A bag contains coins of denominations ₹1, ₹2 and ₹5 only in the ratio of 12 : 5 : 3. If the total amount in the bag is ₹3,626, then what is the number of coins of ₹5 in the bag?

Let the numbers of ₹1, ₹2 and ₹5 coins be in the same ratio as given, i.e. $$12:5:3$$.
Hence write the actual numbers as $$12x,\;5x,\;3x$$ respectively, where $$x \gt 0$$ is the common multiplying factor.

Compute the amount contributed by each type of coin:
• ₹1 coins: $$1 \times 12x = 12x$$ rupees
• ₹2 coins: $$2 \times 5x = 10x$$ rupees
• ₹5 coins: $$5 \times 3x = 15x$$ rupees

Therefore the total amount in the bag is the sum of the three contributions:
$$12x + 10x + 15x = 37x$$ rupees $$\;-(1)$$

The question states that this total equals ₹3,626:

Using $$(1)$$, set up the equation
$$37x = 3626$$

Solve for $$x$$:
$$x = \frac{3626}{37} = 98$$ because $$37 \times 98 = 3626$$.

The required number of ₹5 coins is $$3x$$, hence
$$3x = 3 \times 98 = 294$$.

Option D which is: 294