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Question
A person spent Rs 564 in buying geese and ducks. If each goose costs Rs 7, each duck Rs 3, and if the total number of birds bought was 108, how many of each did he buy?
A person spent Rs 564 in buying geese and ducks. If each goose costs Rs 7, each duck Rs 3, and if the total number of birds bought was 108, how many of each did he buy?
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Solution
The correct option is A 60 and 48
In questions of this kind, it is essential to have all quantities expressed in the same denomination; in the present instance, it will be convenient to express the money in rupees.
Let x be the number of geese. Then 108 -x is the number of ducks.
Since each goose costs 7 rupees, x geese cost 7x rupees.
And since each duck costs 3 rupees, 108 -x ducks cost 3(108 -x) rupees.
Therefore, the amount spent is 7x + 3(108 -x) rupees; but the question states that the amount is Rs 564. Hence,
7x+3(108−x)=564
or 7x+324−3x=564
or 4x=240
Therefore, the number of geese, x=60, and the number of ducks, 108−x=48.
In questions of this kind, it is essential to have all quantities expressed in the same denomination; in the present instance, it will be convenient to express the money in rupees.
Let x be the number of geese. Then 108 -x is the number of ducks.
Since each goose costs 7 rupees, x geese cost 7x rupees.
And since each duck costs 3 rupees, 108 -x ducks cost 3(108 -x) rupees.
Therefore, the amount spent is 7x + 3(108 -x) rupees; but the question states that the amount is Rs 564. Hence,
7x+3(108−x)=564
or 7x+324−3x=564
or 4x=240
Therefore, the number of geese, x=60, and the number of ducks, 108−x=48.
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