Question

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

• A. 7
• B. 9
• C. 13
• D. 15

Hint:

The phrase "1/3rd extra" or "1/3rd more" means the new quantity is (1 + 1/3) = 4/3 of the original quantity. The "extra" amount itself, which is the difference, is simply 1/3 of the original quantity.

Answer 1

The Correct Option is D

Let's solve this word problem using simple algebra. Step 1: Define the variables. Let 'x' be the number of gold coins in the first bag.

Step 2: Express the number of coins in the second bag. The second bag has "1/3rd extra" coins compared to the first bag. This means it has the original amount (x) plus an extra (1/3) of x. Number of coins in the second bag = \(x + \frac{1}{3}x = \frac{3x}{3} + \frac{1x}{3} = \frac{4}{3}x\).

Step 3: Set up an equation based on the given difference. We are told that the difference in the number of coins between the two bags is 5. Difference = (Coins in second bag) - (Coins in first bag) \[ 5 = \frac{4}{3}x - x \]

Step 4: Solve the equation for x. \[ 5 = \frac{4x - 3x}{3} \] \[ 5 = \frac{1}{3}x \] To find x, multiply both sides by 3: \[ x = 5 \times 3 \] \[ x = 15 \] The number of coins in the first bag is 15. Check the answer: If the first bag has 15 coins, the second bag has 15 + (1/3)*15 = 15 + 5 = 20 coins. The difference is 20 - 15 = 5. This matches the problem statement.