# maths

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A and B together can do a piece of work in 12 days; B and C together can do it in 15 days. If A is twice as good a workman as C, in how many days A alone will do the same work

• maths -

Let the rate at which A works be a; the rate at which B works be b; the rate at which C work be c:

(a + b)*12 = 1
(b + c)*15 = 1
a = 2*c

gives

b + a/2 = 1/15
b = 1/15 - a/2
Substituting into the first equation:

(a + 1/15 - a/2)*12 = 1

a/2 + 1/15 = 1/12

a/2 = 1/12 - 1/15 = (15-12)/(15*12)

a/2 = 3/(15*12) = 1/(5*12) = 1/60

a = 1/30

The rate at which a works is 1/30 of the work per day; so a will complete the task in 30 days.

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