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Two friends A and B take a job for Rs. 8000. Had they worked alone, A would have taken 15 days while B would have taken 40 days. They started working together but after 6 days, A left and B completed the remaining work alone. Find the difference between their share.
- a)Rs. 3200
- b)Rs. 4800
- c)Rs. 1600
- d)Can’t be determined
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Two friends A and B take a job for Rs. 8000. Had they worked alone, A ...
Let the total work be LCM of (15, 40) = 120 units
Efficiency of A = 120/15 = 8 units/days
Efficiency of B = 120/40 = 3 units/days
Now, since they work for different number of days, the amount of Rs. 8000 will be divided in the ratio of units of work done.
Work done by A in 6 days = 6 × 8 = 48 units
Work done by B in 6 days = 6 × 3 = 18 units
Remaining work = 120 – (48 + 18) = 120 – 66 = 54 units
∵ These 54 units of work will be done by B alone.
∴ Total work done by B = 18 + 54 = 72 units
Ratio of work done by A and B = 48 ∶ 72 = 2 ∶ 3
∴ Amount received by A = 8000 × 2/5 = Rs. 3200
And amount received by B = 8000 × 3/5 = Rs. 4800
Required difference = 4800 – 3200 = Rs. 1600
Efficiency of A = 120/15 = 8 units/days
Efficiency of B = 120/40 = 3 units/days
Now, since they work for different number of days, the amount of Rs. 8000 will be divided in the ratio of units of work done.
Work done by A in 6 days = 6 × 8 = 48 units
Work done by B in 6 days = 6 × 3 = 18 units
Remaining work = 120 – (48 + 18) = 120 – 66 = 54 units
∵ These 54 units of work will be done by B alone.
∴ Total work done by B = 18 + 54 = 72 units
Ratio of work done by A and B = 48 ∶ 72 = 2 ∶ 3
∴ Amount received by A = 8000 × 2/5 = Rs. 3200
And amount received by B = 8000 × 3/5 = Rs. 4800
Required difference = 4800 – 3200 = Rs. 1600
Most Upvoted Answer
Two friends A and B take a job for Rs. 8000. Had they worked alone, A ...
To solve this problem, we can first calculate the individual work rates of A and B.
Let's assume that A's work rate is X units per day, and B's work rate is Y units per day.
We are given that A would have taken 15 days to complete the job alone, so we can set up the equation 15X = 1 (where 1 represents the whole job).
Similarly, B would have taken 40 days to complete the job alone, so we can set up the equation 40Y = 1.
Simplifying these equations, we find that X = 1/15 and Y = 1/40.
Now, let's calculate the work done by A and B in the first 6 days.
Since A's work rate is 1/15 units per day, A would have completed 6 * (1/15) = 6/15 = 2/5 of the job.
Similarly, B's work rate is 1/40 units per day, so B would have completed 6 * (1/40) = 6/40 = 3/20 of the job.
Therefore, the remaining work left for B to complete alone is 1 - (2/5 + 3/20) = 1 - 11/20 = 9/20 of the job.
Since B completes the remaining work alone, we can calculate his share of the money as (9/20) * Rs. 8000 = Rs. 3600.
To find A's share, we subtract B's share from the total amount: Rs. 8000 - Rs. 3600 = Rs. 4400.
Therefore, the difference between A's and B's shares is Rs. 4400 - Rs. 3600 = Rs. 800.
Therefore, the correct answer is option a) Rs. 800.
Let's assume that A's work rate is X units per day, and B's work rate is Y units per day.
We are given that A would have taken 15 days to complete the job alone, so we can set up the equation 15X = 1 (where 1 represents the whole job).
Similarly, B would have taken 40 days to complete the job alone, so we can set up the equation 40Y = 1.
Simplifying these equations, we find that X = 1/15 and Y = 1/40.
Now, let's calculate the work done by A and B in the first 6 days.
Since A's work rate is 1/15 units per day, A would have completed 6 * (1/15) = 6/15 = 2/5 of the job.
Similarly, B's work rate is 1/40 units per day, so B would have completed 6 * (1/40) = 6/40 = 3/20 of the job.
Therefore, the remaining work left for B to complete alone is 1 - (2/5 + 3/20) = 1 - 11/20 = 9/20 of the job.
Since B completes the remaining work alone, we can calculate his share of the money as (9/20) * Rs. 8000 = Rs. 3600.
To find A's share, we subtract B's share from the total amount: Rs. 8000 - Rs. 3600 = Rs. 4400.
Therefore, the difference between A's and B's shares is Rs. 4400 - Rs. 3600 = Rs. 800.
Therefore, the correct answer is option a) Rs. 800.
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Two friends A and B take a job for Rs. 8000. Had they worked alone, A would have taken 15 days while B would have taken 40 days. They started working together but after 6 days, A left and B completed the remaining work alone. Find the difference between their share.a)Rs. 3200b)Rs. 4800c)Rs. 1600d)Can’t be determinedCorrect answer is option 'C'. Can you explain this answer?
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Two friends A and B take a job for Rs. 8000. Had they worked alone, A would have taken 15 days while B would have taken 40 days. They started working together but after 6 days, A left and B completed the remaining work alone. Find the difference between their share.a)Rs. 3200b)Rs. 4800c)Rs. 1600d)Can’t be determinedCorrect answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Two friends A and B take a job for Rs. 8000. Had they worked alone, A would have taken 15 days while B would have taken 40 days. They started working together but after 6 days, A left and B completed the remaining work alone. Find the difference between their share.a)Rs. 3200b)Rs. 4800c)Rs. 1600d)Can’t be determinedCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two friends A and B take a job for Rs. 8000. Had they worked alone, A would have taken 15 days while B would have taken 40 days. They started working together but after 6 days, A left and B completed the remaining work alone. Find the difference between their share.a)Rs. 3200b)Rs. 4800c)Rs. 1600d)Can’t be determinedCorrect answer is option 'C'. Can you explain this answer?.
Two friends A and B take a job for Rs. 8000. Had they worked alone, A would have taken 15 days while B would have taken 40 days. They started working together but after 6 days, A left and B completed the remaining work alone. Find the difference between their share.a)Rs. 3200b)Rs. 4800c)Rs. 1600d)Can’t be determinedCorrect answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Two friends A and B take a job for Rs. 8000. Had they worked alone, A would have taken 15 days while B would have taken 40 days. They started working together but after 6 days, A left and B completed the remaining work alone. Find the difference between their share.a)Rs. 3200b)Rs. 4800c)Rs. 1600d)Can’t be determinedCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two friends A and B take a job for Rs. 8000. Had they worked alone, A would have taken 15 days while B would have taken 40 days. They started working together but after 6 days, A left and B completed the remaining work alone. Find the difference between their share.a)Rs. 3200b)Rs. 4800c)Rs. 1600d)Can’t be determinedCorrect answer is option 'C'. Can you explain this answer?.
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