Let's solve the problem step by step.

Step 1: Determine the number of Rs. 1 coins

The total value of Rs. 1 coins is Rs. 15. Each Rs. 1 coin is worth Re. 1, so the number of Rs. 1 coins is:

$\text{Number of Rs. 1 coins} = 15$

Step 2: Ratio of Rs. 1 coins to Rs. 2 coins

The ratio of the number of Rs. 1 coins to Rs. 2 coins is given as $5:7$. Let the number of Rs. 2 coins be $x$. Then:

$\frac{\text{Number of Rs. 1 coins}}{\text{Number of Rs. 2 coins}} = \frac{5}{7}$

Substitute the known value of Rs. 1 coins:

$\frac{15}{x} = \frac{5}{7}$

Cross-multiply:

$5x = 15 \cdot 7$

$x = 21$

So, the number of Rs. 2 coins is $21$.

Step 3: Ratio of Rs. 2 coins to Rs. 5 coins

The ratio of Rs. 2 coins to Rs. 5 coins is given as $7:6$. Let the number of Rs. 5 coins be $y$. Then:

$\frac{\text{Number of Rs. 2 coins}}{\text{Number of Rs. 5 coins}} = \frac{7}{6}$

Substitute the known value of Rs. 2 coins:

$\frac{21}{y} = \frac{7}{6}$

Cross-multiply:

$7y = 21 \cdot 6$

$y = 18$

So, the number of Rs. 5 coins is $18$.

Step 4: Total value of Rs. 5 coins

The value of Rs. 5 coins is:

$\text{Total value} = \text{Number of Rs. 5 coins} \times 5$

$\text{Total value} = 18 \cdot 5 = 90$

Final Answer:

The total value of Rs. 5 coins is Rs. 90.

Correct Option: (a) Rs. 90

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Would you like to discuss this further or clarify any step? Here are some related questions:

1. What happens if the ratio between Rs. 2 and Rs. 5 coins changes?
2. How would the answer vary if the total value of Rs. 1 coins was different?
3. Can you find the total value of all coins in the bag?
4. What is the percentage contribution of Rs. 5 coins to the total value?
5. How would the calculation change if another denomination was introduced?

Tip: Always double-check the ratios and their corresponding values when working with proportion problems.