According to the question, A : B = 200 : 150
and B : C = 200 : 192
? A : C = (A/B) x (B/C) = (200/150) x (200/192) = 200/144
So, A beats C by (200 - 177) = 56 m
26.823 x 27.923 x 4.5001
? 27 x 28 x 4.5000 = 756 x 4.5000 = 3402 ? 3400
Part filled by A in 1 h = 1/16
Part fill by B in 1 h = 1/10
Part filled by ( A + B ) in 2 h = 1/16 + 1/10 = 13/80
? Part filled by ( A + B ) in 12 h = 6 x 13/80 = 78/80
? Remaining part = 1 - 78/80 = 2/80 = 1/40
Now, it is the turn of A
Time taken by A to fill 1/40 part of the tank = (1/40) x 16 = 2/5 h
? Total time taken ( 12 + 2/5) h = 122/5 h
As we know from the formula,
A3 + B3 + C3 = ( A + B + C) (A2 + B2 + C2 ? AB ? BC ? CA) + 3ABC
If A + B + C = 0 then,
A3 + B3 + C3 = 0 x (A2 + B2 + B2 ? AB ? BC ? CA) + 3ABC
A3 + B3 + C3 = 0 + 3ABC
A3 + B3 + C3 - 3ABC= 0
As we know that from given question,
A = a, B = b and C = 1, Put these value in above equation, we will get
a3 + b3 + 13 - 3 x a x b x 1 = 0
a3 + b3 + 1 - 3ab = 0
We know that, a3 + b3 + c3 - 3abc = (a + b + c ) ( a2 + b2 + c2 - ab - bc - ca )
? (a + b + c) = ( a3 + b3 + c3 - 3abc ) / ( a2 + b2 + c2 - ab - bc - ca ) .......................(i)
Given that in question,
(2.247)3 + (1.730)3 + (1.023)3 - 3 x 2.247 x 1.730 x 1.023 / (2.247)2 + (1.730)2 + (1.023)2 - (2.247 x 1.730) - (1.730 x 1.023) - (2.247 x 1.023)
Apply the formula given in Equation (i) and we will get,
= ( a + b + c )
= ( 2.247 + 1.730 + 1.023) [ from eq. (i) ]
= 5.000 = 5
Let the first pipe be shut up after x minutes
Now, applying the given rule, we have 30{1 - (x + 10)/40 } = x
[Here t = (x + 10) minutes]
or x = 90/7 minutes
Time taken by A to cover 200 m = 200/2 = 100 s
? B covers (200 - 10) = 190 m in (100 + 5) = 105 s
? B' s speed = 190/105 = 38/21 = 117/21 m/s
Required area = Length x Breadth
= 100 x 40 = 4000 sq m
= 4 x 103 sq m
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