Question

A fruit seller sells apples as the rate of rs 9 per kg and thereby loses 20%

Answer 1

Solutions :-

This question is incomplete. Right question is =>

Q: A fruit seller sells apples as the rate of Rs 9 per kg and thereby loses 20%. At what price per kg, he should have sold them to make a profit of 5%.

Given :

Selling price of 1 kg apples = Rs 9
Loss = 20%

Find the cost price of apple :-

C.P = (S.P × 100)/(100 - loss)
= (9× 100)/(100 - 20)
= 900/80
= 11.25

Now,
Cost Price = Rs 11.25
To make profit of 5%

Find the Selling price of apple to make a profit of 5 % :-

S.P = C.P + Profit % of C.P
= 11.25 + 5 % of 11.25
= 11.25 + 0.05 × 11.25
= 11.25 + 0.5625
= 11.8125

Hence,

The Selling price of apple to make a profit of 5 % is Rs 11.8125

Answer 2

The question is incomplete. The correct question is:

A fruit seller sells apples at the rate of Rs.9 per kg and thereby loses 20%. At what price per kg, he should have sold them to make a profit of 5%?

Answer:

SP = Rs. 9 / kg

Loss % = 20%

Let the CP be x

=> Loss % = $\dfrac{Loss}{CP} \times 100$

=> Loss % = $\dfrac{ x - 9 }{x} \times {100}$

$\implies 20 = \dfrac{x - 9}{x} \times 100\\\\\implies 20 x = ( x - 9 ) 100\\\\\implies 20x = 100x - 900$

=> 100x - 20x = 900

=> 80x = 900

=> 8x = 90

=> x = 90 / 8 = 11.25

So the CP is Rs. 11.25

Now let us calculate the Profit of 5%.

Let the SP now be denoted as y

$\implies 5 \% = \dfrac{ y - 11.25}{11.25} \times 100\\\\\implies5 \times 11.25 = ( y - 11.25 ) 100\\\\\implies 56.25 = 100y - 1125\\\\\implies 100y = 1125 + 56.25 \\\\\implies 100y = 1181.25\\\\\implies y = \dfrac{1181.25}{100} \implies 11.81$

Hence he must have sold it at Rs. 11.81 to gain a profit of 5 %.