A can do a piece of work in 4 days. B can do it in 5 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?a.4 daysb.5 daysc.20 daysd.10 days
Question
A can do a piece of work in 4 days. B can do it in 5 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?a.4 daysb.5 daysc.20 daysd.10 days
Solution
To solve this problem, we first need to understand the concept of work and rate. The rate of work is the amount of work that can be done in a certain amount of time.
Step 1: Find the rate of A and B A can do the work in 4 days, so A's rate is 1/4 of the work per day. B can do the work in 5 days, so B's rate is 1/5 of the work per day.
Step 2: Find the combined rate of A, B, and C A, B, and C together can do the work in 2 days, so their combined rate is 1/2 of the work per day.
Step 3: Find the rate of C We know that the combined rate of A, B, and C is the sum of their individual rates. So, we can find C's rate by subtracting A and B's rates from the combined rate. C's rate = (A, B, and C's rate) - (A's rate + B's rate) = (1/2) - (1/4 + 1/5) = 1/2 - 9/20 = 1/20 of the work per day.
Step 4: Find the time C can do the work alone The time it takes for C to do the work alone is the reciprocal of C's rate, which is 20 days.
So, the answer is c. 20 days.
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