Question

After selling a certain quantity of fruits, Manoj realized that he was selling at a loss of 15%. He then sold the remaining fruits that he had at 20% profit such that he ended up with 0 net loss and 0 net profit. If he had sold 40 kg of fruits on loss, how many kgs of fruits did he sell on profit.

Answer 1

Answer:

Let the Fruits Sold at 20% Profit be n, and those who sold at 15% Loss be (40 – n).

$\underline{\bigstar\:\textbf{According to the Question :}}$

$:\implies\sf Total\:SP=Total\:CP\\\\{\scriptsize\qquad\bf{\dag}\:\:\texttt{As there is No Profit, No Loss}}\\\\:\implies\sf [n \times (100+Profit)\%]+[(40-n) \times (100-Loss)\%]=40\\\\\\:\implies\sf [n \times (100+20)\%]+[(40-n) \times (100-15)\%]=40\\\\\\:\implies\sf [n \times 120\%]+[(40-n) \times 85\%]=40\\\\\\:\implies\sf \bigg\lgroup n \times \dfrac{120}{100}\bigg\rgroup + \bigg\lgroup(40 - n) \times \dfrac{85}{100}\bigg\rgroup = 40\\\\\\:\implies\sf \dfrac{120n + (40 \times 85) - 85n}{100} = 40\\\\\\:\implies\sf 120n - 85n + (40 \times 85) = (40 \times 100)\\\\\\:\implies\sf 35n = (40 \times 100) - (40 \times 85)\\\\\\:\implies\sf 35n = 40 \times (100 -85)\\\\\\:\implies\sf 35n = 40 \times 15\\\\\\:\implies\sf n = \dfrac{40 \times 15}{35}\\\\\\:\implies\underline{\boxed{\sf n = 17.14\:kg}}$

⠀

$\therefore\:\underline{\textsf{Hence, Manoj sold \textbf{17.14 kg} fruits on profit}}.$

$\rule{150}{1}$

$\boxed{\begin{minipage}{6.5 cm}\underline{\text{Some Important Formulae Related to it :}}\\ \\ SP=CP\times(100+\sf Profit)\%\\ \\SP=CP\times(100-Loss)\%\\ \\Profit\%=\dfrac{Profit}{CP}\times100 \\ \\Loss\%=\dfrac{Loss}{CP}\times100\end{minipage}}$

Answer 2

Answer:

30 kg

Step-by-step explanation:

let the CP of the fruit per kg be X. Let the quantities sold on profit be Y kg.

therefore,

X * 0.15 * 40 = X * 0.2 * Y

Y= 30 kg