Select the correct answerThe labourers A, B, C were given a contract of Rs.750 for doing a certain piece of work. All the three together can finish the work in 8 days. A and C together can do it in 12 days, while A and B together can do it in 13 1/3 days. The money will be divided in the ratio?Options4 : 7 : 54 : 5 : 65 : 7 : 45 : 6 : 8
Question
Select the correct answerThe labourers A, B, C were given a contract of Rs.750 for doing a certain piece of work. All the three together can finish the work in 8 days. A and C together can do it in 12 days, while A and B together can do it in 13 1/3 days. The money will be divided in the ratio?Options4 : 7 : 54 : 5 : 65 : 7 : 45 : 6 : 8
Solution
To solve this problem, we first need to find out how much work each labourer can do in a day.
- All three labourers together can finish the work in 8 days. So, their combined work rate is 1/8 of the work per day.
- A and C together can do the work in 12 days. So, their combined work rate is 1/12 of the work per day.
- A and B together can do the work in 13 1/3 days. So, their combined work rate is 3/40 of the work per day.
Now, we can set up equations to find out the individual work rates of A, B, and C.
Let's denote the work rates of A, B, and C as a, b, and c respectively.
From the given information, we have the following equations:
a + b + c = 1/8 (equation 1) a + c = 1/12 (equation 2) a + b = 3/40 (equation 3)
Subtract equation 2 from equation 1, we get b = 1/8 - 1/12 = 1/24. Subtract equation 3 from equation 1, we get c = 1/8 - 3/40 = 1/30. Substitute b and c into equation 2, we get a = 1/12 - 1/30 = 3/60 = 1/20.
So, the work rates of A, B, and C are 1/20, 1/24, and 1/30 respectively.
The ratio of their work rates is the same as the ratio of the money they will get.
To find the ratio, we need to find the least common multiple (LCM) of 20, 24, and 30. The LCM is 120.
So, the ratio of the money A, B, and C will get is 120/20 : 120/24 : 120/30 = 6 : 5 : 4.
Therefore, the correct answer is 6 : 5 : 4.
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