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Probability
Question
The dimensions of a rectangular box are in the ratio of 2 : 3 : 4 and the difference between the cost of covering it with sheet of paper at the rates of र 8 and र 9.50 per m2 is र1248. Find the dimensions of the box.
Solution
Let the dimensions of the box be 2k, 3k and 4k.
Total surface area = 2(lb + bh + hl)
= 2(2k ⋅ 3k + 3k ⋅ 4k + 4k ⋅ 2k)
= 52k2 m2
Cost of covering at the rate of र 8 per m2 = 52k2 x 8 = र416 k2
Cost of covering at the rate of र 9.50 per m2 = 52k2 x 9.50 = र 494k2
Difference between the costs = र 494k2 – र 416k2 = र 78k2
According to the question,
78k2 = 1248 ⇒ k2 = 16 ⇒ k = 4 Hence, the dimensions of the box are 8 m, 12 m and 16 m.
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Mock Test Series
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