Ram Singh goes to the Pushkar mela with Rs 10,000, planning to spend the…
2025
Ram Singh goes to the Pushkar mela with Rs 10,000, planning to spend the entire amount to buy exactly 100 animals. He finds that cows are sold at Rs 1,000 each, horses at Rs 300 each, and chickens at Rs 50 each. How many chickens should he buy?
- A.
100
- B.
90
- C.
98
- D.
94
Show answer & explanation
Correct answer: D
Concept: This is a two-equation, three-unknown word problem restricted to non-negative integers (a linear Diophantine system) - one equation for the total number of animals, another for the total cost (the entire Rs 10,000 is spent). Combining the two by elimination reduces it to a single two-variable equation; since this is a multiple-choice question, the valid general solutions are then matched against the given options to pick the one that is actually offered.
Let x = number of cows, y = number of horses, z = number of chickens.
Total-animals equation: x + y + z = 100.
Total-cost equation (the entire Rs 10,000 is spent): 1000x + 300y + 50z = 10000, which simplifies (dividing by 50) to 20x + 6y + z = 200.
Subtracting the total-animals equation from the simplified cost equation eliminates z: (20x + 6y + z) - (x + y + z) = 200 - 100, giving 19x + 5y = 100.
Since 5y is always a multiple of 5, 19x must also leave a remainder of 0 when divided by 5, so x must be a multiple of 5; and since 19x <= 100, the only possible values are x = 0 and x = 5.
x = 0 gives y = 20 and z = 80; x = 5 gives 19(5) + 5y = 100, so y = 1 and z = 94.
Among the given options (100, 90, 98, 94), only z = 94 is a valid solution to the system, so 94 is the answer.
Cross-check: 1000(5) + 300(1) + 50(94) = 5000 + 300 + 4700 = 10000, matching the full amount spent, and 5 + 1 + 94 = 100, matching the total count.