Question

The dimensions of a rectangular box are in the ratio 4 is to 2 is to three the difference between cost of covering it with paper at rupees 12 per metre square and with paper at the rate of 13.50 per metre square is rupees 1248 find the dimensions of the box.

Answer 1

Since the dimensions are in the ratio 2 : 3 : 4. So let it be 2x, 3x and 4x

Curved Surface Area of the Cuboid = 2(lb + bh + lh)

Curved Surface Area of the Cuboid = 2(2x*3x + 3x*4x + 2x*4x)

= 2(6x2 + 12x2 + 8x2)

= 2(26x2) = 2 * 26x2 

= 52x2 m2

Cost of papering at the rate of Rs. 9.50 per m2 = Rs. (52x2 * 9.50)

Cost of papering at the rate of Rs. 8 per m2 = Rs. (52x2 * 8)

Differenc between the costs = Rs. (52x2 * 9.50) - Rs. (52x2 * 8)

= 52x2 (9.50 - 8) = Rs.1248

52x2 * 1.50 = Rs.1248

x2 = 1248 / (1.50 * 52) = 16

or, x = sqrt.(16) = 4m

DImensions of the Box are 

Length = 2x = 2*4m = 8m

Breadth = 3x = 3*4m = 12m

Height = 4x = 4*4m = 16m

Hope it helps !!