10. A, B and C together can do a piece of work in 15 days, B alone can do it in 30 days
and C alone can do it in 40 days. In how many days will A alone do the work?
4
can lough a field in 4 = days. A and C together can do
Answers
Answer:
You want to accomplish a piece of work… you need to do x work.
15A + 15B + 15C = x
30B = x
40C = x
We can set this up as an easy matrix:
[15 15 15 | 1
0 30 0 | 1
0 0 40 | 1]
It's easiest to convert as many things on the LHS to 1 as possible:
[1 1 1 | 1/15
0 1 0 | 1/30
0 0 1 | 1/40]
Then we subtract the bottom rows from the top rows
[1 0 0 | 1/15 - 1/30 - 1/40
0 1 0 | 1/30
0 0 1 | 1/40]
[1 0 0 | 8/120 - 4/120 - 3/120
0 1 0 | 1/30
0 0 1 | 1/40]
[1 0 0 | 1/120
0 1 0 | 1/30
0 0 1 | 1/40]
Then lastly convert the the RHS to 1 on the row where A is solved
[120 0 0 | 1
0 1 0 | 1/30
0 0 1 | 1/40]
Thus it takes 120 hours for A to do the work alone.
A+B+C=15 DAYS
B IN 30 DAYS i.e. in 1 day he can finish work/30(x/30)
C IN 40 DAYS i.e. in 1 day x/40
A+B+C=15 DAYS i.e. in 1 day x/15
A’s work per day taken as ‘y’
A+B+C=15
y+x/30+x/40=x/15
y+7x/120 (LCM OF x/30 +x/40)=x/15
y=x/15–7x/120
y=8x-7x/120
y=x/120
so by A in 1 day work can done is x/120
it takes 120 days to do work to A
hope this helps you... plzz Mark as BRAINLIEST answer❤
Explanation:
10)
work done by A b and C in 1 day= 1/15
work done by b in one day= 1/30
work done by c in one day=1/40
therefore, the work done by a= 1/15-(1/30+1/40)
=1/15-(4 + 3/120)
=1/15-7/120
=8-7/120
=1/120
therefore, A alone can do the work in 120 days
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