Q.1. The dimensions of a rectangular box are in the ratio of 2:3:4 and the difference between the cost of covering it with the sheet of paper at the rates of Rs.8 and Rs 9.50 per metre square is Rs.1248. Find the dimensions of the box.
Guyss the answer is 8m,12m,16m ..... can anyone explain this question by doing stepwise calculations with statements
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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 ☺️☺️
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 ☺️☺️
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