To solve the problem of finding the number of each type of coin in a bag containing ₹187 in the form of 1 rupee, 50 paise, and 10 paise coins in the ratio 3:4:5, we will follow a detailed, step-by-step approach:
1. Understand the Problem:
- Total money = ₹187
- Ratio of 1 rupee : 50 paise : 10 paise = 3 : 4 : 5
2. Convert the total money to the smallest denomination (paise):
- 1 rupee = 100 paise
- ₹187 = 187 × 100 = 18700 paise
3. Determine the total parts of the ratio:
- The ratio given is 3:4:5
- Total parts = 3 + 4 + 5 = 12 parts
4. Calculate the value of one part in terms of paise:
- Total money in paise = 18700 paise
- Value of one part = Total money / Total parts = 18700 paise / 12 = 1558.33 paise per part
5. Calculate the number of each type of coin:
- 1 rupee coins: Since 1 rupee = 100 paise, the number of 1 rupee coins is given by the part of the ratio for 1 rupee multiplied by the value of one part, and then converted back to rupees.
[tex]\[
\text{Number of 1 rupee coins} = \frac{3 \times 1558.33}{100} = 46 \text{ coins}
\][/tex]
- 50 paise coins: Since 50 paise = 0.5 rupees or 50 paise, the number of 50 paise coins is given by the part of the ratio for 50 paise multiplied by the value of one part, and then converted back to the number of 50 paisa coins.
[tex]\[
\text{Number of 50 paise coins} = \frac{4 \times 1558.33}{50} = 124 \text{ coins}
\][/tex]
- 10 paise coins: Since 10 paise = 0.1 rupees or 10 paise, the number of 10 paise coins is given by the part of the ratio for 10 paise multiplied by the value of one part, and then converted back to the number of 10 paisa coins.
[tex]\[
\text{Number of 10 paise coins} = \frac{5 \times 1558.33}{10} = 779 \text{ coins}
\][/tex]
6. Conclusion:
The number of each type of coins are:
- 1 rupee coins: 46
- 50 paise coins: 124
- 10 paise coins: 779
Given the choices:
(a) 102, 136, 170
(b) 136, 102, 170
(c) 170, 102, 136
(d) None of these
The correct answer is:
(d) None of these
