UPSC Prelims 2019·CSAT·Quantitative Aptitude·Number System

Suppose you have sufficient amount of rupee currency in three denominations: Rs. 1, Rs. 10 and Rs. 50. In how many different ways can you pay a bill of Rs. 107?

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Last updated 23 May 2026, 3:31 pm IST
  1. A16
  2. B17
  3. C18Correct
  4. D19

Explanation

Let the number of ₹50, ₹10, and ₹1 notes be x, y, and z respectively. The equation is: 50x + 10y + z = 107. Case 1: x = 2 (two ₹50 notes → ₹100 used, ₹7 remaining) y can only be 0, z = 7. → 1 way Case 2: x = 1 (one ₹50 note → ₹57 remaining) y can be 0, 1, 2, 3, 4, or 5. For each y, z = 57 − 10y. → 6 ways Case 3: x = 0 (no ₹50 notes → ₹107 remaining) y can be 0, 1, 2, ..., 10. For each y, z = 107 − 10y. → 11 ways Total: 1 + 6 + 11 = 18 ways.
Quantitative Aptitude: Suppose you have sufficient amount of rupee currency in three denominations: Rs. 1, Rs. 10 and Rs. 50. In how many diffe
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