A government project involves laying electrical cables between

Question

A government project involves laying electrical cables between a national grid and a town being newly established. The total length of wire needed in this project has been estimated to be 500 miles. The cost of wire used is directly proportional to the volume of wire used. The shape of wire is of a long and thin cylinder. Volume of a cylinder is $ πr^2 l $ where r is the radius of the cylinder and l is its length. The project has received three bids from wire manufacturing companies - A, B, and C. The ratio of the radii of the wires used by the three companies is 2:3:4; the ratio of the prices per unit volume of the wires used by the three companies is 3:2:1. The bid by company A is $240,000.

In the table, select the values that represent the approximate value of the bids by company B and company C respectively. Make only two selections, one in each column.

In the table, select the values that represent the approximate value of the bids by company B and company C respectively. Make only two selections, one in each column.

Priyanshu_57 · Accepted Answer

A : B : C 
 2 : 3 : 4 --ratio of radii given
 4 : 9 : 16 --Ratio of volume as volume is proportional to square of radius.
 3 : 2 : 1 --ratio of cost per unit volume given
 12 : 18 : 16 --Ratio of total cost obtained by multiplying volume and cost per unit volume.
 6 : 9 : 8 --Reduced ratio of total cost

6 is total cost of A which is equivalent to 240000
By unitary method 1 is equivalent to 240000/6 = 40000
So for B, 9 is equivalent to 9*4000 = $360,000
for C, 8 is equivalent to 8*4000 = $320,000

Gemmie · Answer

c: cost of wire
v: volume
p: price per unit volume

c = p * v

........A.........B..........C
r.......2x........3x........4x
v......4y.........9y........16y
p......3..........2..........1

c_A = 240 = v * p = 4y * 3 = 12y

=> y =  \frac{240}{12} = 20

c_B = 18y = 20 * 18 = 360

c_C = 16y = 16 * 20 = 320

sayan640 · Answer

Let , radii = 2y , 3y and 4y
Per unit cost = 3x , 2x and x,

pi * (2y)^2 * 3x * 500 = 240,000
pi*y^2*x = 40

Hence , for C , it's pi*4^2*y^2*x*500 = 40*16*500 = 320,000

for B , it's pi*9*y^2*2x*500 = 360, 000

whatsarc · Answer

Given
A:B:C
Radius is 2:3:4
R^2 is 4:9:16
Price per unit is 3:2:1

Company A quoted 240k

Quick approach 
For A 240k = 4x3x20k (4x3 is given and 20k is the relationship deduced)

So for B
9x2x20k (use same deduced relationship) = 360k

And for C
16x1x20k (use same deduced relationship) =320k

Dream009 · Answer

Can someone explain why did price ration multiply with radii ratio. Isn't radii ratio alone gives the cost ration? See this is my logic volume ratio is giving the total cost and volumne ratio is same as radii ration - so why did they give price per unit and why should we even multiply those 2 ratio. I was able to get to the answer - observing pattern - but logically it makes less sense.

Bunuel · Answer

The cost of wire used is directly proportional to the volume of wire used just means cost = k * volume, but the value of k can be different for each company. The ratio 3:2:1 is the ratio of this constant for A, B, and C.

And volume depends on r^2, so 2:3:4 becomes 4:9:16.

So the cost ratio A:B:C = (3 * 4) : (2 * 9) : (1 * 16).

Company B	Company C	Bid
		$180,000
		$320,000
		$360,000
		$480,000
		$640,000

A government project involves laying electrical cables between

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A government project involves laying electrical cables between