Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?

Profit (%) = 9.09 % = 1/11

Since the ratio of water and milk is  1 : 11,

Therefore the ratio of water is to mixture = 1:12

Thus the quantity of water in mixture of 1 liter = 1000 x (1/12) = 83.33 ml

(a + b)/2 = 25
a + b = 50
?ab = 7
ab = 49
Hence, A can either be 7 or 49.
So, 49 is the answer.

P² + 4Q² = 4PQ
? P² + 4Q² - 4PQ = 0
? (P - 2Q)² = 0
? P - 2Q = 0
? P = 2Q
? P/Q = 2/1
? P : Q = 2 : 1

? Probability of machine failing during a day p = 0.95
? q = Probability of its working during a day = 1 - p = 1 - 0.95 = 0.05

Required probability = q⁴ = (0.05)⁴
= 0.00000625

Given that
A : B = 3 : 4 = ( 3 x 2 ) : (4 x 2 ) = 6 : 8
B : C = 8 : 9
? A : B : C = 6 : 8 : 9
As consequent of the first ratio is equal to the antecedent of second ratio.

Time from 6 am on a day to 11 pm on 4th day = 89 h
Now, 23 h 44 min of this clock = 24 h of correct clock
89 h of this clock = 24 x (15/356) x 89 h of correct clock = 90 h of correct clock
? Correct time will be 12 o' clock (mid-night).

Given that n = 2 and (n + 1) = 3(n < 6)
The hands will be at the same straight line at
? (5n + 30) x 12/11 min past n.
? (5 x 2 + 30 ) x 12/11 min past 2.
? (10 + 30) x 12/11 min past 2.
? 40 x 12/11 min past 2.
? 480/11 min past 2.

Required mean proportional = ?9 x 64
= 3 x 8 = 24

Let term = l = ar^{n - 1} a = 5 and l = 20480
r = 20/5 = 4
? 20480 = 5 x (4)^n-1
(4)^n-1 = 20480/5 = 4096 = (4)⁶
n - 1 = 6
? n = 7