​In a bag, there are a certain number of coins of the denominations ₹1,₹2 and ₹5 in the ratio of 3:4:5. If the total value of the coins in the bag is ₹ 756 , then the total number of coins in the bag is ​

Correct option is C

Given:

1. Coins of denominations ₹1, ₹2, and ₹5 are in the ratio of 3:4:5 .

2. Total value of all coins = ₹756.

Formula Used:$$\text{Total value} = 3x \cdot 1 + 4x \cdot 2 + 5x \cdot 5$$​

1. Value of coins of a particular denomination = (Number of coins) \times (Denomination value).

2. Total value = Sum of the values of coins of all denominations.

3. Let the number of coins of ₹1, ₹2, and ₹5 denominations be 3x, 4x, and 5x respectively.

$$\text{Total value} = 3x \cdot 1 + 4x \cdot 2 + 5x \cdot 5$$​

Simplify to find x , and then calculate the total number of coins:

Total number of coins = 3x + 4x + 5x.

Solution:

1. Write the equation for the total value:

$$3x \cdot 1 + 4x \cdot 2 + 5x \cdot 5 = 756$$​

Simplify:

3x + 8x + 25x = 756

36x = 756

2. Solve for x :

$$x = \frac{756}{36} = 21$$​

3. Calculate the total number of coins:

Total number of coins = 3x + 4x + 5x = 12x

Substitute x = 21 :

Total number of coins = $$12 \cdot 21 = 252$$​

Final Answer:

The total number of coins in the bag is 252