MECL's Management Representative.

Chi and Monk are going to the market purchasing toys for children. Mani has Rs 84 in her purse, while Monk has Rs 85. Mahi has 36 coins of Rs 2 and Rs 5. Monk has Rs 1 and Rs 2 coins, and the ratio of her coins is 5:6.

i) Find the number of Rs 2 coins in Mani's purse.

ii) Find the number of Rs 2 coins in Monk's purse.

iii) Write the equation for finding the number of coins in Mahi's purse.



Answer :

Sure, let's solve the problem step-by-step.

### Part i: Finding Number of Rs 2 Coins in Mani's Purse

1. Understanding the given conditions:
- Mani has 36 coins in her purse.
- The coins are either Rs 2 coins or Rs 5 coins.

2. Setting up equations:
- Let [tex]\( x \)[/tex] be the number of Rs 2 coins.
- Let [tex]\( y \)[/tex] be the number of Rs 5 coins.

We have two conditions:
- The total number of coins is 36: [tex]\( x + y = 36 \)[/tex]
- The total amount of money is Rs 84: [tex]\( 2x + 5y = 84 \)[/tex]

3. Solving the system of equations:
[tex]\[ \begin{cases} x + y = 36 \quad \text{(Equation 1)}\\ 2x + 5y = 84 \quad \text{(Equation 2)} \end{cases} \][/tex]

First, solve Equation 1 for [tex]\( y \)[/tex]:

[tex]\[ y = 36 - x \][/tex]

Next, substitute [tex]\( y \)[/tex] in Equation 2:

[tex]\[ 2x + 5(36 - x) = 84 \][/tex]

Simplify this equation:

[tex]\[ 2x + 180 - 5x = 84 \][/tex]

Combine like terms:

[tex]\[ -3x + 180 = 84 \\ -3x = 84 - 180 \\ -3x = -96 \\ x = 32 \][/tex]

So, the number of Rs 2 coins ([tex]\( x \)[/tex]) is 32.

To find [tex]\( y \)[/tex]:

[tex]\[ y = 36 - 32 \\ y = 4 \][/tex]

Verification:
[tex]\[ 2(32) + 5(4) = 64 + 20 = 84 \][/tex]

The calculations are correct.

- Number of Rs 2 coins in Mani's purse: 32

### Part ii: Finding the Number of Coins of Rs 2 in Moni's Purse

1. Understanding the given conditions:
- Moni has Rs 85 with coins of Rs 1 and Rs 2.
- The ratio of Rs 1 coins to Rs 2 coins is 5:6.

2. Setting up the ratio:
- Let the number of Rs 1 coins be [tex]\( 5k \)[/tex].
- Let the number of Rs 2 coins be [tex]\( 6k \)[/tex].

3. Forming the equation using the total amount:
[tex]\[ 5k + 12k = 85 \][/tex]
Simplify this:

[tex]\[ 17k = 85 \\ k = 5 \][/tex]

So, the number of Rs 1 coins:
[tex]\[ 5k = 5 \times 5 = 25 \][/tex]

And the number of Rs 2 coins:
[tex]\[ 6k = 6 \times 5 = 30 \][/tex]

Verification:
[tex]\[ 1(25) + 2(30) = 25 + 60 = 85 \][/tex]

The calculations are correct.

- Number of Rs 2 coins in Moni's purse: 30

### Part iii: Writing the Equation for Finding the Number of Coins in Mahi's Purse

Given that Mahi has a situation similar to Mani’s in having Rs 2 and Rs 5 coins, we can model the number of coins in Mahi's purse as we did for Mani.

If [tex]\( x \)[/tex] is the number of Rs 2 coins and [tex]\( y \)[/tex] is the number of Rs 5 coins in Mahi's purse, and she also has a total of 36 coins worth a specific total value (unknown here), the core equation to find the number of coins of each type is:

1. Total coins equation:
[tex]\[ x + y = 36 \][/tex]

2. Value equation:
[tex]\[ 2x + 5y = \text{[Total Amount in Rupees]} \][/tex]

These are the fundamental equations for solving the problem related to Mahi's purse assuming the format remains the same as Mani's.