ravi can do a piece of work in 10 days and kamala can do the same work in 16 days.with the help of reeta,they do the work in 4 days only.in how many days can reeta do the work alone?
Answers
Answer:
let we have like this
A can do a piece of work in 24 days while B alone can do it in 16 days. With the help of C, they finish the work in 8 days. In how many days can C do the work alone?
Step-by-step explanation:
A can do a piece of work in 24 days while B alone can do it in 16 days. With the help of C, they finish the work in 8 days. In how many days can C do the work alone?
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A finishes work W in 24 days
B finishes work W in 16 days
C finishes work W in x days
Together they complete work in 8 days.
What is the rate of work that A, B & C can complete?
A’s rate is W/24 days (Work per day)
B’s rate is W/16 days
C’s rate is W/x days
When A, B & C work together, their rates get added (unless they get in each other’s way!), since there are more people doing more work per day than before.
Therefore the number of days taken to complete work W when A, B & C work together is W/(A’s rate + B’s rate + C’s rate)
We know the number of days taken for them to complete wor together is 8 days.
Therefore:
8 = W/(W/24 + W/16 + W/x) , or
8 = W/(W *16*24 + W*24*x + W*16*x)/24*16*x
or 8 = 384*x/(384 + 40*x)
or 384*8 + 40*8*x = 384*x
or 3072 = 64*x
or x = 48 days
Therefore C would take 48 days to complete the work alone.
hope it's helpful