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:<br/>1. 25 notes of 50 are used and the remaining are in the denominations of 20 and 10.<br/>2. 35 notes of 20 are used and the remaining are in the denominations of 50 and 10.<br/>3. 20 notes of 10 are used and the remaining are in the denominations of 50 and 20.<br/><br/>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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