Class 10 chapter 1(Real number)

Case based: 3

Raman is hosting the new year party for his friends. He wants to purchase some eatables like patties and buns for making burgers, some towels and some shining papers and glitter papers for decorting his house.

Class 10 Case based problem of Chapter 1 Real Number 3

When he reaches the store, he finds that patties come in a pack of 6, and buns in a pack of 8. Moreover, no small towels are available and the only size available is 16m×20m. The shiny paper comes in lengths of 36 inches and the glitter paper in lengths of 40 inches.(Class 10 Case based problem of Chapter 1 Real Number 3)

(A) Assuming one patty is required for one bun, what is the smallest number of packs of each, Raman must buy so that no patty or bun is left out ?

(B) Square towels has to be cut from the piece of cloth measuring 16m×20m. Find the minimum number of towels that can be cut so that there is no wastage.

Solution:

(A) As each packet of patties contains 6 patties and packet of buns has 8 buns, we have to take the LCM of 6 and 8 to find the minimum number of packets of each so that no patty or bun is left out.

Factor of 6 = 2 × 3

Factor of 8 = 2 × 2 × 2

LCM (6, 8) = 2 × 2 × 2 × 3 = 24

Therefore, 24 patties and 24 buns are required.

Number of packets of patties = 24/6 = 4

Number of packets of buns = 24/8 = 3

(B) Since there should be no wastage, the edge of the towel should exactly divide the length & breadth of the piece of cloth. The dimension of the towel is that highest number which completely divides 16 and 20. So, here we have to find the HCF(16, 20).

Factor of 16 = 2 × 2 × 2 × 2

And factor of 20 = 2 × 2 × 5

∴ HCF(16, 20) = 2 × 2 = 4

So, the dimensions of one small towel that can be cut are 4 m × 4 m.

The minimum number of towels possible = (16 × 20)/(4 × 4)

= 20