Question

a retailer has 250 kg of rice a part of which he sells at 10% profit. The remaining quantity of rice is of low quality and he sold it at 5% loss. Overall he made a profit of 7%. Find the quality of rice sold at 5% costs.

Answer 1

Answer:

by using alligation-

3/5×250kg =150kg

Answer 2

Given:

total quantity of rice$=250kg$, a part of which is sold at a profit of 10% and remaining at a loss of 5%.

Overall profit made$=7\%$

To find: the quality of rice sold at 5% loss.

Solution:

Assume that the quantity of rice sold at 10% profit is x kg.

and then the quantity sold at 5% loss will become $(250-x)$kg.

Form the equations according to the conditions given in the question,

$\[\frac{{110}}{{100}} \times x + \frac{{95}}{{100}} \times \left( {250 - x} \right) = \frac{{107}}{{100}} \times 250\]$

$\[ \Rightarrow \frac{{110x + \left( {23750 - 95x} \right)}}{{100}} = \frac{{5 \times 107}}{2}\]$

$\[ \Rightarrow \frac{{25x + 23750}}{{100}} = \frac{{5 \times 107}}{2}\]$

$\[ \Rightarrow 25x + 23750 = \frac{{5 \times 107 \times 100}}{2}\]$

$\[\begin{array}{l} \Rightarrow 25x + 23750 = 26750\\ \Rightarrow 25x = 26750 - 23750\\ \Rightarrow 25x = 3000\end{array}\]$

$\[\begin{array}{l} \Rightarrow x = \frac{{3000}}{{25}}\\ \Rightarrow x = 120\end{array}\]$

Find the quantity of rice sold at 5% loss.

Quantity$=(250-x)$

             $=250-120\\=130 kg$

Hence, the quantity of rice sold at 5% loss is 130 kg.