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A and B can do a piece of work for Rs.800. A alone can do it in 8 days while B alone can do it in 12 days. With help of C, they finish it in 4 days. Find the ratio of share of B and C.
- a)5 : 4
- b)3 : 4
- c)1 : 5
- d)2 : 1
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A and B can do a piece of work for Rs.800. A alone can do it in 8 days...
From the given data,
A’s one day’s work = 1/8
B’s one day’s work = 1/12
C’s one day’s work = ¼ - (1/8 + 1/12) = 1/24
∴ A : B : C = ratio of their 1 day’s work = 1/8 : 1/12 : 1/24 = 3 : 2 : 1
∴ ratio of share of B and C = 2 : 1
A’s one day’s work = 1/8
B’s one day’s work = 1/12
C’s one day’s work = ¼ - (1/8 + 1/12) = 1/24
∴ A : B : C = ratio of their 1 day’s work = 1/8 : 1/12 : 1/24 = 3 : 2 : 1
∴ ratio of share of B and C = 2 : 1
Most Upvoted Answer
A and B can do a piece of work for Rs.800. A alone can do it in 8 days...
Given:
A+B = Rs.800
A alone can do the work in 8 days
B alone can do the work in 12 days
A+B+C = Rs.800 and they finish the work in 4 days
To find: The ratio of share of B and C
Let the efficiency of A be x
Then, the efficiency of B will be (2/3)x (since B takes 12 days to do the work that A takes 8 days to do, B's efficiency is 2/3 of A's efficiency)
Let the efficiency of C be y
Efficiency formula: Efficiency = Work done / Time taken
Using the above formula, we can write the following equations:
x + (2/3)x + y = 1 (Work done is 1 unit)
x(8) + (2/3)x(12) + y(4) = 1 (Total work done is 1 unit and it is completed in 4 days)
Solving the above equations, we get:
x = 1/24
y = 1/8
(2/3)x = 1/36
Share of B = (2/3)x * 800 = (1/36) * 800 = Rs.22.22
Share of C = y * 800 = (1/8) * 800 = Rs.100
Ratio of share of B and C = 22.22/100 = 2:1
Therefore, the correct answer is option D, 2:1.
A+B = Rs.800
A alone can do the work in 8 days
B alone can do the work in 12 days
A+B+C = Rs.800 and they finish the work in 4 days
To find: The ratio of share of B and C
Let the efficiency of A be x
Then, the efficiency of B will be (2/3)x (since B takes 12 days to do the work that A takes 8 days to do, B's efficiency is 2/3 of A's efficiency)
Let the efficiency of C be y
Efficiency formula: Efficiency = Work done / Time taken
Using the above formula, we can write the following equations:
x + (2/3)x + y = 1 (Work done is 1 unit)
x(8) + (2/3)x(12) + y(4) = 1 (Total work done is 1 unit and it is completed in 4 days)
Solving the above equations, we get:
x = 1/24
y = 1/8
(2/3)x = 1/36
Share of B = (2/3)x * 800 = (1/36) * 800 = Rs.22.22
Share of C = y * 800 = (1/8) * 800 = Rs.100
Ratio of share of B and C = 22.22/100 = 2:1
Therefore, the correct answer is option D, 2:1.
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A and B can do a piece of work for Rs.800. A alone can do it in 8 days while B alone can do it in 12 days. With help of C, they finish it in 4 days. Find the ratio of share of B and C.a)5 : 4b)3 : 4c)1 : 5d)2 : 1Correct answer is option 'D'. Can you explain this answer?
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