Civil Services Prep

Prelims 2022 · CSAT / Quantitative Aptitude · Question 8

A bill for 1,840 is paid in the denominations of 50, 20 and 10 notes. 50 notes in all are used. Consider the following statements:

  1. 25 notes of 50 are used and the remaining are in the denominations of 20 and 10.
  2. 35 notes of 20 are used and the remaining are in the denominations of 50 and 10.
  3. 20 notes of 10 are used and the remaining are in the denominations of 50 and 20.

Which of the above statements are not correct?

  1. 1 and 2 only
  2. 2 and 3 only
  3. 1 and 3 only
  4. 1, 2 and 3

Answer

1, 2 and 3

Let the numbers of ₹50, ₹20 and ₹10 notes be x, y, z. Then x + y + z = 50 and 50x + 20y + 10z = 1840, i.e. 5x + 2y + z = 184. Subtracting gives 4x + y = 134.

  1. If x = 25, then y = 34 and z = -9, which is impossible. Statement 1 is not correct.
  2. If y = 35, then 4x + 35 = 134 ⇒ x = 24.75, not an integer. Statement 2 is not correct.
  3. If z = 20, then x + y = 30 and 5x + 2y = 164. Solving gives x = 34.67, not an integer. Statement 3 is not correct.

Hence, all 1, 2 and 3 are not correct.

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