QUESTION

CSAT

Medium

Reasoning

Prelims 2022

Five friends P. O, 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. O 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?

Select an option to attempt

Explanation

Given information:

  1. From Statement 1: Z=X+8Z = X + 8 ….(i)
  2. From Statement 2: P+Q=21P + Q = 21 ….(ii)
  3. From Statement 3: Q=P5Q = P - 5 ….(iii)
  4. From Statement 4: X+Y=28X + Y = 28 ….(iv)
  5. From Statement 5: P=X+5P = X + 5 ….(v)

We need to calculate the total number of notebooks: P+Q+X+Y+ZP + Q + X + Y + Z.

  1. Using equations (ii) and (iii): P=13P = 13 Then, Q=P5=8Q = P - 5 = 8.

  2. With P=13P = 13 and using equation (v): X=P5=8X = P - 5 = 8

  3. Using X=8X = 8 in equation (i): Z=X+8=16Z = X + 8 = 16

  4. Finally, using X=8X = 8 in equation (iv): Y=288=20Y = 28 - 8 = 20

Total Calculation: P+Q+X+Y+Z=13+8+8+20+16=65P + Q + X + Y + Z = 13 + 8 + 8 + 20 + 16 = 65

The cost of all the notebooks is:

65×40=Rs.260065 \times 40 = Rs. 2600

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