Question

Sarita wants to gift a stationery kit, which inchides a pencil an eraser and a sharpener, to some kids in her
village. She went to a wholesaler for purchasing these items. The seller sells Pencils in packing of 12. erasers
in a packing of 18 and sharpeners in a packing of 10. She purchases the minimum number of packets of
pencils, erasers and sharpeners so that a fix number of kits can be prepared without any item being umused or
short. What is the number of packets of pencils purchased by her?
O 12
10
15
IS​

Answer 1

Answer:

Rakesh went to a stationary shop to purchase a total of 38 pens, erasers and sharpeners. He purchased at least 11 items of each. He purchased more sharpeners than erasers and more erasers than pens. If each pen cost Rs. 2 each eraser cost Rs. 3 and each sharpener cost Rs. 4. find the minimum expenditure be could have incurred on the items (in Rs.)

MEDIUM

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ANSWER

Given that Rakesh purchased at least 11 items of each

Let the number of pens, erasers, and sharpeners be (11+p),(11+e), and (11+s) respectively, such that-

(i) s>e>p (Given)

(ii) s,e,p∈I

+

Rakesh went to a stationary shop to purchase a total of 38 pens, eraser, and sharpeners.

∴(11+p)+(11+e)+(11+s)=38

⇒p+e+s+33=38

⇒p+e+s=5

0,2 and 3 are the only unequal positive integral values which results 5 on addition.

∵s>e>p

∴p=0,e=2,s=3

Hence, no. of pens Rakesh purchased =11+0=11

no. of erasers Rakesh purchased =11+2=13

no. of sharpners Rakesh purchased =11+3=14

Given that If each pen cost Rs. 2 each eraser cost Rs. 3 and each sharpener cost Rs. 4.

∴ total expenditure=11×2+13×3+14×4=22+39+56=Rs.117

The minimum expenditure be could have incurred on the items = Rs. 17

How satisfied are you with the answers?

Answer 2

Given :- Sarita wants to gift a stationery kit, which includes a pencil an eraser and a sharpener, to some kids in her village. She went to a wholesaler for purchasing these items. The seller sells Pencils in packing of 12. erasers in a packing of 18 and sharpeners in a packing of 10. She purchases the minimum number of packets of pencils, erasers and sharpeners so that a fix number of kits can be prepared without any item bemg unused or short. What is the number of packets of pencils purchased by her ?

A) 15

B) 18

C) 12

D) 10

Solution :

from given data we have :-

• The seller sells Pencils in packing of 12 .
• erasers in a packing of 18
• sharpeners in a packing of 10.
• and, she needs minimum number of packets of pencils, erasers and sharpeners .

So, in order to find minimum number of packets , we will find LCM of 12, 18 and 10 .

Prime factors of 12 18 and 10 :-

→ 12 = 2 * 2 * 3

→ 18 = 2 * 3 * 3

→ 10 = 2 * 5

→ LCM = 2 * 2 * 3 * 3 * 5 = 180.

Therefore, she need minimum 180 pencil 180 sharpeners and 180 erasers, so that a fix number of kits can be prepared without any item being unused or short.

Now,

→ Number of packets of pencil = (Total number of pencil) / (pencil in each packet) = 180 / 12 = 15 packets.

Hence she purchased 15 packets of pencil .

Extra :

→ Packets of eraser she purchased = 180 / 18 = 10 packets.

→ Packets of sharpeners she purchased = 180 / 10 = 18 packets.

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