Question:medium

In a bag there are some gold coins. In another bag there are 1/3rd extra gold coins as compared to the first bag. If the difference in the number of gold coins in the first and second bag is 5, then how many coins are there in the first bag?

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When “fraction extra” is mentioned, add it to the original quantity, then subtract to find the difference and solve for the original.
Updated On: Jul 15, 2026
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The Correct Option is D

Approach Solution - 1

Step 1: Set up the ratio.
The second bag has one-third extra coins compared to the first bag, so if the first bag is 3 parts, the second bag is 3 parts plus 1 part, which is 4 parts. The ratio of first bag to second bag is 3 : 4.

Step 2: Find the value of one part.
The difference between the two bags is \(4 - 3 = 1\) part, and this difference is given as 5 coins. So 1 part equals 5 coins.

Step 3: Find the number of coins in the first bag.
The first bag has 3 parts, so it holds \(3 \times 5 = 15\) coins.

Step 4: Check the answer.
The second bag then has 4 parts, or \(4 \times 5 = 20\) coins. One-third of 15 is 5, and \(15 + 5 = 20\), which matches, and the difference \(20 - 15 = 5\) matches the question too.
\[ \boxed{15} \]
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Approach Solution -2

Step 1: Set up a proportion.
The extra coins in the second bag amount to one-third of the first bag's coins, so the relationship between the extra amount and the first bag can be written as a proportion: \( \frac{1}{3} = \frac{5}{x} \), where \(x\) is the number of coins in the first bag, since 5 is the extra amount, which is also the stated difference.

Step 2: Cross-multiply.
Cross-multiplying \( \frac{1}{3} = \frac{5}{x} \) gives \( 1 \times x = 3 \times 5 \), so \( x = 15 \).

Step 3: Verify.
If the first bag has 15 coins, one-third of 15 is 5, so the second bag has \( 15 + 5 = 20 \) coins, and the difference \( 20 - 15 = 5 \) matches the question exactly.

Step 4: Final Answer:
The first bag contains 15 coins.
\[ \boxed{15} \]
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