Question

A man sold two tapes for ₹600 each and gained 20% on one, lost 20% on the other. What is the overall gain or loss percentage?

• A. 4%
• B. 5%
• C. 6%
• D. 8%

Answer 1

The correct option is A 4%

SP of each tape = ₹ 600
Total SP = 2 $\times$ 600 = ₹ 1200

Profit made on first tape = 20%

Let CP = ₹ 100
Then, Profit = 20% of 100 = ₹ 20
So, SP = 100 + 20 = ₹ 120
Thus, when SP is ₹ 120, CP is ₹ 100.
Now, if when SP is ₹ 1, then CP will be ₹ $\frac{100}{120}.$
$\therefore$ When SP is ₹ 600, CP is ₹ $(\frac{100}{120}\times 600).$
$\Rightarrow$ CP = ₹ 500

Loss suffered on second tape = 20%

Let CP = ₹ 100
Then, Loss = 20% of 100 = ₹ 20
So, SP = 100 - 20 = ₹ 80
Thus, when SP is ₹ 80, CP is ₹ 100.
Now, if SP is ₹ 1, CP is ₹ $\frac{100}{80}.$
$\therefore$ When, SP is ₹ 600, CP is ₹ $(\frac{100}{80}\times 600).$
$\Rightarrow$ CP = ₹ 750

So, total CP = 500 + 750 = ₹ 1250

Here, Net CP > Net SP
Loss = CP - SP
$\Rightarrow$ Loss = 1250 - 1200 = ₹ 50

$Overallloss\%=\frac{\text{Loss}}{\text{Net CP}}\times 100\%$
$\Rightarrow Loss\%=\frac{50}{1250}\times 100\%=4\%$