Given:-

The bigger of dimensions 25 cm× 20 cm× 5 cm and the smaller dimensions 15 cm× 12 cm×5cm.

all the overlaps, 5% of TOTAL surface area is REQUIRED extra.

the cost of cardboard is rs 4 for 1000 cm square.

To FIND:-

Find the cost of cardboard required for supplying 250 boxes of each kind.

Solutions:-

Length of bigger box = 25cm

Breadth of bigger box = 20cm

Height of bigger box = 5cm

Total surface area bigger box = 2(lb + bh + hl)

= 2(25 × 20 + 20 × 5 + 5 × 25)

= 2(500 + 100 + 125)

= 2 × 725

= 1450cm²

Extra area required for overlapping = 1450 × 5 / 100

= 1450/20

= 72.5cm²

While considering all overlaps total of 1 bigger box.

= 1450 + 72.5

= 1522.5cm²

Area of cardboard sheet required for 250 such bigger boxes.

= 1522.5 × 250

= 380625cm²

Total surface area of smaller box.

= 2(15 × 12 + 15 × 5 + 12 × 5)

= 2(180 + 75 + 60)

= 2 × 315

= 630

Therefore,

Extre area of required for overlapping.

= 630 × 5 / 100

= 63/2

= 31.5cm²

Total surface area of 1 smaller box while considering all overlaps.

= 630 + 31.5

= 661.5cm²

Area of cardboard sheet required for 250 smaller boxes.

= 250 × 661.5

= 165375cm²

Total cardboard sheet required = 380632 + 165375

= 546000cm²

Cost of 1000cm² cardboard sheet = Rs 4.

Cast of 546000cm² cardboard sheet.

= Rs (546000/1000 × 4)

= Rs 546 × 4

= Rs 2184

Hence, the cost of cardboard sheet required for 250 such boxes of each will be Rs 2184.