Divya and Bhabya went to the market to buy some gifts for their friend Momita's
birthday. Divya had Rs.80 in her bag while Bhabya had Rs.85. Divya had coins of
denominations Rs.2 and Rs.5, Bhabya had coins of denominations Rs.1 and Rs.2 and
the ratio of the number of coins of both was 5:6.
Based on the above information answer the following questions.
(i) Write an equation to find the number of coins in Divya's bag.
(ii) Write an equation to find the number of coins in Bhabya's bag.
(iii) Find the number of Rs. 2 coins in Bhabya's and also in Dibya's bag.

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 \( y \).

---

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.

Divya and Bhabya went to the market to buy some gifts for their friend Momita's birthday. Divya had Rs.80 in her bag while Bhabya had Rs.85. Divya had coins of denominations Rs.2 and Rs.5, Bhabya had coins of denominations Rs.1 and Rs.2 and the ratio of the number of coins of both was 5:6. Based on the above information answer the following questions. (i) Write an equation to find the number of coins in Divya's bag. (ii) Write an equation to find the number of coins in Bhabya's bag. (iii) Find the number of Rs. 2 coins in Bhabya's and also in Dibya's bag.

Learn how to solve linear equations for Divya and Bhabya's coin problem. This problem involves finding the number of coins in their bags using algebraic equations, ratio, and proportion. Suitable for students in Grades 6-8.

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