Question

From a number of mangoes, a man sells half the number of existing mangoes plus $1$ to the first customer, then sells $\frac{1}{3}$rd of the remaining number of mangoes plus $t$o the second customer, then $\frac{1}{4}$ of the remaining number of mangoes plus $1$ to third customer and $\frac{1}{5}$th of the remaining number of mangoes plus $1$ to the fourth customer. He then finds that he does not have any mango left. How many mangoes did he have originally ?

• A. $12$
• B. $14$
• C. $15$
• D. $13$

Answer 1

The correct option is B $14$

Let the number of mangoes that the man has originally $=x$
Number of mangoes sold to Balance
1st customer $=\frac{x}{2}+1$ $\frac{x-2}{2}$

2nd customer $=\frac{x-2}{6}+1$ $\frac{x-5}{3}$
3rd customer $=\frac{x-5}{12}+1$ $\frac{x-9}{4}$
4th customer $=\frac{x-9}{20}+1$ $0$
$\frac{x-9}{20}+1=\frac{x-9}{4}$

$\Rightarrow \frac{x+11}{20}=\frac{x-9}{4}$
$\Rightarrow 4x+44=20x-180$
$\Rightarrow 16x=224$

$\Rightarrow x=14$