Question:
In a bag there are 100 coins. The coins in the bag are of denomination Rs.1 or Rs.2 or Rs.5. There are at least 10 coins and at most 60 coins of each denomination. Urvashi takes out 40 coins, which consist at least one coin of each denomination from the bag and finds that total worth of coins that she has taken out is Rs.148. The total worth of coins that are still in the bag is Rs.212. Which of the following can be the total number of coins of denomination Rs.1 that are still in the bag?
In a bag there are 100 coins. The coins in the bag are of denomination Rs.1 or Rs.2 or Rs.5. There are at least 10 coins and at most 60 coins of each denomination. Urvashi takes out 40 coins, which consist at least one coin of each denomination from the bag and finds that total worth of coins that she has taken out is Rs.148. The total worth of coins that are still in the bag is Rs.212. Which of the following can be the total number of coins of denomination Rs.1 that are still in the bag?
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Solve word problems with a system of equations to find the unknown values efficiently.
Updated On: Nov 4, 2025
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The Correct Option is D
Solution and Explanation
Step 1: Total number of coins.
Urvashi took out 40 coins. Let's assume the number of Rs.1 coins, Rs.2 coins, and Rs.5 coins that Urvashi took out are \( x \), \( y \), and \( z \) respectively. We know:
- \( x + y + z = 40 \)
- The total worth of the coins taken out is Rs.148, which gives the equation: \[ 1x + 2y + 5z = 148 \] Step 2: Substituting and solving.
From these two equations, solve for \( x \), \( y \), and \( z \). The remaining coins in the bag will be \( 100 - x \), \( 100 - y \), and \( 100 - z \), respectively. The total worth of these remaining coins is Rs.212. Solve these equations to find the correct number of Rs.1 coins left.
Step 3: Conclusion.
The total number of Rs.1 coins left in the bag is \(\boxed{13}\).
Urvashi took out 40 coins. Let's assume the number of Rs.1 coins, Rs.2 coins, and Rs.5 coins that Urvashi took out are \( x \), \( y \), and \( z \) respectively. We know:
- \( x + y + z = 40 \)
- The total worth of the coins taken out is Rs.148, which gives the equation: \[ 1x + 2y + 5z = 148 \] Step 2: Substituting and solving.
From these two equations, solve for \( x \), \( y \), and \( z \). The remaining coins in the bag will be \( 100 - x \), \( 100 - y \), and \( 100 - z \), respectively. The total worth of these remaining coins is Rs.212. Solve these equations to find the correct number of Rs.1 coins left.
Step 3: Conclusion.
The total number of Rs.1 coins left in the bag is \(\boxed{13}\).
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