A bag consista of Rs.1, Rs.2 and Rs, 6 conns. The sumber of Rs. 2 coins is equal to twice the number of Rs. 1 cons. The number of Rs. 5 is equal to thrice the number of Rs. 2 coins . If the total amount in the bad is Rs. 700, then find the total number of coins in the beg.

Options

A. 150
B. 160
C. 280
D. 200

Answer

To solve the problem step by step, let's denote the number of Rs. 1 coins as \( x \).

### Step 1: Define the Variables
- Let the number of Rs. 1 coins be \( x \).
- The number of Rs. 2 coins is twice the number of Rs. 1 coins, so it will be \( 2x \).
- The number of Rs. 5 coins is thrice the number of Rs. 2 coins, so it will be \( 3 \times (2x) = 6x \).

### Step 2: Calculate the Total Value of Coins
Now, let's calculate the total value of the coins:
- The total value from Rs. 1 coins is \( 1 \times x = x \).
- The total value from Rs. 2 coins is \( 2 \times (2x) = 4x \).
- The total value from Rs. 5 coins is \( 5 \times (6x) = 30x \).

### Step 3: Set Up the Equation
According to the problem, the total amount in the bag is Rs. 700. Therefore, we can set up the equation:
\[ x + 4x + 30x = 700 \]

### Step 4: Combine Like Terms
Combine the terms on the left side:
\[ 35x = 700 \]

### Step 5: Solve for \( x \)
To find \( x \), divide both sides by 35:
\[ x = \frac{700}{35} = 20 \]

### Step 6: Find the Number of Each Type of Coin
Now that we have \( x \):
- The number of Rs. 1 coins is \( x = 20 \).
- The number of Rs. 2 coins is \( 2x = 2 \times 20 = 40 \).
- The number of Rs. 5 coins is \( 6x = 6 \times 20 = 120 \).

### Step 7: Calculate the Total Number of Coins
Finally, to find the total number of coins in the bag, we add the number of each type of coin:
\[ \text{Total coins} = x + 2x + 6x = 20 + 40 + 120 = 180 \]

### Final Answer
The total number of coins in the bag is **180**.

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