To solve the problem, let's break it down into parts and create equations based on the given information.

(i) Equation to find the number of coins in Divya's bag

• Divya has Rs. 80 in total, and her coins are of denominations Rs. 2 and Rs. 5.
• Let the number of Rs. 2 coins be $x$.
• Let the number of Rs. 5 coins be $y$.

The total value of coins in Divya's bag is given by: $2x + 5y = 80$ This is the equation to find the number of coins in Divya's bag.

(ii) Equation to find the number of coins in Bhabya's bag

• Bhabya has Rs. 85 in total, and her coins are of denominations Rs. 1 and Rs. 2.
• Let the number of Rs. 1 coins be $m$.
• Let the number of Rs. 2 coins be $n$.

The total value of coins in Bhabya's bag is given by: $1m + 2n = 85 \quad \text{or simply} \quad m + 2n = 85$

Additionally, it is mentioned that the ratio of the number of Rs. 1 coins to Rs. 2 coins is 5:6, which gives us another equation: $\frac{m}{n} = \frac{5}{6}$ or equivalently: $6m = 5n$

(iii) Find the number of Rs. 2 coins in both Divya's and Bhabya's bags

For Divya's bag, we already have the equation: $2x + 5y = 80$ We need more information to solve this, such as another equation to relate $x$ and $y$, which could be derived from additional constraints.

For Bhabya's bag, we have the system of equations:

1. $m + 2n = 85$
2. $6m = 5n$

Substituting $m = \frac{5n}{6}$ into the first equation: $\frac{5n}{6} + 2n = 85$ Multiplying the whole equation by 6 to eliminate the fraction: $5n + 12n = 510$ $17n = 510$ $n = 30$

So, Bhabya has 30 Rs. 2 coins. Substituting $n = 30$ into $m = \frac{5n}{6}$: $m = \frac{5 \times 30}{6} = 25$ So Bhabya has 25 Rs. 1 coins.

Now, to determine the number of Rs. 2 coins in Divya's bag, we would need to solve $2x + 5y = 80$ with additional information about either $x$ or $y$.

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Do you want further details on solving Divya's equation or any other questions about this problem?

Related questions:

1. How many total coins are in Bhabya's bag?
2. What is the ratio of total coins between Divya and Bhabya?
3. Can you find the number of Rs. 5 coins in Divya's bag?
4. What if Bhabya had Rs. 100 instead of Rs. 85? How would the equations change?
5. Can you verify the ratio of the Rs. 1 to Rs. 2 coins for Bhabya?

Tip:

When dealing with word problems, it's helpful to define all variables clearly and create equations from the relationships described in the problem.