16. A and B can do some work in 10 days. B and C can do the same work in 20 days and A and C together can do it in 12 days. How long will each take to do the work alone?
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In 10 days A and B does 1 work.
∴ In 1 day A and B will do
10
1
work -(i)
In 15 days B and C does 1 work
∴ In 1 day B and C will do
15
1
work -(ii)
In 20 days C and A does 1 work
∴ In 1 day C and A will do
20
1
work - (iii)
Adding equation(i),(ii)and (iii)
In1 day 2(A+B+C) will do(
10
1
+
15
1
+
20
1
)
In1 day 2(A+B+C) will do
60
13
work.
In 1 day (A+B+C) will do
120
13
work
In 1 d a y(A+B)+(C) will do
120
13
work
A+B does
10
1
work in 1 day
∴ work done by C in 1 day
=
120
13
−
10
1
=
120
1
120
1
work is done by C in 1 day.
∴1 work is done by C in 120
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