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?
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 $$x = 5$$
=> $$y = \frac{100 - 95}{5} = 1$$
$$\therefore$$ Nikhil must buy 1 gulabjamun.
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