Question

A person purchases his goods for Rs.1600. He sells $\frac{3}{4}$th of his goods at a profit of 10%. At what profit percent should he sell his remaining goods so as to make a gain of 16% on the whole transaction ?

Answer 1

Let the man purchase y kg of goods at Rs.1600

Then his total CP=Rs.1600
He sells $\frac{3y}{4}$ kg of his goods at a profit of 10%

Now CP of $\frac{3y}{4}$kg of his goods $=Rs.1600\times \frac{3}{4}=Rs.1200$
$\therefore$ SP of $\frac{3y}{4}$kg of his goods = Rs. $\frac{110}{100}\times 1200=Rs.1320$

Now CP of the remaining $\frac{y}{4}$kg of his goods $=Rs.1600\times \frac{1}{4}=Rs.400$
Let the man sell the remaining $\frac{y}{4}$kg of his goods at a profit of x%
Then SP of $\frac{y}{4}$kg of his good = Rs.$\frac{100+x}{100}\times 400=Rs.(400+4x$
$\therefore$ Total SP of y kg of goods $=Rs.(1320+400+4x)=Rs.(4x+1720)$
If the man makes a gain of 16% on the whole transaction then S.P. of y kg of goods = Rs. $\frac{116}{100}\times 1600=Rs.1856$
$\therefore$ 4x + 1720 = 1856 $\Rightarrow 4x=1856-1720=136\Rightarrow x=\frac{136}{4}=34$
Hence the required profit = 34%