Ram Singh goes to Pushkar Mela with Rs 10000 to buy exactly 100 animals. He finds that cows are sold at Rs 1000, horses at Rs 300 and chicken at Rs 50. How many chicken should be buy to meet his target of 100 animals?
Let x,y and z be the number of cows, horses and chickens, respectively.
Since he has Rs 10,000.
$$1000x+300y+50z$$ = 10,000 ....(I)
$$ x+y+z$$ = 100 ....(II)
300*eqn(II)- eqn(I) gives
$$250z - 700x = 20,000$$
$$z\ =\ \ \frac{\ 20,000+700x}{250}$$
since $$z$$ is an integer then $$Remainder\left(\frac{\ 20,000+700x}{250}\right)$$ = 0
$$Remainder\left(\frac{\ 20,000+700x}{250}\right)$$ =Â $$Remainder\left(\frac{200x}{250}\right)$$
$$Remainder\left(\frac{200x}{250}\right)$$ = 0 is possible when x takes values 5 ,10, 15 and so on
When x = 5, then z = 94 and y = 1
When x = 10, then z = 108 ( rejected as the total number of animals has to be 100)
For all the values of x greater than 10, the value of z exceeds 100 and does not satisfy the given conditions.
Thus, he has to buy 94 chickens.
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