Five friends P, Q, X, Y and Z purchased some notebooks. The relevant information is given below:<br/>1. Z purchased 8 notebooks more than X did.<br/>2. P and Q together purchased 21 notebooks.<br/>3. Q purchased 5 notebooks less than P did.<br/>4. X and Y together purchased 28 notebooks.<br/>5. P purchased 5 notebooks more than X did.<br/><br/>If each notebook is priced 40, then what is the total cost of all the notebooks?

Re-examination: My earlier derived_answer was incorrect; the working actually gives (a).

• Let X = x. From P purchased 5 more than X, P = x + 5. Verdict: correct setup.
• From Q purchased 5 less than P, Q = (x + 5) - 5 = x. Verdict: Q = X.
• From P + Q = 21, (x + 5) + x = 21 ⇒ 2x = 16 ⇒ x = 8. Hence X = 8, P = 13, Q = 8. Verdict: correct.
• From X + Y = 28, 8 + Y = 28 ⇒ Y = 20. Verdict: correct.
• From Z purchased 8 more than X, Z = 8 + 8 = 16. Verdict: correct.
• Total notebooks = 13 + 8 + 8 + 20 + 16 = 65; total cost = 65 × 40 = 2600. Verdict: correct option is (a).
  Error identified: The earlier explanation computed 2600 correctly but mistakenly marked option (c) instead of (a).