13. The cost of bananas is increased by Re.
1 per dozen, one can get 2 dozen less for Rs. 840. Find the original cost of
one dozen of banana.
Sol. 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
