A contractor undertook to complete a piece of work in 120 Days and employed 140 men upon it. At the end of 66 days only half of the work was done,so he put on 25 extra men. By how much time did he exceed the specific time ?

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.