Oranges are bought at 7 for Rs 3. At what rate per hundred must they be sold to gain 33%?

Given: Oranges are bought at 7 for Rs 3.

To find: Here we have to find the rate per hundred oranges must be sold to gain 33% profit.

Solution:

Cost Price of 7 Oranges = Rs. 3

Cost Price of 1 Orange = Rs. $\frac{3}{7}$

Cost Price of 100 Oranges = Rs. $\frac{3}{7}\ \times\ 100$

Cost Price of 100 Oranges = Rs. $\frac{300}{7}$

Calculating Selling Price (SP) of 100 Oranges to gain 33% profit:

We know that,

$SP\ =\ CP\ \times\ \frac{( 100\ +\ Gain)}{100}$ 

$SP\ =\ \frac{300}{7}\ \times\ \frac{( 100\ +\ 33)}{100}$

$SP\ =\ \frac{300\ \times \ 133}{7\ \times \ 100}$

$SP\ =\ 3\ \times\ 19$

$SP\ =$ Rs. 57

So, oranges must be sold Rs. 57 per hundred to gain 33% profit.