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Question

The dimensions of a rectangular box are in the ration 4:2:3. The difference between cost of covering it with paper at Rs. 12 per m2 and with paper at the rate of 13.50 per m2 is Rs. 1,248. Find the dimensions of the box.

A
12 `m, 9 m and 13 m
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B
16 m, 8 m and 12 m
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C
11 m, 7 m and 11 m
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D
19 m, 2 m and 9 m
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Solution

The correct option is B 16 m, 8 m and 12 mGiven a rectangular box with dimension in ratio 4:2:3. Also, difference between cost of covering it with paper at rate Rs 12 per sq m and at rate Rs 13.5 per sq m is 1248.Let the dimension of cuboid be 4 x, 2 x, 3 x.For covering it with paper we need to find area of paper = Total surface area of cuboid =2(lb+bh+lb)=2(4x×2x+2x×3x+4x×3x)=2(8x2+6x2+12x2)=2(26x2)=52x2Cost of covering it at rate Rs. 12 per sq m =52x2×12=624x2Cost of covering it at rate Rs. 13.5 per sq m =52x2×13.5=704x2Difference in the cost of two paper= 1248⇒704x2−624x2=1248⇒78x2=1248⇒x2=16⇒x=4Dimensions of cuboid =4x=4×4=16m=2x=2×4=8m=3x=3×4=12

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