Ramesh buys some apple at the rate of Rs. 5 per apple. He also buys an equal number of bananas at the rate of Rs. 2 per banana. He makes a 20% profit on apples and a 15% profit on bananas. At the end of the day, all the fruits are sold out. His total profit is Rs. 390. Find the number of apples purchased.

Given:

Cost price of 1 apple = ₹ 5

Cost price of 1 banana = ₹ 2

Number of apples = Number of bananas

Profit on apples = 20%

Profit on bananas = 15%

Total profit = ₹ 390

To find:

The number of apples purchased.

Solution:

Let the number of apples purchased = a

Given that number of bananas are equal to the number of apples. So, the number of

bananas purchased = a

Now,

Cost price of 1 apple = ₹ 5

Cost price of a apples = ₹ 5a

Also,

Cost price of 1 banana = ₹ 2

Cost price of a bananas = ₹ 2a

% profit is already given in the problem. So,

$Profit\ on\ 5a\ apples\ =\ 5a\ \times \ \frac{20}{100} \ =\ 5a\ \times \ \frac{1}{5} \ =\ ₹\ a$

Profit on 2a bananas = $2a\times\frac{15}{100} = 2a\times\frac{3}{20}=\frac{3a}{10}$

Given that the total profit is ₹ 390. So,

Profit of 5a apples + Profit of 2a bananas = 390

$a\ +\ \frac{3a}{10} \ =\  390$

$\frac{10a\ +\ 3a}{10} \ =\  390$

$\frac{13a}{10} \ =\  390$

$a\ =\  390\ \times \ \frac{10}{13}$

$\mathbf{a\ =\ 300}$

So, number of apples purchased is equal to 300.