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?

Accepted Answer

A. Let number of kajubarfi, gulabjamun, sandesh be $x, y, z \ge 1$. 1) $x + y + z = 100$ 2) $10x + 3y + 0.5z = 100 \implies 20x + 6y + z = 200$. Subtract (1) from (2): $19x + 5y = 100$. Since $5y = 100 - 19x$, for $y$ to be a positive integer, $100 - 19x$ must be divisible by 5. $x = 5 \implies 19(5) + 5y = 100 \implies 95 + 5y = 100 \implies y = 1$. Then $z = 100 - 5 - 1 = 94$. Thus, number of gulabjamuns $y = 1$.

Nikhil's Sweet Purchases

Explanation

Practise this under exam conditions