In which of the following options is the amount of gold identical in the two coins? (Pure gold is 24 carat)
Understanding Gold Purity (Carat)
Pure gold is defined as 24 carat. The carat system indicates the proportion of pure gold in an alloy. A coin or piece of jewelry that is less than 24 carat contains a mixture of gold and other metals.
To find the amount of pure gold in a metal with a given carat, we use the ratio of its carat value to 24. The formula to calculate the amount of pure gold is:
\(\text{Amount of Pure Gold} = \text{Total Weight of Coin} \times \frac{\text{Carat Value}}{24}\)
Using this formula, we can calculate the amount of pure gold present in each coin described in the options.
Calculating Gold in Each Coin
Let's apply the formula to the coins mentioned in each option:
| Option | Coin 1 Details | Coin 1 Gold Amount | Coin 2 Details | Coin 2 Gold Amount | Identical Gold Amount? |
|---|---|---|---|---|---|
| 1 | 24g coin of 22 carat | \(24 \text{ g} \times \frac{22}{24} = 22 \text{ g}\) | 22g coin of 24 carat | \(22 \text{ g} \times \frac{24}{24} = 22 \text{ g}\) | Yes |
| 2 | 22g coin of 22 carat | \(22 \text{ g} \times \frac{22}{24} = 22 \text{ g} \times \frac{11}{12} \approx 20.17 \text{ g}\) | 24g coin of 24 carat | \(24 \text{ g} \times \frac{24}{24} = 24 \text{ g}\) | No |
| 3 | 22g coin of 22 carat | \(22 \text{ g} \times \frac{22}{24} \approx 20.17 \text{ g}\) | 22g coin of 24 carat | \(22 \text{ g} \times \frac{24}{24} = 22 \text{ g}\) | No |
| 4 | 24g coin of 22 carat | \(24 \text{ g} \times \frac{22}{24} = 22 \text{ g}\) | 24g coin of 24 carat | \(24 \text{ g} \times \frac{24}{24} = 24 \text{ g}\) | No |
Comparing the Results
From the calculations shown in the table:
- In Option 1, the 24g coin of 22 carat contains 22g of pure gold, and the 22g coin of 24 carat also contains 22g of pure gold. The amounts are identical.
- In Option 2, the amounts of pure gold are approximately 20.17g and 24g, which are not identical.
- In Option 3, the amounts of pure gold are approximately 20.17g and 22g, which are not identical.
- In Option 4, the amounts of pure gold are 22g and 24g, which are not identical.
Therefore, the amount of gold is identical only in the coins described in Option 1.
Important Questions from Miscellaneous
A stone is thrown horizontally from the top of a 20 m high building with a speed of 12 m/s. It hits the ground at a distance R from the building. Taking g = 10 m/s2 and neglecting air resistance will give :
A mass is attached to a spring that hangs vertically. The extension produced in the spring is 6 cm on Earth. The acceleration due to gravity on the surface of the Moon is one-sixth of its value on the surface of the Earth. The extension of the spring on the Moon would be:
Directions: Each item in this section consists of a sentence with an underlined word followed by four words (a), (b), (c), and (d). Select the option that is opposite in meaning to the underlined word and mark your response in your Answer Sheet accordingly.
The deluge affected the population.The major source of vitamins and minerals for vegetarians is
Which of the following statements about the Deccan Riots Commission is/are correct?
1. The Commission did not hold enquiries in the districts which were not affected.
2. The Commission did record the statements of ryots, sahukars and eye-witnesses.
Select the correct answer using the code given below:
