UPSC Prelims 2022·CSAT·Quantitative Aptitude·Arithmetic

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?

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Last updated 8 Jul 2026, 4:39 pm IST
  1. A2,600Correct
  2. B2,400
  3. C2,360
  4. D2,320

Explanation

Let p, q, x, y, z be the number of notebooks purchased by P, Q, X, Y, Z respectively.

From the given information:

  1. z = x + 8
  2. p + q = 21
  3. q = p - 5
  4. x + y = 28
  5. p = x + 5

Step-by-step calculation:

  1. Solve for P and Q using statements 2 and 3: Substitute (3) into (2): p + (p - 5) = 21 => 2p - 5 = 21 => 2p = 26 => p = 13. Using p = 13 in (3): q = 13 - 5 => q = 8. So, P purchased 13 notebooks and Q purchased 8 notebooks.

  2. Solve for X using statement 5 and p = 13: 13 = x + 5 => x = 13 - 5 => x = 8. So, X purchased 8 notebooks.

  3. Solve for Z using statement 1 and x = 8: z = 8 + 8 => z = 16. So, Z purchased 16 notebooks.

  4. Solve for Y using statement 4 and x = 8: 8 + y = 28 => y = 28 - 8 => y = 20. So, Y purchased 20 notebooks.

Total notebooks purchased = p + q + x + y + z = 13 + 8 + 8 + 20 + 16 = 65 notebooks.

Each notebook is priced at 40. Total cost = Total notebooks * Price per notebook = 65 * 40 = 2600.

Therefore, the total cost of all the notebooks is 2,600.

The final answer is A) 2,600.

Quantitative Aptitude: Five friends P , Q , X , Y and Z purchased some notebooks. The relevant information is given below: 1. Z Purchased 8 not
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