A can do a certain work in 30 days. B is 25% more efficient than A, and C is 20% more efficient than B. A and B work together for 10 days. C alone completes the remaining work in x days. the value of x is
Assuming by "more efficient" you mean that he has a better rate.
Let the job to be done be 1 units of work
Let A's rate be 1/30
then B's rate is 1.25(1/30) = 1.25/30 = 1/24
C's rare is 1.2(1.25/30) = 1/20
combined rate of A and B = 1/30 + 1/24 = 3/40
working for 10 days, work done is 10(3/40) = 3/4
work remaining to be done = 1 - 3/4 = 1/3
time taken by C = x
x = (1/3) / (1/20) = 20/3 days or 6 2/3 days
It should be 1/4 รท 1/20 ??????
Of course, it was a carry-over-typo
Sorry about that.
To find the value of x, we need to determine the combined efficiency of A and B in the first 10 days and then calculate how much work is left for C to complete.
Let's start by finding the efficiency of A and B.
Since A can complete the work in 30 days, his efficiency would be 1/30 of the work per day.
B is 25% more efficient than A, so his efficiency would be 1/30 * (1 + 25%) = 1/30 * 1.25 = 5/150 = 1/30 * 5/6 = 1/36 of the work per day.
Now, let's calculate how much work A and B complete together in 10 days.
Combined efficiency of A and B = Efficiency of A + Efficiency of B = 1/30 + 1/36 = 6/180 + 5/180 = 11/180 of the work per day.
Together, A and B complete 11/180 * 10 = 11/18 of the work in the first 10 days.
Now, we calculate how much work is left for C to complete.
Since C is 20% more efficient than B, his efficiency would be 1/36 * (1 + 20%) = 1/36 * 1.2 = 6/216 = 1/36 * 6/9 = 1/54 of the work per day.
Therefore, the work left for C to complete is 1 - 11/18 = 7/18.
Now, we can determine the value of x by finding how many days C would take to complete 7/18 of the work.
Efficiency of C = 1/54 of the work per day.
Let x be the number of days C takes to complete the remaining work.
Therefore, x * (1/54) = 7/18.
To solve for x, we multiply both sides of the equation by 54:
x = (7/18) * 54 = 7 * 3 = 21.
So, the value of x is 21 days.