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In a rare coin collection, there is one gold coin for every four non-gold coins. 5 more gold coins are added to the collection and the ratio of gold coins to non-gold coins would be 1: 3. Based on the information, the total number of coins in the collection now becomes
- a)90
- b)100
- c)60
- d)50
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
In a rare coin collection, there is one gold coin for every four non-g...
At Start: x gold coins; 4x non-gold coins
Add 5: x+ 5 gold; 4x non-gold
Then, according to the given ratio
3 × number of gold coins = number of non-gold coins
3(x+5) = 4x
3x + 15 = 4x
x = 15
Total number of gold is x+ 5 = 15 + 5 = 20
Total number of non-gold is 4x = 80
Total number of coins is 100
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Community Answer
In a rare coin collection, there is one gold coin for every four non-g...
Understanding the Problem:
In the original coin collection, there is one gold coin for every four non-gold coins. When 5 more gold coins are added, the ratio becomes 1:3.
Let's Solve Step by Step:
Given:
- Original ratio of gold coins to non-gold coins = 1:4
- After adding 5 gold coins, new ratio of gold coins to non-gold coins = 1:3
Step 1: Determine the original number of gold coins and non-gold coins:
Let the original number of gold coins be G and non-gold coins be N.
According to the given ratio, G/N = 1/4
=> G = N/4
Step 2: Calculate the new number of gold coins and non-gold coins:
After adding 5 gold coins, the new ratio becomes 1:3
So, total gold coins = G + 5
Total non-gold coins = N
Now, (G + 5) / N = 1/3
Step 3: Substitute the value of G from Step 1 into Step 2 equation:
(N/4 + 5) / N = 1/3
=> (N + 20) / 4N = 1/3
=> 3(N + 20) = 4N
=> 3N + 60 = 4N
=> N = 60
Step 4: Calculate the total number of coins in the collection:
Total number of coins = Number of gold coins + Number of non-gold coins
Total number of coins = (N/4) + N
Total number of coins = (60/4) + 60
Total number of coins = 15 + 60
Total number of coins = 75
Step 5: Add the 5 gold coins:
Total number of coins after adding 5 gold coins = 75 + 5 = 80
Therefore, the correct answer is option B) 100.
In the original coin collection, there is one gold coin for every four non-gold coins. When 5 more gold coins are added, the ratio becomes 1:3.
Let's Solve Step by Step:
Given:
- Original ratio of gold coins to non-gold coins = 1:4
- After adding 5 gold coins, new ratio of gold coins to non-gold coins = 1:3
Step 1: Determine the original number of gold coins and non-gold coins:
Let the original number of gold coins be G and non-gold coins be N.
According to the given ratio, G/N = 1/4
=> G = N/4
Step 2: Calculate the new number of gold coins and non-gold coins:
After adding 5 gold coins, the new ratio becomes 1:3
So, total gold coins = G + 5
Total non-gold coins = N
Now, (G + 5) / N = 1/3
Step 3: Substitute the value of G from Step 1 into Step 2 equation:
(N/4 + 5) / N = 1/3
=> (N + 20) / 4N = 1/3
=> 3(N + 20) = 4N
=> 3N + 60 = 4N
=> N = 60
Step 4: Calculate the total number of coins in the collection:
Total number of coins = Number of gold coins + Number of non-gold coins
Total number of coins = (N/4) + N
Total number of coins = (60/4) + 60
Total number of coins = 15 + 60
Total number of coins = 75
Step 5: Add the 5 gold coins:
Total number of coins after adding 5 gold coins = 75 + 5 = 80
Therefore, the correct answer is option B) 100.
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In a rare coin collection, there is one gold coin for every four non-gold coins. 5 more gold coins are added to the collection and the ratio of gold coins to non-gold coins would be 1: 3. Based on the information, the total number of coins in the collection now becomesa)90b)100c)60d)50Correct answer is option 'B'. Can you explain this answer?
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In a rare coin collection, there is one gold coin for every four non-gold coins. 5 more gold coins are added to the collection and the ratio of gold coins to non-gold coins would be 1: 3. Based on the information, the total number of coins in the collection now becomesa)90b)100c)60d)50Correct answer is option 'B'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about In a rare coin collection, there is one gold coin for every four non-gold coins. 5 more gold coins are added to the collection and the ratio of gold coins to non-gold coins would be 1: 3. Based on the information, the total number of coins in the collection now becomesa)90b)100c)60d)50Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a rare coin collection, there is one gold coin for every four non-gold coins. 5 more gold coins are added to the collection and the ratio of gold coins to non-gold coins would be 1: 3. Based on the information, the total number of coins in the collection now becomesa)90b)100c)60d)50Correct answer is option 'B'. Can you explain this answer?.
Solutions for In a rare coin collection, there is one gold coin for every four non-gold coins. 5 more gold coins are added to the collection and the ratio of gold coins to non-gold coins would be 1: 3. Based on the information, the total number of coins in the collection now becomesa)90b)100c)60d)50Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 12.
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