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- Quantitative Aptitude
A merchant buys $4000\, kg$ of wheat, one$-$fifth of which he sells at a gain of $5$ per cent, one$-$fourth at a gain of $10 \%$, one-half at a gain of $12$ percent, and the remainder at a gain of $16$ percent. If he had sold the whole at a gain of $11$ percent, he would have made $Rs.\, 72.80$ more. What was the cost price of the crop per kg? (in $Rs.$)
$2$
$2.60$
$2.50$
$2.80$
Solution
In the given question, let the total profit$\%$ be $p \%$
$\Rightarrow$ Total Profit $p \%=\frac{1}{5} \times 5+\frac{1}{4} \times 10+\frac{1}{2} \times 12+\left[1-\left(\frac{1}{5}+\frac{1}{4}+\frac{1}{2}\right)\right] \times 16$
$\Rightarrow 1+\frac{5}{2}+6+\left(\frac{1}{20} \times 16\right) \Rightarrow \frac{103}{10} \%$
Now if he would have sold whole wheat at $11 \%$, he would had made $Rs. 72.80$ more
$11 \%-\frac{103}{10} \%= Rs .72 .80, \quad \frac{7}{10} \%= Rs .72 .80$
$1 \%=\operatorname{Rs} \cdot \frac{72.80 \times 10}{7} \quad[$ Unitary method $]$
$100 \%=$ Rs. $10,400 \quad$ [Total $CP$ of $4000 kg$ wheat $]$
$CP$ of $crop / kg = Rs . \frac{10400}{4000}= Rs .2 .60$
