1/144 units of work in 1 hour.
- Therefore, 16 men can complete 1/18 units of work in 1 day.
- We can use this information to form an equation in terms of work done by 1 man and 1 boy:
- 16(1/96)M = 12(1/144)B
- Simplifying this equation, we get: M = (3/4)B
- Now, let's use this equation to find the work done by 40 men and 45 boys in 1 day:
- 40M + 45B = 40(3/4)B + 45B = 75B
- So, 40 men and 45 boys can complete 75/144 units of work in 1 day.
- Finally, we can use this information to find the number of days required to complete the given work:
- Let's assume that the given work is W units.
- We need to complete 3W units of work.
- So, the number of days required would be: (3W)/(75/144) = (3W)(144/75) = (12W)/5 = 2.4W
- Since we need the answer in days, we can round up to the nearest integer: 3 days.
Answer:
- The number of days required by 40 men and 45 boys to complete a piece of work three times as great is 3 days.
- However, this is not the correct answer as per the given options.
- Let's try to find the correct
- A group of 8 men and 12 boys can complete a piece of work in 12 days.
- 16 men can complete as much work in 8 hours as 12 boys can complete in 24 hours.
- We need to find the number of days a group of 40 men and 45 boys can complete a piece of work three times as great.
Approach:
- Let's first find the work done by 1 man and 1 boy in 1 day using the first piece of information.
- Then, we can use the second piece of information to form an equation in terms of work done by 1 man and 1 boy.
- Using this equation, we can find the number of days required by 40 men and 45 boys to complete the given work.
Calculation:
- Let's assume that the work to be done is 1 unit.
- From the first piece of information, we can say that:
- 8 men and 12 boys can complete 1 unit of work in 12 days.
- So, in 1 day, 8 men and 12 boys can complete 1/12 units of work.
- We can divide both sides of the equation by 8 to get the work done by 1 man and 1 boy in 1 day.
- 1 man can complete 1/96 units of work in 1 day.
- 1 boy can complete 1/144 units of work in 1 day.
- From the second piece of information, we can say that:
- 16 men can complete as much work in 1 day as 12 boys can complete in 24 hours.
- So, 16 men can complete 1/144 units of work in 1 hour.
- Therefore, 16 men can complete 1/18 units of work in 1 day.
- We can use this information to form an equation in terms of work done by 1 man and 1 boy:
- 16(1/96)M = 12(1/144)B
- Simplifying this equation, we get: M = (3/4)B
- Now, let's use this equation to find the work done by 40 men and 45 boys in 1 day:
- 40M + 45B = 40(3/4)B + 45B = 75B
- So, 40 men and 45 boys can complete 75/144 units of work in 1 day.
- Finally, we can use this information to find the number of days required to complete the given work:
- Let's assume that the given work is W units.
- We need to complete 3W units of work.
- So, the number of days required would be: (3W)/(75/144) = (3W)(144/75) = (12W)/5 = 2.4W
- Since we need the answer in days, we can round up to the nearest integer: 3 days.
Answer:
- The number of days required by 40 men and 45 boys to complete a piece of work three times as great is 3 days.
- However, this is not the correct answer as per the given options.
- Let's try to find the correct
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Solve the following question.A group of 8 men and 12 boys can complete a piece of work in 12 days. In how many days can a group of 40 men and 45 boys complete a piece of work three times as great, if 16 men can complete as much work in 8 hours as 12 boys can complete in 24 hours? (in days)Correct answer is '8'. Can you explain this answer?
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Solve the following question.A group of 8 men and 12 boys can complete a piece of work in 12 days. In how many days can a group of 40 men and 45 boys complete a piece of work three times as great, if 16 men can complete as much work in 8 hours as 12 boys can complete in 24 hours? (in days)Correct answer is '8'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Solve the following question.A group of 8 men and 12 boys can complete a piece of work in 12 days. In how many days can a group of 40 men and 45 boys complete a piece of work three times as great, if 16 men can complete as much work in 8 hours as 12 boys can complete in 24 hours? (in days)Correct answer is '8'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve the following question.A group of 8 men and 12 boys can complete a piece of work in 12 days. In how many days can a group of 40 men and 45 boys complete a piece of work three times as great, if 16 men can complete as much work in 8 hours as 12 boys can complete in 24 hours? (in days)Correct answer is '8'. Can you explain this answer?.
Solve the following question.A group of 8 men and 12 boys can complete a piece of work in 12 days. In how many days can a group of 40 men and 45 boys complete a piece of work three times as great, if 16 men can complete as much work in 8 hours as 12 boys can complete in 24 hours? (in days)Correct answer is '8'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Solve the following question.A group of 8 men and 12 boys can complete a piece of work in 12 days. In how many days can a group of 40 men and 45 boys complete a piece of work three times as great, if 16 men can complete as much work in 8 hours as 12 boys can complete in 24 hours? (in days)Correct answer is '8'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve the following question.A group of 8 men and 12 boys can complete a piece of work in 12 days. In how many days can a group of 40 men and 45 boys complete a piece of work three times as great, if 16 men can complete as much work in 8 hours as 12 boys can complete in 24 hours? (in days)Correct answer is '8'. Can you explain this answer?.
Solutions for Solve the following question.A group of 8 men and 12 boys can complete a piece of work in 12 days. In how many days can a group of 40 men and 45 boys complete a piece of work three times as great, if 16 men can complete as much work in 8 hours as 12 boys can complete in 24 hours? (in days)Correct answer is '8'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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