A fruit vendor buys some oranges at the rate of Rs. $5$ per orange. He also buys an equal number of bananas at the rate of Rs. $2$ per banana. He makes a $20$ % profit on orange and $15$ % profit on bananas. At the end of the day, all the fruit is sold out. His total profit is Rs. $390$ . Find the number of oranges purchased.

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Solution

Let the no. of oranges $= x =$ no. of bananas

cost price $= 5 x + 2 x = 7 x$

Gain on oranges $= \frac{20}{100} \times 5 x = x$

Gain on Bananas $= \frac{15}{100} \times 2 x = 0.3 x$

Profit $\Rightarrow 1.3 x = 390$

$\Rightarrow x = \frac{390}{1.3} = 300$

No. of oranges purchased $= 300$ .

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Let the no. of oranges =x= no. of bananas cost price =5x+2x=7xGain on oranges =20100×5x=xGain on Bananas =15100×2x=0.3xProfit ⇒1.3x=390⇒x=3901.3=300No. of oranges purchased =300.

Let the no. of oranges $= x =$ no. of bananas

cost price $= 5 x + 2 x = 7 x$

Gain on oranges $= \frac{20}{100} \times 5 x = x$

Gain on Bananas $= \frac{15}{100} \times 2 x = 0.3 x$

Profit $\Rightarrow 1.3 x = 390$

$\Rightarrow x = \frac{390}{1.3} = 300$

No. of oranges purchased $= 300$ .