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Question

By selling two transistors for $$Rs\ 600$$, each a shopkeeper gains $$20$$ percent on one transistor and loses $$20$$ percent on the other. 
Find :
profit or loss percent on the whole.


Solution

Let the cost price be $$x_1$$ for the transistor gaining $$20\%$$:
$$20 \%$$ gain  $$\implies x_1+\dfrac{20x_1}{100}=600$$

$$1.2\ x_1=600\implies x_1=500$$


Let the cost price be $$x_2$$ for the transistor losing $$20\%$$:
$$20 \%$$ loss  $$\implies x_2-\dfrac{20x_2}{100}=600$$

$$0.8\ x_2=600\implies x_2=750$$
So,
Total C.P of both the transistors $$=x_1+x_2= 500 + 750 = ₹\,1250 $$
Total S.P of both the transistors $$= 600 + 600 = ₹\,1200$$

We know that

Total loss = C.P – S.P

Substituting the values

$$= 1250 – 1200$$

$$= ₹\,50$$

So the loss percent $$= (loss \times 100)/ C.P$$

Substituting the values

$$= (50 \times 100)/ 1250$$

$$= 4\%$$


Mathematics

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