1. 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?
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By: anil on 05 May 2019 02.37 am
Let Nikhil buy $$x, y$$ and $$z$$ pieces of kajubarfi, gulabjamun and sandesh respectively. $$(x,y,z geq 1)$$ => $$x + y + z = 100$$ --------------Eqn(I) Also, $$10x + 3y + frac{1}{2} z = 100$$ => $$20x + 6y + z = 200$$ ----------Eqn(II) Subtracting eqn(I) from (II), we get : => $$19x + 5y = 100$$ => $$y = frac{100 - 19x}{5}$$ If $$x = 1$$, $$y$$ will not be natural. The only value of $$x$$ for natural $$y$$ is $$x = 5$$ => $$y = frac{100 - 95}{5} = 1$$ $$ herefore$$ Nikhil must buy 1 gulabjamun.
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