A villager buys a goat and a sheep together for Rs.14,250. He sold the sheep at a profit of 10% and the goat at a loss of 20%. If he sold both the animals at the same price, then what was the cost price of the cheaper animal?Options8,2507,5006,0006,600
Question
A villager buys a goat and a sheep together for Rs.14,250. He sold the sheep at a profit of 10% and the goat at a loss of 20%. If he sold both the animals at the same price, then what was the cost price of the cheaper animal?Options8,2507,5006,0006,600
Solution
Let's denote the cost price of the sheep as S and the cost price of the goat as G.
According to the problem, the villager bought both for Rs.14,250. So, we have the equation:
S + G = 14,250
The villager sold the sheep at a profit of 10% and the goat at a loss of 20%, but both for the same price. This gives us two more equations:
1.1S = 0.8G (since the selling price of the sheep is 110% of its cost price and the selling price of the goat is 80% of its cost price)
Now we have a system of two equations, and we can solve it step by step.
First, let's express S from the first equation:
S = 14,250 - G
Now we can substitute S in the second equation:
1.1(14,250 - G) = 0.8G
This simplifies to:
15,675 - 1.1G = 0.8G
Combine like terms:
1.9G = 15,675
Finally, solve for G:
G = 15,675 / 1.9 = 8,250
So, the cost price of the goat was Rs.8,250.
Substitute G = 8,250 in the first equation to find S:
S = 14,250 - 8,250 = 6,000
So, the cost price of the sheep was Rs.6,000.
Therefore, the cost price of the cheaper animal was Rs.6,000.
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