Selling rubber bands at the rate of 32 a rupee, a man loses 40%. How many rubber bands for a rupee should he sell in order to gain 20%?

Correct option is D

Given:

Loss at selling 32 rubber bands per ₹1 = 40%

Desired gain = 20%

Solution:

Let the cost price (CP) of 1 rubber band be ₹x.

At 40% loss, selling price (SP) = 60% of CP
At 20% gain, SP = 120% of CP

Loss Case: SP = ₹1 for 32 rubber bands

SP per band = $$\frac{₹1 }{ 32}$$​​

SP (Loss) = $$\frac{1}{32} = 0.6x$$​

x $$= \frac{1}{32 \times 0.6}$$​

Gain Case: SP = 1.2x

Find number of rubber bands = $$\frac{₹1 }{ 1.2x}$$​​

Find CP per rubber band:

​$$\frac{1}{32} = 0.6x$$​​

x =$$\frac{1}{32 \times 0.6} = \frac{1}{19.2}$$​

SP for 20% gain = 1.2x =$$1.2 \times \frac{1}{19.2} = \frac{1.2}{19.2} = \frac{1}{16}$$​​

So, to get ₹1, number of rubber bands to be sold =

​$$\frac{1}{\frac{1}{16}} = 16$$​

16 rubber bands per rupee.

Alternate Method:

$$\frac{1}{32}\times\frac{120\%}{60\%}=\frac 1{16}$$

​16 rubber bands per rupee.