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Q.

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 Rs.8 and Rs.50 per sq. m is Rs. 1248. Find the dimensions of the box.

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a

Length is 8

m

, breadth is 12

m

and height is 16

m

b

Length is 12

m

, breadth is 16

m

and height is 8

m

c

Length is 8

m

, breadth is 8

m

and height is 12

m

d

Length is 16

m

, breadth is 12

m

and height is 8

m

answer is A.

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Detailed Solution

Given, dimensions of a rectangular box in the ratio of 2:3:4.
The difference between the cost of covering box with sheet of paper at the rates of Rs.8 and Rs.50 per sq. m is Rs. 1248.
Consider the length be 2x, breadth be 3x and height be 4x.
Surface area of the box is given by

S = 2 l b + b h + l h

Substituting the values and simplify,

S = 2 2 x × 3 x + 3 x × 4 x + 2 x × 4 x ⇒ S = 2 6 x 2 + 12 x 2 + 8 x 2 ⇒ S = 2 × 26 x 2 ⇒ S = 52 x 2

The cost for the paper at a rate Rs.8

= 52 x 2 × 8

⇒ C o s t f o r t h e p a p e r a t a r a t e R s .8 = 416 x 2

Cost for the paper at a rate Rs.9.50

= 52 x 2 × 9.50

⇒ C o s t f o r t h e p a p e r a t a r a t e R s .9.50 = 494 x 2

Now calculating the difference of the cost and equate it with Rs.1248,

494 x 2 − 416 x 2 = 1248

Simplify the term,

⇒ 78 x 2 = 1248

⇒ x 2 = 124878

⇒ x 2 = 16

⇒ x = 16 ⇒ x = 4

Substitute the value of

x

to calculate the length,

l = 2 x ⇒ l = 2 × 4 ⇒ l = 8 m

Substitute the value of

x

to calculate the breadth,

b = 3 x ⇒ b = 3 × 4 ⇒ b = 12 m

Substitute the value of

x

to calculate the height,

h = 4 x ⇒ h = 4 × 4 ⇒ h = 16 m

So, the length is 8

m

, breadth is 12

m

and height is 16

m

.
Hence option (1) is correct.

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