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

Step 1: From "A, B and C together have Rupees 150 more than A," we get \(B+C=150\). From "B has five times that of C," \(B=5C\).

Step 2: Substituting \(B=5C\) into \(B+C=150\) gives \(6C=150\), so \(C=25\) and \(B=5(25)=125\).

Step 3: Using "A and B together have three times what B and C have," \(A+B=3(B+C)\), so \(A+125=3(150)=450\), giving \(A=325\).

\[ \boxed{A = Rupees\ 325} \]