Question 22

# 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?

Solution

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

$$Remainder\left(\frac{\ 20,000+700x}{250}\right)$$ = $$Remainder\left(\frac{200x}{250}\right)$$

$$Remainder\left(\frac{200x}{250}\right)$$ = 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 y = 108 ( rejected as total number of animals has to be 100 )

Thus he has to buy 94 chickens

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