Question

Mansi medical store was placing an order for making cardboard boxes for packing their medicals. Two sizes of boxes were required. The bigger of dimensions $25cm\times 20cm\times 5cm$ and the smaller of dimensions $15cm\times 12cm\times 5cm$. For all the overlaps, $5\%$ of the total surface area required is extra in case of each box. If the cost of the cardboard is $₹4\text{for}1000{\text{cm}}^2$ area, find the total cost of cardboard required for supplying 250 boxes of each kind.

• A. ₹ 2184
• B. ₹ 2194
• C. ₹ 2186
• D. ₹ 2284

Answer 1

The correct option is A ₹ 2184

Length $\left(l_1\right)$ of bigger box = 25 cm.
Breadth $\left(b_1\right)$ of bigger box = 20 cm.
Height $\left(h_1\right)$ of bigger box = 5 cm.
Total surface area of bigger box
$=2(lb+lh+bh)$
$=\left[2\right(25\times 20+25\times 5+20\times 5\left)\right]c{m}^2$
$=\left[2\right(500+125+100\left)\right]c{m}^2$
$=1450c{m}^2$
Extra area required for overlapping
$=\left(\frac{1450\times 5}{100}\right)c{m}^2$

$=72.5c{m}^2$
While considering all overlaps, total surface area of 1 bigger box
$=(1450+72.5)c{m}^2=1522.5c{m}^2$
Area of cardboard sheet required for 250 such bigger boxes
$=(1522.5\times 250)c{m}^2=380625c{m}^2$
Similarly, total surface area of smaller box $=\left[2\right(15\times 12+15\times 5+12\times 5]c{m}^2$
$=\left[2\right(180+75+60\left)\right]c{m}^2$
$=(2\times 315)c{m}^2$
$=630c{m}^2$
Therefore, extra area required for overlapping$=\left(\frac{630\times 5}{100}\right)c{m}^2=31.5c{m}^2$.

Total surface area of 1 smaller box while considering all overlaps
$=(630+31.5)c{m}^2=661.5c{m}^2$
Area of cardboard sheet required for 250 smaller boxes
$=(250\times 661.5)c{m}^2$
$=165375c{m}^2$
Total cardboard sheet required $=(380625+165375)c{m}^2=546000c{m}^2$
Cost of $1000c{m}^2$ cardboard sheet = ₹ 4.
Cost of 546000 cm² cardboard sheet
$=₹\left(\frac{546000\times 4}{1000}\right)=₹2184$
Therefore, the cost of cardboard sheet required for 250 such boxes of each kind will be ₹ 2184.