2ab = ($ a $2 + $ b $2) - $\left( a - b \right)$2
= $\left(29 - 9\right)$ = 20
$\Rightarrow$ ab= 10.
Let the number of students in rooms A and B be $ x $ and $ y $ respectively.
Then, $ x $ - 10 = $y $ + 10 $\Rightarrow$ $ x $ - $ y $ = 20 .... (i)
and $ x $ + 20 = 2$\left( y - 20\right)$ $\Rightarrow$ $ x $ - 2$ y $ = -60 .... (ii)
Solving (i) and (ii) we get: $ x $ = 100 , $ y $ = 80.
$\therefore$ The required answer A = 100.
Suppose the man works overtime for $ x $ hours.
Now, working hours in 4 weeks = $\left(5 \times 8 \times 4\right)$ = 160.
$\therefore$ 160 x 2.40 + $ x $ x 3.20 = 432
$\Rightarrow$ 3.20$ x $ = $\left(432 - 384\right)$ = 48
$\Rightarrow x $ = 15.
Hence, total hours of work = $\left(160 + 15\right)$ = 175.
Let the number be x
22x + 308 = 44x
=> 44x - 22x = 308
=> 22x = 308
=> x = 308/22 = 154/11 = 14
$(a - b)^2 = a^2 - 2ab + b^2$
=> (a - b)2 = a2 - 2ab + b2
=> 62 = 116 - 2ab
=> 36 = 116 - 2ab
=> 2ab = 116 - 36 = 80
=> ab = 40
$\text{Number of pieces = }\dfrac{4250}{85} = \dfrac{850}{17} = 50$
Let the number of correct answers be x
Then, number of wrong answers = $\left(80 - x\right)$
4x – $\left(80 - x\right)$ = 120
=> 4x – 80 + x = 120
=> 5x = 200
=> x = 200/5 = 40
i.e., he does 40 questions correctly
Let Cs share = Rs. $ x $
Then, Bs share = Rs.$ \dfrac{x}{4} $, As share = Rs. $\left(\dfrac{2}{3}\times\dfrac{x}{4}\right)$=Rs.$\dfrac{x}{6}$
$\therefore \dfrac{x}{6} $+$ \dfrac{x}{4} $+ $ x $ = 1360
$\Rightarrow \dfrac{17x}{12} $= 1360
$\Rightarrow x $ =$ \dfrac{1360 \times 12}{17} $= Rs. 960
Hence, Bs share = Rs.$ \left(\dfrac{960}{4} \right) $= Rs. 240.
26 trees have 25 gaps between them.
Length of each gap = 300/25 = 12
i.e., distance between two consecutive trees = 12