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Shanti sweets stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of the dimensions 25cm × 20 cm × 5 cm and the smaller of dimensions 15cm × 12cm × 5cm. For all the overlaps, 5% of the total surface area is required extra. If the cost of the cardboard is Rs.4 for 1000 ${cm}^{2}$ , find the cost of the cardboard required for supplying 250 boxes of each kind.

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Rs 1092

Rs 2184

Rs 2114

Rs 1184

answer is B.

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Detailed Solution

Given: Length of big box (l) = 25 cm
Breadth of big box (b) = 20 cm
Height of the big box (h) = 5 cm
We know that,
Total surface area of cuboid = 2(

lb + bh + hl

)
Total surface area of bigger box = 2(

25 \times 20 + 20 \times 5 + 5 \times 25

)

= 2 (500 + 100 + 125)

= 2 (725)

= 1450

{cm}^{2}

Now, 5% is required for overlapping i.e., 5% of 1450

= \frac{5}{100} \times 1450 = 72.5 {cm}^{2}

Now, Length of small box (l) = 15 cm
Breadth of small box (b) = 12 cm
Height of the small box (h) = 5 cm
We know that,
Total surface area of cuboid = 2(

lb + bh + hl

)
Total surface area of smaller box

= 2

(

15 \times 12 + 12 \times 5 + 5 \times 15

)

= 2 (180 + 60 + 75)

= 2 (315)

= 630

{cm}^{2}

Now, 5% is required for overlapping i.e., 5% of 630 =

\frac{5}{100} \times 630 = 31.5 {cm}^{2}

Thus, the total surface area of both the boxes =

1450

{cm}^{2}

72.5 {cm}^{2}

630

{cm}^{2}

31.5 {cm}^{2}

= 2184 {cm}^{2}

Now, total surface area of 250 such boxes

= 250 \times 2184 = 546, 000 {cm}^{2}

Since, the cost of

1000 {cm}^{2}

= Rs 4
Cost of

546, 000 {cm}^{2}

= Rs 4

\times 546 = Rs 2184

Hence, 2 is the correct option.

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