Ram Singh goes to Pushkar Mela with ₹ 10000 to buy exactly 100 animals. He finds that cows are sold at ₹ 1000, horses at ₹ 300 and chicken at ₹ 50. How many chicken should he buy to meet his target of 100 animals?
(a)88
(b)90
(c)92
(d)94
Answer
Answer (as printed): D
Explanation
Let the number of cows and horses bought be $x$ and $y$ respectively. Then, number of chicken bought $=100-(x+y)$. $$\begin{array}{ll} & 1000 x+300 y+50[100-(x+y)]=10000 \\ \Rightarrow & 1000 x+300 y+5000-50(x+y)=10000 \\ \Rightarrow & 950 x+250 y=5000 \Rightarrow 50(19 x+5 y)=5000 \\ \Rightarrow & 19 x+5 y=100 \Rightarrow 5 y=100-19 x \Rightarrow y=\frac{100-19 x}{5} . \end{array}$$ Clearly, for $y$ to be a whole number, $(100-19 x)$ must be divisible by 5 and this is possible only when $x=5$. When $x=5, y=\frac{100-19 \times 5}{5}=\frac{5}{5}=1$. ∴ Number of chicken $=[100-(5+1)]=94$.
Explanation as extracted from the printed page; notation may be imperfect.