Question

If the cost of banana is increased by Rs.1 then he get two dozens of banana less in Rs.840 then find the original cost of banana per dozen.

Answer 1

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

hope it helps you

Answer 2

Answer:

20

Step-by-step explanation:

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