Question:
Anu collected a certain number of coins of denominations Rs. 1, Rs. 2 and Rs. 5. She has a certain number of Rs. 2 coins, 4 times as many Rs. 1 coins as Rs. 5 coins and 15 more Rs. 2 coins than Rs. 1 coins. If the total value is Rs. 490, how many Rs. 2 coins are there?
Anu collected a certain number of coins of denominations Rs. 1, Rs. 2 and Rs. 5. She has a certain number of Rs. 2 coins, 4 times as many Rs. 1 coins as Rs. 5 coins and 15 more Rs. 2 coins than Rs. 1 coins. If the total value is Rs. 490, how many Rs. 2 coins are there?
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Write the Rs. 5 and Rs. 2 coin counts in terms of the Rs. 1 coins, then form one equation from the total value.
Updated On: Jul 21, 2026
- 11
- 20
- 35
- 60
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The Correct Option is C
Solution and Explanation
Step 1: Assign a variable.
Let the number of Rs. 1 coins be \( x \).
Step 2: Express the other coin counts using \( x \).
The number of Rs. 5 coins is four times the Rs. 1 coins, so Rs. 5 coins \( = 4x \).
The number of Rs. 2 coins is 15 more than the Rs. 1 coins, so Rs. 2 coins \( = x + 15 \).
Step 3: Write the total value equation.
\( 1(x) + 2(x + 15) + 5(4x) = 490 \).
Step 4: Simplify and solve for \( x \).
\( x + 2x + 30 + 20x = 490 \).
\( 23x + 30 = 490 \).
\( 23x = 460 \).
\( x = 20 \).
Step 5: Find the number of Rs. 2 coins.
Rs. 2 coins \( = x + 15 = 20 + 15 = 35 \).
Final Answer:
The number of Rs. 2 coins is 35. \[ \boxed{35} \]
Let the number of Rs. 1 coins be \( x \).
Step 2: Express the other coin counts using \( x \).
The number of Rs. 5 coins is four times the Rs. 1 coins, so Rs. 5 coins \( = 4x \).
The number of Rs. 2 coins is 15 more than the Rs. 1 coins, so Rs. 2 coins \( = x + 15 \).
Step 3: Write the total value equation.
\( 1(x) + 2(x + 15) + 5(4x) = 490 \).
Step 4: Simplify and solve for \( x \).
\( x + 2x + 30 + 20x = 490 \).
\( 23x + 30 = 490 \).
\( 23x = 460 \).
\( x = 20 \).
Step 5: Find the number of Rs. 2 coins.
Rs. 2 coins \( = x + 15 = 20 + 15 = 35 \).
Final Answer:
The number of Rs. 2 coins is 35. \[ \boxed{35} \]
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