Ritu had $400$ mangoes. She sold $60$ mangoes at $25 %$ gain , $80$ mangoes at $20 %$ gain, $120$ mangoes at $10 %$ gain, $140$ mangoes at $20 %$ loss. Her net gain or loss percent is :

7 \frac{1}{2}

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4 \frac{3}{4}

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3 \frac{3}{4}

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3 \frac{4}{3}

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None of these

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Solution

The correct option is E $3 \frac{3}{4}$
Let's assume cost price of a mangoes = x

$∴ C o s t p r i c e o f 400 m a n g o e s = 400 x$

On $60$ mangoes, gain $= 25 %$

$\Rightarrow G a i n_{1} = \frac{C o s t o f 60 m a n g o e s \times 25}{100} = \frac{60 x \times 25}{100} = 15 x$

On $80$ mangoes, gain $= 20 %$

$\Rightarrow G a i n_{2} = \frac{C o s t o f 80 m a n g o e s \times 20}{100} = \frac{80 x \times 20}{100} = 16 x$

On $120$ mangoes, gain $= 10 %$

$\Rightarrow G a i n_{3} = \frac{C o s t o f 120 m a n g o e s \times 10}{100} = \frac{120 x \times 10}{100} = 12 x$

On $140$ mangoes, loss $= 20 %$

$\Rightarrow L o s s_{1} = \frac{C o s t o f 140 m a n g o e s \times 20}{100} = \frac{140 x \times 20}{100} = 28 x$

$T o t a l G a i n = G a i n_{1} + G a i n_{2} + G a i n_{3} = 15 x + 16 x + 12 x = 43 x$

$T o t a l L o s s = L o s s_{1} = 28 x$

$O v e r a l l G a i n = T o t a l G a i n - T o t a l L o s s = 43 x - 28 x = 15 x$

$∴ G a i n P e r c e n t a g e = \frac{G a i n \times 100}{C o s t P r i c e} = \frac{15 x \times 100}{400 x} = 3 \frac{3}{4} %$

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Ritu had 400 mangoes. She sold 60 mangoes at 25% gain , 80 mangoes at 20% gain, 120 mangoes at 10% gain, 140 mangoes at 20% loss. Her net gain or loss percent is :

Ritu had $400$ mangoes. She sold $60$ mangoes at $25 %$ gain , $80$ mangoes at $20 %$ gain, $120$ mangoes at $10 %$ gain, $140$ mangoes at $20 %$ loss. Her net gain or loss percent is :