Cost price of 200 bulbs = RS. 200 x 10 = RS. 2000
5 bulbs were fused. Hence, number of bulbs left = 200 – 5 = 195
These were sold at RS. 12 each.
The SP of 195 bulbs = RS. 195 x 12 = RS. 2340
He obviously made a profit (as SP > CP).
Profit = RS. 2340 – RS. 2000 = RS. 340
On RS. 2000, the profit is RS. 340. 
Profit \(=\frac{340}{2000} \times 100 \%=17 \%\)

Present duration each period = (50 - 5) minutes = 45 minutes.
Let the present number of period be 'x'.
Since, more the number of periods, less is the duration of a period.
\(\therefore\) It is a case of inverse variation.
We have:

\(\therefore \ 9\times 50=x\times 45\Rightarrow x=\frac { 9\times 50 }{ 45 } =10\)

Thus the required number of periods = 10.

More is the number of persons, less is the time to complete the task.
\(\therefore\) It is a case of inverse variation,
Now, we have:

\(\therefore \ 5\times 4=4\times x\Rightarrow x=\frac { 5\times 4 }{ 4 } =5\)
Thus, the required number of days = 5.

Number of persons added = 5
\(\therefore\) Present number of persons = 20 + 5 = 25
Since, for more persons, the food will last less number of days
\(\therefore\) It is a case of inverse variation.
\(\therefore \ 25\times x=20\times 10\Rightarrow x=\frac { 20\times 10 }{ 25 } =8\)
\(\therefore\) The food will now last for 8 days.

We have, perimeter = 77 cm 
\(\therefore\) (x + 1)+ (x + 2) + (2x + 2) + (2x + 1)+ (x + 1) = 77
7x + 7= 77  7x = (77 - 7)
7x = 70  x = 70 x\(\frac { 1 }{ 7 } \)
Hence, the required value of x is 10 cm 

Let the number of winners be x.
Then, the number of participants who did not win = 36-x
Amount spent on x prizes = Rs. 500 x x = Rs. 500x
Amount spent on (36 - x) prizes = Rs. 100 x (36 - x) =
= Rs. (3600 -100x)
But 500x + (3600 -100x) = 4800
\(\Rightarrow\) 500x + 3600 -100x = 4800
\(\Rightarrow\) 400x = 4800 - 3600
\(\Rightarrow\) x = 1200 x \(\frac { 1 }{ 400 } \Rightarrow x=3\)
So, the number of winners is 3

Rs.450

Letus draw a rough sketch of the quadrilateral.

Steps of construction
Step I Draw AM = 5 cm.
Step II Construct \(\angle\)MAX = 60° and \(\angle\)AMY = 90°.
StepIII Cut the length of AG = 4 cm from AX and the length of EM = 4.5 cm from MY.
StepIV Join GE.

Thus, we get the quadrilateral GAME by construction.

Steps of construction
StepI Draw MT = 6 cm and draw \(\angle\)TMX = 45°.
StepII Cut MA from MX, so that MA = 10 cm.
StepIII Draw an arc of 5 cm with centre T and draw an arc of 3 cm with centre A.
StepIV Mark the intersection point of both the arcs as E. Join TE and AE.

Thus, quadrilateral TEAM is constructed.

Let ABCDEFGH be the regular octagonal surface as shown below in the figure:

Given, each side of octagon = 5m,AD = 11 m
perpendicular from B to AD i.e. BP =4m .Join HE
Since, it is a regular octagon, so trapeziums ABCD and HEFG will be congruent and ADEH is a rectangle.
Now, area of trapezium ABCD = Area of trapezium HEFG
 = (AD+BC)BP
 = \(\frac { 1 }{ 2 } \)(11+5)\(\times\) 4 =\(\frac { 1 }{ 2 } \) \(\times\)16\(\times\)4
 = 8 \(\times\)4 =32 m²
and area of rectangle ADEH = AD\(\times\) DE =11 \(\times\)5 =55m²
Now, area of octagon ABCDEFGH
= Area of trapezium ABCD +Area of rectangle ADEH +Area of trapezium HFGH
= 32 + 55 + 32= 119 m²
Hence, required area of octagonal surface is 119 m²

[(4m)² + 2(4m)(5n) + (5n)²] + [(5m)² + 2(5m)(4n) +(4n)²]
= 16m² + 40mn + 25n² + 25m² + 40mn + 16n²
=  (16 + 25)m²+ (40 + 40)mn + (25 + 16​​​​​)²
= 41m² + 80mn + 41n²

(7m - 8n)² + (7m + 8n)²
= [(7m)² - 2(7m)(8n) + (8n)²] + [(7m)² + 2(7m)(8n) + (8n)²]
and (a-b)²= a² -2ab+b²
= (49m² -112mn + 64n²)+(49m² +112mn + 64n²)
= 49m² -112mn + 64n² + 49m² +112mn + 64n²
= 98m² + 128n²

First expression = 2x(z - x - y)
= (2x) x z - (2x) x (x) - (2x) xy
= 2xz - 2x² - 2xy
Second expression = 2y(z - y - x)
= (2y)x(z)-(2y) x (y)-(2y)x(x)
= 2yz - 2y² - 2yx
On adding above expressions, we get
2xz - 2x² - 2xy
+              -2yx + 2yz - 2y²
_________________________
2xz - 2x² - 4xy + 2yz - 2y²
__________________________

For subtraction, write the like terms one below the other, we get
12a -9ab +5b -3
+4a - 7ab + 3b + 12
(-)     (+)     (-)    (-)
_________________
8a - 2ab + 2b -15
_________________
Thus, the required answer is 8a - 2ab + 2b - 15.