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Nikhil's Sweet Purchases

XAT 2012 · Quantitative Ability & Data Interpretation · Medium · Linear Equations

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Nikhil's mother asks him to buy 100 pieces of sweets worth 100/-. The sweet shop has 3 kinds of sweets, kajubarfi, gulabjamun and sandesh. Kajubarfi costs 10/- per piece, gulabjamun costs 3/- per piece and sandesh costs 50 paise per piece. If Nikhil decides to buy at least one sweet of each type, how many gulabjamuns should he buy?

  1. A.

    1

  2. B.

    2

  3. C.

    3

  4. D.

    4

  5. E.

    5

Answer

A

Explanation

Let number of kajubarfi, gulabjamun, sandesh be x,y,z≥1x, y, z \ge 1.

  1. x+y+z=100x + y + z = 100
  2. 10x+3y+0.5z=100  ⟹  20x+6y+z=20010x + 3y + 0.5z = 100 \implies 20x + 6y + z = 200. Subtract (1) from (2): 19x+5y=10019x + 5y = 100. Since 5y=100−19x5y = 100 - 19x, for yy to be a positive integer, 100−19x100 - 19x must be divisible by 5. x=5  ⟹  19(5)+5y=100  ⟹  95+5y=100  ⟹  y=1x = 5 \implies 19(5) + 5y = 100 \implies 95 + 5y = 100 \implies y = 1. Then z=100−5−1=94z = 100 - 5 - 1 = 94. Thus, number of gulabjamuns y=1y = 1.

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