Please guide me to solve the below problem:
'A'an do 2/3 of a work in 40 days.'B'can do 1/2 of the work in 75 days.'C'can do 3/4of work in 75 days.If all them together work in how many days will they do 5/6 0f the work.
I had solved the above problem like this:
A can do the work=3/2*40=60 days.
A's one day work =1/60
B can do the work=2/1*75=150 days
B's one day work=1/150
C can do the work=4/3*75=100 days.
C's one day the work=1/100
They together=1/60+1/150+1/100
=5+2+3/100
=10/300=1/30
They complete the 5/6 of the work =1/30*5/6
=1/36
Therefore ,they complete the 5/6 of the work in 36 days.
Here is another way:
rate=rate1+rate2+rate3
= W/60+W/150+W/100= W(5+2+3)/300
= W/30 check same as yours.
So time= amountwork/rate= 5W/6 /(W/30)
time= 150/6=25 days
So our answers are different, check mine, then yours.I don't agree with how you get 1/36, time= work/rate, not multiplied
To solve the problem, you need to calculate the individual work rates of A, B, and C. Then you can find their combined work rate and use that to determine how many days it would take them to complete 5/6 of the work.
Let's break down the calculations step by step:
1. First, calculate how long it takes A to complete the entire work:
A can do 2/3 of the work in 40 days.
So, if 2/3 of the work takes 40 days, then the entire work will take (40 * 3/2) = 60 days.
Therefore, A can complete the work in 60 days.
2. Next, calculate A's work rate per day:
To find A's work rate per day, divide the work completed (1) by the number of days (60):
A's one day work = 1 / 60.
3. Repeat the same calculations for B and C:
B can do 1/2 of the work in 75 days.
So, B can complete the work in (75 * 2/1) = 150 days.
B's one day work = 1 / 150.
C can do 3/4 of the work in 75 days.
So, C can complete the work in (75 * 4/3) = 100 days.
C's one day work = 1 / 100.
4. Find their combined work rate:
To find the combined work rate, add the individual work rates of A, B, and C:
Combined work rate = A's one day work + B's one day work + C's one day work.
5. Calculate the time taken to complete 5/6 of the work:
To find how many days it takes to complete 5/6 of the work, divide 5/6 by the combined work rate:
Time taken = (5/6) / Combined work rate.
Plugging in the values:
Combined work rate = 1/60 + 1/150 + 1/100
= (5 + 2 + 3) / 300
= 10/300
= 1/30
Time taken = (5/6) / (1/30)
= (5/6) * (30/1)
= 5 * 5
= 25
Therefore, they will complete 5/6 of the work in 25 days.