Question

A and B have together three times what B and C have, while A, B and C together have 150 rupees more than that of A. If B has five times that of C, then A has

• A. Rupees 300
• B. Rupees 325
• C. Rupees 375
• D. Rupees 225

Hint:

When multiple "together/than" comparisons are given, convert each sentence into a linear equation. Use easy substitutions (like \(B=5C\)) to reduce variables quickly.

Answer 1

The Correct Option is B

Let the amounts with A, B, C be \(A, B, C\) respectively.
Step 1: Translate the statements to equations.
(i) "A and B together have three times what B and C have" \(\Rightarrow A+B = 3(B+C) \Rightarrow A = 2B + 3C.\)
(ii) "A, B and C together have Rupees 150 more than A" \(\Rightarrow A+B+C = A + 150 \Rightarrow B+C = 150.\)
(iii) "B has five times that of C" \(\Rightarrow B = 5C.\)
Step 2: Solve for \(B\) and \(C\).
From (ii) and (iii): \(B+C = 150 \Rightarrow 5C + C = 150 \Rightarrow 6C = 150 \Rightarrow C = 25.\)
Hence \(B = 5C = 125.\)
Step 3: Find \(A\).
Using (i): \(A = 2B + 3C = 2(125) + 3(25) = 250 + 75 = 325.\)
\[\boxed{A = Rupees\; 325}\]

Answer 2

Rather than solving for A directly, first pin down B and C from the two conditions that do not involve A, then test which option for A is consistent with the remaining condition.

1. Rupees 300: With \(B=125\) and \(C=25\) fixed (from \(B+C=150\) and \(B=5C\)), checking \(A+B=3(B+C)\) gives \(300+125=425\), but \(3(B+C)=3(150)=450\). Since \(425\neq450\), this value of A does not satisfy the condition.
2. Rupees 325: Checking the same condition, \(325+125=450\), which exactly equals \(3(150)=450\). This is consistent.
3. Rupees 375: Here \(375+125=500\), which does not equal \(450\), so this value fails.
4. Rupees 225: Here \(225+125=350\), again not equal to \(450\), so this value fails as well.

Since \(B+C=150\) and \(B=5C\) fix \(B=125\) and \(C=25\) independently of A, the only value of A that keeps \(A+B=3(B+C)\) true is \(325\).

So the correct answer is Rupees 325.