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A and B undertake to complete a piece of work for Rupees 1200. A can do it in 8 days, B can do it in 12 days and with the help of C they complete the work in 4 days. Find the share of C?
- a)100
- b)200
- c)300
- d)400
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A and B undertake to complete a piece of work for Rupees 1200. A can d...
1/8 + 1/12 + 1/C = 1/4, we get C = 24 days
now efficiency of A, B and C are in the ratio of 1/8 :1/12 : 1/24
3:2:1, so share of C is 1/6 * 1200 = 200
now efficiency of A, B and C are in the ratio of 1/8 :1/12 : 1/24
3:2:1, so share of C is 1/6 * 1200 = 200
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A and B undertake to complete a piece of work for Rupees 1200. A can d...
Given:
Total work = Rs. 1200
A's efficiency = 1/8
B's efficiency = 1/12
(A+B+C)'s efficiency = 1/4
Let C's efficiency be x.
Calculation:
We know that work done = efficiency * time
According to the question,
A completes the work in 8 days.
Therefore, A's efficiency = 1/8.
Hence, A can complete the work in 1 day = 1/8.
Similarly,
B completes the work in 12 days.
Therefore, B's efficiency = 1/12.
Hence, B can complete the work in 1 day = 1/12.
Now, with the help of C, they complete the work in 4 days.
Therefore, (A+B+C)'s efficiency = 1/4.
i.e., A's efficiency + B's efficiency + C's efficiency = 1/4
1/8 + 1/12 + x = 1/4
x = 1/4 - 1/8 - 1/12
x = 1/24
Thus, C's efficiency = 1/24.
Hence, C can complete the work in 1 day = 1/24.
Let the share of C be x.
Then, the ratio of the work done by A, B, and C will be:
A:B:C = 1/8 : 1/12 : 1/24
Simplifying, we get:
A:B:C = 3:2:1
Therefore, C's share will be:
C's share = (1/6) * Total work
C's share = (1/6) * 1200
C's share = 200
Hence, the share of C is Rs. 200. Therefore, the correct answer is option B.
Total work = Rs. 1200
A's efficiency = 1/8
B's efficiency = 1/12
(A+B+C)'s efficiency = 1/4
Let C's efficiency be x.
Calculation:
We know that work done = efficiency * time
According to the question,
A completes the work in 8 days.
Therefore, A's efficiency = 1/8.
Hence, A can complete the work in 1 day = 1/8.
Similarly,
B completes the work in 12 days.
Therefore, B's efficiency = 1/12.
Hence, B can complete the work in 1 day = 1/12.
Now, with the help of C, they complete the work in 4 days.
Therefore, (A+B+C)'s efficiency = 1/4.
i.e., A's efficiency + B's efficiency + C's efficiency = 1/4
1/8 + 1/12 + x = 1/4
x = 1/4 - 1/8 - 1/12
x = 1/24
Thus, C's efficiency = 1/24.
Hence, C can complete the work in 1 day = 1/24.
Let the share of C be x.
Then, the ratio of the work done by A, B, and C will be:
A:B:C = 1/8 : 1/12 : 1/24
Simplifying, we get:
A:B:C = 3:2:1
Therefore, C's share will be:
C's share = (1/6) * Total work
C's share = (1/6) * 1200
C's share = 200
Hence, the share of C is Rs. 200. Therefore, the correct answer is option B.
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A and B undertake to complete a piece of work for Rupees 1200. A can do it in 8 days, B can do it in 12 days and with the help of C they complete the work in 4 days. Find the share of C?a)100b)200c)300d)400e)None of theseCorrect answer is option 'B'. Can you explain this answer?
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