Coin Denominations Problem Explained

Let the number of coins for each denomination (Rs. 1, Rs. 5, and Rs. 10) be '$x$'. This is because the question states there are an equal number of coins in all denominations.

Calculating the Value of Coins

The total value contributed by each denomination can be calculated as follows:

• Value from Rs. 1 coins = $1 \times x = x$
• Value from Rs. 5 coins = $5 \times x = 5x$
• Value from Rs. 10 coins = $10 \times x = 10x$

Setting Up the Total Amount Equation

The sum of the values from all denominations equals the total amount in the box, which is Rs. 1360.

So, the equation is:

$x + 5x + 10x = 1360$

Solving for the Number of Each Coin Type

Combine the terms on the left side of the equation:

$16x = 1360$

Now, solve for '$x$' by dividing the total amount by 16:

$x = \frac{1360}{16}$

$x = 85$

This means there are 85 coins of Rs. 1, 85 coins of Rs. 5, and 85 coins of Rs. 10.

Calculating the Total Number of Coins

The total number of coins is the sum of the counts for each denomination:

Total Coins = Number of Rs. 1 coins + Number of Rs. 5 coins + Number of Rs. 10 coins

Total Coins = $x + x + x = 3x$

Substitute the value of '$x$' we found:

Total Coins = $3 \times 85$

Total Coins = 255

Therefore, the total number of coins in the box is 255.