coins in all denominations. What is the total number of coins in the box?
Calculate Total Coins with Equal Denominations
The problem requires finding the total number of coins given the total amount and the denominations (Rs. 1, Rs. 5, Rs. 10), with the condition that the count of each coin type is equal.
Determine the Value of One Set of Coins
Let '$x$' represent the number of coins for each denomination. Since there are equal numbers of Rs. 1, Rs. 5, and Rs. 10 coins, the value contributed by one coin of each denomination is:
- Value of Rs. 1 coins: $1 \times x = x$ rupees
- Value of Rs. 5 coins: $5 \times x = 5x$ rupees
- Value of Rs. 10 coins: $10 \times x = 10x$ rupees
The combined value of one set (one coin of each denomination) is the sum of their individual values:
Value per set = $x + 5x + 10x = 16x$ rupees
Calculate the Number of Coins Per Denomination
The total amount in the box is Rs. 4320. Since each set of coins (one of each denomination) is worth Rs. 16x, we can find the value of '$x$' by dividing the total amount by the value per set:
Total Amount = Number of sets $\times$ Value per set
Rs. 4320 = $x \times 16x$ (This interpretation seems wrong based on the problem statement - 'x' is the number of *each* coin, not the number of sets. Let's correct the approach.)
Let '$x$' be the number of coins of *each* denomination (Rs. 1, Rs. 5, Rs. 10).
The total value is given by:
$ (1 \times x) + (5 \times x) + (10 \times x) = 4320 $Combine the terms:
$ 1x + 5x + 10x = 4320 $ $ 16x = 4320 $Solve for '$x$':
$ x = \frac{4320}{16} $ $ x = 270 $This means there are 270 coins of each denomination (270 one rupee coins, 270 five rupee coins, and 270 ten rupee coins).
Determine 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 '$x$':
Total Coins = $3 \times 270$
Total Coins = 810
Important Questions from Ratio and Proportion
- The sum of three terms is 14380. The ratio between first term and second term is 14:15 and the ratio between second term and the third term is 16:17. Find the difference between first and last term.
- A box containing the denominations of fifty paise coins, two rupee coins and five rupee coins amount to Rs. 1275. There are equal number of coins in all denominations. What is the value of two rupee coins in the box? (In Rs.)
- Three numbers are in the ratio 19:21:23. If the difference between thrice the third number and the sum of first and second number is 841. Find the difference between the first and third number?
- The ratio between the number of males and females in a college is 27:28. If the number of males are increased by 20% and the number of females are increased by 30%, then what will the new ratio of males and females in the college?
- A box containing the denominations of one rupee coins, two rupee coins and ten rupee coins amount to Rs.2730. There are equal number of coins in all denominations. What is the total number of one rupee coins in the box?
