if the cost of Bananas is increased by 10 rupees per dozen and can get 3 dozen less for rs 600 find the original cost of one dozen bananas
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See a solution process below:
If:
1 dozen=91 rs
Then we can multiply each side of the equation by 10 to find the cost of 10 dozen oranges:
10×1 dozen=10×91 rs
10 dozen=910 rs
If:
1 dozen=91 rs
Then we can multiply each side of the equation by 10 to find the cost of 10 dozen oranges:
10×1 dozen=10×91 rs
10 dozen=910 rs
ash191:
how you get 1 dozen =91
Let x be the original cost of a dozen bananas. For Rs.600 let us one gets y dozens.
xy = 600 … (1)
(x+10)(y-3) = 600 … (2)
From (1) y = 600/x. Putting that value in (2), we get,
(x+10)(600/x-3) = 600 or
(x+10)(600–3x)/x = 600 or
(10+x)(600 -3x) = 600x or
6000 + 570x - 3x^2 = 600x or
6000 - 30x - 3x^2 = 0 or
2000 - 10x - x^2 = 0
x^2 + 10x - 2000 = 0
(x+50)(x-40) = 0
So x = -50 or 40. Since cost of bananas cannot a negative figure, x = 40.
So at Rs.40 per dozen one can buy 15
xy = 600 … (1)
(x+10)(y-3) = 600 … (2)
From (1) y = 600/x. Putting that value in (2), we get,
(x+10)(600/x-3) = 600 or
(x+10)(600–3x)/x = 600 or
(10+x)(600 -3x) = 600x or
6000 + 570x - 3x^2 = 600x or
6000 - 30x - 3x^2 = 0 or
2000 - 10x - x^2 = 0
x^2 + 10x - 2000 = 0
(x+50)(x-40) = 0
So x = -50 or 40. Since cost of bananas cannot a negative figure, x = 40.
So at Rs.40 per dozen one can buy 15
dozens for Rs.600. If the cost goes up by Rs.10, the person can get 600/(40+10) = 600/50 = 12 dozens which is 3 dozens short of the previous purchasing power!
So the original cost of bananas is Rs.40 per dozen.
So the original cost of bananas is Rs.40 per dozen.
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