there are three galaries in a coal mine . on the first day, two gallaries are operative and after some time,?

Question

third gallary is made operative. with this, the output of the mine became half as large again. what is the capacity of the second gallary as a percentage of the first , if it is given that four-month output of the first and third gallaries was the same as the annual output of the second gallery ?

plz. explain in detail.
ans is 64% but how to get this answer.

Answer 1

Let's call the galleries A, B, and C.

From gallery A we get a per hour and so on.

When we turn on gallery C, we get 150% of the output of gallery A and B together, or

c = .5 * (a + b)

In four months, a + c put out as much as b did in a year. In a year, a + c do 3b (four months being one-third of a year.)

a + c = 3b
c = 3b - a

.5(a + b) = 3b - a

.5a + .5b = 3b - a

1.5a = 2.5b

b/a = 1.5/2.5 = .6

Not sure how they got 64%

Answer 2

ok, we're going to label monthly outputs as 1st, 2nd and 3rd.
from the text
3rd = .5 (1st+2nd)
and
4(1st+3rd) = 12 (2nd)
and we want 2nd/1st without reference to 3rd. sub 1st eq into 2nd.
4*(1st + .5 1st + .5 2nd) = 12* 2nd
6*1st + 2*2nd = 12* 2nd
6 * 1st = 10*2nd
2nd = 6/10 * 1st.

So I get 60% not 64%. u can check my work or your answer...