Question:
Answer the questions based on the following information.
A, B, C and D collected one-rupee coins following the given pattern.
Together they collected 100 coins. Each one of them collected even number of coins.
Each one of them collected at least 10 coins. No two of them collected the same number of coins.
If A collected 54 coins and B collected two more coins than twice the number of coins collected by C, then the number of coins collected by B could be
Answer the questions based on the following information.
A, B, C and D collected one-rupee coins following the given pattern.
Together they collected 100 coins. Each one of them collected even number of coins.
Each one of them collected at least 10 coins. No two of them collected the same number of coins.
If A collected 54 coins and B collected two more coins than twice the number of coins collected by C, then the number of coins collected by B could be
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When solving problems with relationships between variables, set up equations based on the given conditions and solve systematically.
Updated On: Aug 4, 2025
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The Correct Option is D
Solution and Explanation
We are given that A collected 54 coins and B collected two more coins than twice the number of coins collected by C. Let the number of coins collected by C be \( x \), then the number of coins collected by B is:
\[
B = 2x + 2.
\]
The total number of coins collected is 100, so:
\[
54 + B + C + D = 100.
\]
Substitute \( B = 2x + 2 \) and \( C = x \) into this equation:
\[
54 + (2x + 2) + x + D = 100.
\]
Simplifying:
\[
3x + 56 + D = 100 \quad \Rightarrow \quad 3x + D = 44.
\]
The number of coins collected by D must be an even number, so \( D = 44 - 3x \) must be even. Therefore, \( x \) must be even. Let \( x = 6 \), so:
\[
B = 2(6) + 2 = 14 \quad \text{and} \quad D = 44 - 3(6) = 26.
\]
Therefore, the number of coins collected by B is 22.
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