Question

The dimensions of a rectangle box are in the ratio of 2:3:4 and the difference between the cost of covering it at the rates of Rs.8 and Rs.9.50 per m2 is Rs.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
I hope it help you ☺️☺️