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Problem on ratio / HCF / LCM from PP


priyasom

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I found this problem in a Powerprep test that i gave recently :

 

The jewels in a crown consist of diamonds,rubies and emeralds. If the ratio of diamonds to rubies is 5 : 6 and ratio of rubies to emeralds is 8 : 3, what is the least number of jewels that could be in the tiara ?

 

  • 16
  • 22
  • 40
  • 53
  • 67

Can someone provide with an answer and an explanation ?

 

Priya

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The jewels in a crown consist of diamonds,rubies and emeralds. If the ratio of diamonds to rubies is 5 : 6 and ratio of rubies to emeralds is 8 : 3, what is the least number of jewels that could be in the tiara ?

 

 

  • 16
  • 22
  • 40
  • 53
  • 67

Let the no. of diamonds, rubies, emeralds be d,r,e.

d/r=5/6 ====> d=(5/6)*r

r/e=8/3 ====> e=(3/8)*r

 

So the ratio of diamonds, rubies and emeralds is:

 

5/6 : 1 : 3/8

==> 20 : 24 : 9 -----> this is the same ratio expressed in terms of the smallest integers possible.

 

For the least no. of jewels, d=20,r=24,e=9

 

So, least possible total no. of jewels=20+24+9=53.

 

Hey Priya, could you follow my solution?

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thanks sam for the nice explanation. That was the answer given in PP too :-)

 

The jewels in a crown consist of diamonds,rubies and emeralds. If the ratio of diamonds to rubies is 5 : 6 and ratio of rubies to emeralds is 8 : 3, what is the least number of jewels that could be in the tiara ?

 

 

 

  • 16
  • 22
  • 40
  • 53
  • 67

Let the no. of diamonds, rubies, emeralds be d,r,e.

d/r=5/6 ====> d=(5/6)*r

r/e=8/3 ====> e=(3/8)*r

 

So the ratio of diamonds, rubies and emeralds is:

 

5/6 : 1 : 3/8

==> 20 : 24 : 9 -----> this is the same ratio expressed in terms of the smallest integers possible.

 

For the least no. of jewels, d=20,r=24,e=9

 

So, least possible total no. of jewels=20+24+9=53.

 

Hey Priya, could you follow my solution?

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