Five friends P, Q, X, Y and Z purchased some notebooks. The relevant information is given below : 1. Z purchased 8 notebooks more than X did. 2. P and Q together purchased 21 notebooks. 3. Q purchased 5 notebooks less than P did. 4. X and Y together purchased 28 notebooks. 5. P purchased 5 notebooks more than X did. If each notebook is priced ₹ 40, then what is the total cost of all the notebooks?
- (a) ₹ 2,600 ✓ UPSC's answer
- (b) ₹ 2,400
- (c) ₹ 2,360
- (d) ₹ 2,320
Why the answer is (a)
• From statements 2 and 3, P + Q = 21 and P - Q = 5, which gives P = 13 and Q = 8.
• From statement 5, P purchased 5 more than X, so X = P - 5 = 13 - 5 = 8.
• From statement 1, Z purchased 8 more than X, so Z = X + 8 = 8 + 8 = 16.
• From statement 4, X + Y = 28, so Y = 28 - X = 28 - 8 = 20.
• The total number of notebooks is P + Q + X + Y + Z = 13 + 8 + 8 + 20 + 16 = 65.
• The total cost is 65 notebooks × ₹40 = ₹2,600, which corresponds to option (a).
Why the other options are wrong
- (b) ₹ 2,400
- This option implies a total of 60 notebooks, which is 5 less than the correct total of 65.
- (c) ₹ 2,360
- This option implies a total of 59 notebooks, which is 6 less than the correct total of 65.
- (d) ₹ 2,320
- This option implies a total of 58 notebooks, which is 7 less than the correct total of 65.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2022, held on 5 June 2022. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.