if the cost of Bananas is increased by rupees 2 per dozen one can get one dozen less bananas for Rs 840 find original cost of one dozen banana
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Let the cost of banana per dozen be Rs. x.
Amount for which bananas are bought = Rs. 840
No. of dozens of bananas for Rs 840 = 840/x
New cost of banana per dozen = Rs. (x + 1)
New No. of dozens of bananas for Rs 840 = 840/x+1
According to given condition,
840/x – 840 / x + 1 = 2
∴ 840[1/x – 1/x+1] = 2
∴ 840 [x+1- x / x(x+1)] = 2
∴ 840 [1/ (x² + x)] = 2
∴ 840 = 2(x² + x)
∴ 2x2 + 2x – 840 = 0
Dividing by 2, we get
x² + x – 420 = 0
x² – 20x + 21x – 420 = 0
∴ x (x – 20) + 21 (x – 20) = 0
∴ x – 20 = 0 or x + 21 = 0
∴ x = 20 or x = –21
∴ The cost of bananas cannot be negative.
∴ x = 20
The original cost of one dozen banana is Rs. 20
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