A soldier fired two bullets at an interval of 335 seconds moving at a uniform speed v ₁. A terrorist who was running ahead of the soldier in the same direction, hears the two shots at an interval of 330 seconds? If the speed of sound is 1188 km/h, then who is the faster and by how much?

Number of boxes = (Volumes of wooden box in cm³) / (Volume of 1 small box)
= (800 x 700 x 600) / (8 x 7 x 6) = 1000000

Let length = 6k, breadth = 5k and height = 4k in cm
? 2(6k x 5k + 5k x 4k + 6k x 4k) = 33300
? 148k² = 33300
? k² = 33300/148 = 225
? k = 15
? Length = 90 cm, Breadth = 75 cm, Height = 60 cm

Volume of cube formed = 216 cm³
? Edge of the cube = (6 x 6 x 6)^1/3 = 6 cm
Surface area of original metal sheet = 2(27 x 8 + 8 x 1 + 27 x 1) cm² = 502 cm²

Surface area of the cube formed = [6 x (6)²] cm² = 216 cm²

? Required difference in area of two solids = (502 - 216) cm²
= 286 cm²

Let the height of cylinder = h
and height cone = H
Then, ?r² h = 1/3 ?r² H
? h/H = 1/3 = 1 : 3

Let the number of spheres be N
Then, N x 4/3 ? x (3)³ = ? x (2)² x 45
? 36N = 180
? N = 180/36 = 5

Radius of sphere = 9 cm
Volume of sphere = [ 4/3 x ? x (9)³] cm³ = 972? cm³
Radius of wire = 0.2 mm = 2/(10 x 10) cm = 1/50 cm
Let the length of wire be = L cm
Then, 972? = ? x (1/50)² x L
? L = (972 x 50 x 50 ) cm
?972? = ? x (1/50)² x L
? L = (972 x 50 x 50) cm
? Length of wire = (972 x 50 x 50)/100 m = 24, 300 m

Let their height be h and 2h radii be x and y respectively.
Then, ?x²h = ?y²(2h)
? x²/y² = 2/1
? x/y = ?2 / 1 = ?2 : 1

? (1/3)?r² x h = ?r² x 5
? h = 15 cm

Let h and H be the height of water level before and after the dropping of the sphere.
Then, [? x (30)² x H ] - [? x (30)² x h ]
= 4/3 ? x (30)³
? ? x 900 x (H -h) = 4/3 ? x 27000
? (H- h) = 40 cm

Area of 4 walls of the room = [2 (l + b ) x h ]m²
Area of 4 walls of new room = [2 (3l + 3b) x 3h]m²
= 9 x [2(l + b) x h ]m²
? Cost of painting the 4 walls of the new room = Rs. (9 x 350)
= Rs. 3150