Sure, let's solve this step-by-step!
We are given a total amount of ₹740 in coins of denominations ₹1, ₹2, and ₹5. We also know the following relationships about the number of coins for each denomination:
1. The number of ₹2 coins is three times the number of ₹1 coins.
2. The number of ₹5 coins is three times the number of ₹2 coins.
Let's denote the number of ₹1 coins as [tex]\( x \)[/tex].
From the first relationship, the number of ₹2 coins will be [tex]\( 3x \)[/tex].
From the second relationship, the number of ₹5 coins will be [tex]\( 3 \times (3x) = 9x \)[/tex].
Now, we can write the total value of the coins in terms of [tex]\( x \)[/tex]:
- The value of the ₹1 coins is [tex]\( 1 \times x = x \)[/tex].
- The value of the ₹2 coins is [tex]\( 2 \times 3x = 6x \)[/tex].
- The value of the ₹5 coins is [tex]\( 5 \times 9x = 45x \)[/tex].
Summing these values should give us the total amount of ₹740:
[tex]\[ x + 6x + 45x = 740 \][/tex]
Combining like terms, we get:
[tex]\[ 52x = 740 \][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{740}{52} = 14 \][/tex]
So, the number of ₹1 coins is [tex]\( x = 14 \)[/tex].
The number of ₹2 coins is [tex]\( 3x = 3 \times 14 = 42 \)[/tex].
The number of ₹5 coins is [tex]\( 9x = 9 \times 14 = 126 \)[/tex].
Therefore, Manas has:
- 14 coins of ₹1 denomination,
- 42 coins of ₹2 denomination,
- 126 coins of ₹5 denomination.
