Two kinds of rice are sold at same price in which 10% is gained on one kind and 10% is lost on the other. If they be mixed equally and sold at the same price, what percentage will be gained or lost?

A 2% loss

B 1% loss

C 0.5% gain

D 0.8% loss

E 1% gain

Correct Answer: Option B

Let’s assume the cost price of first kind of rice be Rs. x/kg

And, the cost price of second kind of rice be Rs. y/kg

According to the given information,

Selling price of first kind of rice = x + (10% of x) = 1.1x

Selling price of second kind of rice = y – (10% of y) = 0.9y

∵ Selling price of both rices are same

⇒ 1.1x = 0.9y

⇒ x = (9y/11)

∵ Both kind of rices are mixed in equal proportion,

⇒ Cost price of the mixture per kg = Rs. (x + y)/2

⇒ Cost price of the mixture \(= \;\frac{{y + \frac{{9y}}{{11}}}}{2}\; = \;\frac{{10y}}{{11}}\)

∵ the mixture is sold at the same price as before,

Selling price of mixture per kg = 0.9y \(= \;\frac{{9y}}{{10}}\)

As we can see by comparison that selling price < Cost price

∴ loss will be incurred in this transaction.

We know that, % Loss \(= \frac{{Cost\;price\;-\;Selling\;price}}{{Cost\;Price}} \times 100\)

∴% Loss \(= \frac{{\left( {\frac{{10y}}{{11}}} \right)\;-\left( {\frac{{9y}}{{10}}} \right)}}{{\left( {\frac{{9y}}{{10}}} \right)}} \times 100\)

⇒ % loss = 1

∴ There was a loss of 1%