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Question

The dimensions of a rectangular box are in the ratio 1:2:4 and the difference between the costs of covering it with the cloth and sheet at the rate of Rs.20 and Rs.20.50 per square metre, respectively is Rs.126. Find the dimensions of the box.

A
4cm,7cm and 10cm
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B
2cm,4cm and 11cm
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C
3cm,6cm and 12cm
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D
7cm,8cm and 13cm
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Solution

The correct option is C 3cm,6cm and 12cmLet length=x, breadth =2x and height =4x.Area of the box =2(lb+bh+lh)=2(2x2+8x2+4x2)=28x2Given, 20.5×28x2−20×28x2=126⇒28x2×0.5=216⇒x2=9⇒x=3∴ The dimensions are 3cm,6cm and 12cm.

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