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A shopkeeper bought two units of an article at the same price. He sold one unit at a profit of 30%. If on selling the second unit, he incur…

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A shopkeeper bought two units of an article at the same price. He sold one unit at a profit of 30%. If on selling the second unit, he incurred a loss which was one-third of the profit earned on the first unit, what was his overall profit percent ?
  • A16%
  • B12%
  • C8%
  • D5%
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CCommunity
Solution
Let cost price of each unit = Rs. $100x$
=> C.P. of both units = $2 \times 100x = 200x$
Profit % on 1st unit = 30%
=> S.P. of one unit = $\frac{130}{100} \times 100x = 130x$
=> Profit earned on first unit = Rs. $(130x - 100x) = 30x$
Now, loss incurred is one-third of the profit
=> Loss incurred on second unit = Rs. $\frac{30x}{3} = 10x$
=> S.P. of second unit = Rs. $(100x - 10x) = 90x$
Thus, total S.P. of both units = $130x + 90x = 220x$
$\therefore$ Overall profit % = $\frac{220x - 200x}{200x} \times 100$
= $\frac{20}{2} = 10 \%$
0
CCommunity
Solution
Let cost price of each unit = Rs. $100x$
=> C.P. of both units = $2 \times 100x = 200x$
Profit % on 1st unit = 30%
=> S.P. of one unit = $\frac{130}{100} \times 100x = 130x$
=> Profit earned on first unit = Rs. $(130x - 100x) = 30x$
Now, loss incurred is one-third of the profit
=> Loss incurred on second unit = Rs. $\frac{30x}{3} = 10x$
=> S.P. of second unit = Rs. $(100x - 10x) = 90x$
Thus, total S.P. of both units = $130x + 90x = 220x$
$\therefore$ Overall profit % = $\frac{220x - 200x}{200x} \times 100$
= $\frac{20}{2} = 10 \%$