The length, breadth and height of a room are l, b and h, respectively. The perimeter of the ceiling expressed as a percentage of the total area of the four walls, is?

Speed of boat downstream = Distance covered / Time taken
= 30/2 = 15 km/h

Now, speed of boat upstream = Distance covered / Time taken
= 30/6 = 5 km/h

Now, speed of boat = (Speed download + Speed upstream) / 2
= (15 + 5) / 2 = 10 km/h

We know that,
Speed = Distance/ Time
Speed of the train = 220/12 x (18/5) km/h

P.W. = [8 x 100 x 100] / [10 x 10]
= Rs. 800

? log_a x = ( log_abx) / (log_aba)
? The given expression = [[(log_abx) / (log_aba)] / [( log_abx )] - ( log_ab)
= (1/log_aba) - log_ab = log_aab - log_ab = log_a(ab/b)
= log_aa = 1

Here, r = 50% and r₁ = 30%
? Gain per cent = [r(100 - r₁)/100] - r₁
= [50 x (100 - 30)/100] - 30
= 35 - 30 = 5%

According to question ,
Let, the two consecutive odd positive integers be 2x + 1 and 2x + 3 where x is a whole number.
Now, ( 2x + 1 )² + ( 2x + 3 )² = 290
? 4x² + 4x + 1 + 4x² + 12x + 9 = 290
? 8x² + 16x - 280 = 0
? x² + 2x - 35 = 0
? ( x + 7 ) ( x - 5 ) = 0
? x = 7, - 5
But, x = ?7 is not possible, since ?7 is not a whole number .
? x = 5.
We get , 2x + 1 = 2 x 5 + 1 = 11 and 2x + 3 = 2 x 5 + 3 = 13
Thus , two consecutive positive odd integers are 11 and 13 .

The given equation is
x² - 5x + 6 = 0 ? x ² - 2x - 3x+ 6 = 0
? x( x - 2 ) - 3( x - 2 ) = 0
? ( x - 2 ) ( x - 3 ) = 0
? x - 2 = 0 or x - 3 = 0
? x = 2 or x = 3
Thus, the other root of the given quadratic equation is 2.