Question

A man buys lemons at 3 for Rs. 5 and an equal number at 2 for Rs. 4. He mixes them and sells at 5 for Rs. 9. Find his gain or loss per cent. ​

Answer 1

3 lemons cost = Rs. 5

Each lemon cost = Rs. 5/3

2 lemons Cost = Rs. 4

Each lemon cost =

$= \frac{4}{2} = \frac{2}{1} = 2$

Total Cost price of Each lemon =

$\frac{5}{3} + \frac{2}{1}$

LCM = 3

$\frac{5}{3} + \frac{2 \times 3}{1 \times 3} = \frac{6}{3} = \frac{5 + 6}{3} = \frac{11}{3}$

Each lemon Cost =

$= \frac{11}{3} \div \frac{2}{1}$

$= \frac{11}{3} \times \frac{1}{2}$

$= \frac{11}{6}$

Selling price of 5 lemons = 9

Selling price of 1 lemon = 9/5

$loss\% = \frac{loss \times 100}{CP}$

$= \frac{ \frac{4}{6} - \frac{9}{5} \times 100 }{ \frac{11}{6} }$

$= \frac{\frac{55 - 54}{30} \times 100}{ \frac{11}{6} }$

$= \frac{\frac{1}{30} \times 100}{ \frac{11}{6} }$

$= \frac{100}{30} \times \frac{6}{11}$

$= \frac{20}{1} = 1 \frac{9}{11} \% \: loss$

Therefore, Loss% = 1 9/11

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Answer 2

3 lemons cost = Rs. 5

Each lemon cost = Rs. 5/3

2 lemons Cost = Rs. 4

Each lemon cost =

$= \frac{4}{2} = \frac{2}{1} = 2$

Total Cost price of Each lemon =

$\frac{5}{3} + \frac{2}{1}$

LCM = 3

$\frac{5}{3} + \frac{2 \times 3}{1 \times 3} = \frac{6}{3} = \frac{5 + 6}{3} = \frac{11}{3}$

Each lemon Cost =

$= \frac{11}{3} \div \frac{2}{1}$

$= \frac{11}{3} \times \frac{1}{2}$

$= \frac{11}{6}$

Selling price of 5 lemons = 9

Selling price of 1 lemon = 9/5

$loss\% = \frac{loss \times 100}{CP}$

$= \frac{ \frac{4}{6} - \frac{9}{5} \times 100 }{ \frac{11}{6} }$

$= \frac{\frac{55 - 54}{30} \times 100}{ \frac{11}{6} }$

$= \frac{\frac{1}{30} \times 100}{ \frac{11}{6} }$

$= \frac{100}{30} \times \frac{6}{11}$

$= \frac{20}{1} = 1 \frac{9}{11} \% \: loss$