Question

Ram had 14 mangoes and Raj had only 4
Kam gave some mangoes to Raj and then Raj
had exactly half the number of mangoes as
Raj left with. Find the number of mangoes
which Ram gave to Raj.​

Answer 1

Let the number of mangoes be x.

Number of mangoes sold to the first customer

$= \frac{x}{2} + 1$

Number of remaining mangoes

$= x + ( \frac{x}{2} + 1) = \frac{x}{2} - 1$

Number of mangoes sold to the 2nd customer

$\frac{1}{3} ( \frac{x}{2} - 1) + 1 = \frac{x}{6} + \frac{2}{3}$

Number of remaining mangoes

$= ( \frac{x}{2} - 1) - ( \frac{x}{6} - \frac{2}{3}) = \frac{2x}{6} - \frac{5}{3}$

$= \frac{x}{3} - \frac{5}{3}$

Number of mangoes sold to the 3rd customer

$= \frac{1}{4} ( \frac{x}{3} - \frac{5}{3} ) + 1 = \frac{x}{12} + \frac{7}{12}$

Number of remaining mangoes

$= ( \frac{x}{3} - \frac{5}{3} ) - ( \frac{x}{12} + \frac{7}{13} ) = \frac{3x}{12} - \frac{27}{12}$

$= \frac{x}{4} - \frac{9}{4}$

Number of mangoes sold to the 4th customer

$= \frac{1}{5} ( \frac{x}{4} - \frac{9}{4} ) + 1 = \frac{x}{20} + \frac{11}{20}$

Number of remaining mangoes

$= (\frac{x}{4} - \frac{9}{4} ) - ( \frac{x}{20} - \frac{11}{20} ) = \frac{4x}{20} - \frac{56}{20}$

$= \frac{x}{5} - \frac{14}{5}$

$\red{Given:-}$

$\frac{x}{5} - \frac{14}{5} = 0$

$\frac{x}{5} = \frac{14}{5}$

$= > x = 14$

∴ Number of mangoes with the man initially was 14.

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Answer 2

Answer:

And the mangoes Raj has become (4 + x). Now it is given after the trade of mangoes Raj had exactly half the number of mangoes as Ram left with. So Ram gave 2 mangoes to Raj. So this is the required answer.

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