Reasoning : Logical Reasoning & Analytical Ability

Q 84 / 325

UPSC CSE Prelims 2022

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 Rs 40, then what is the total cost of all the notebooks?

EXPLANATION

Correct Option

Let P, Q, X, Y, and Z represent the number of notebooks purchased by each friend. Based on the given information, a system of linear equations can be formulated:

  • Z = X + 8 (Equation 1)
  • P + Q = 21 (Equation 2)
  • Q = P - 5 (Equation 3)
  • X + Y = 28 (Equation 4)
  • P = X + 5 (Equation 5)

To determine the number of notebooks purchased by each individual:

  1. Substitute Equation 3 into Equation 2:
    P + (P - 5) = 21
    2P - 5 = 21
    2P = 26
    P = 13 notebooks.
  2. Substitute the value of P into Equation 3:
    Q = 13 - 5
    Q = 8 notebooks.
  3. Substitute the value of P into Equation 5:
    13 = X + 5
    X = 8 notebooks.
  4. Substitute the value of X into Equation 1:
    Z = 8 + 8
    Z = 16 notebooks.
  5. Substitute the value of X into Equation 4:
    8 + Y = 28
    Y = 20 notebooks.

The total number of notebooks purchased by all five friends is the sum of their individual purchases:

Total notebooks = P + Q + X + Y + Z = 13 + 8 + 8 + 20 + 16 = 65 notebooks.

Given that each notebook is priced at Rs 40, the total cost of all notebooks is calculated as:

Total cost = Total notebooks × Price per notebook = 65 × 40 = Rs 2,600.

Incorrect Options

Options 2 (Rs 2,400), 3 (Rs 2,360), and 4 (Rs 2,320) are incorrect as they do not match the calculated total cost of Rs 2,600 derived from the given information.