Question

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?

• A. 1
• B. 2
• C. 3
• D. 4
• E. 5

Hint:

- For mixture-type problems, always set up equations for both \textbf{quantity} and \textbf{cost}.
- Multiplying to eliminate fractions simplifies calculations.
- Test small integer values systematically to find feasible solutions.

Answer 1

The Correct Option is A

Step 1: Define variables.
Let the number of kajubarfi pieces be \(x\), gulabjamuns be \(y\), and sandesh be \(z\).
Step 2: Frame equations.
Total number of sweets: \[ x + y + z = 100 \] Total cost (in rupees): \[ 10x + 3y + 0.5z = 100 \] Step 3: Eliminate fractions.
Multiply cost equation by 2: \[ 20x + 6y + z = 200 \] Step 4: Subtract the two equations.
\[ (20x + 6y + z) - (x + y + z) = 200 - 100 \] \[ 19x + 5y = 100 \] Step 5: Solve for integer values.
The equation is: \[ 19x + 5y = 100 \] Try values for \(y\):
- If \(y = 1\): \[ 19x + 5 = 100 \Rightarrow 19x = 95 \Rightarrow x = 5 \] Then, \(x + y + z = 100 \Rightarrow 5 + 1 + z = 100 \Rightarrow z = 94\).
This satisfies all conditions.
Thus, the number of gulabjamuns \(y = 1\). \[ \boxed{1} \]