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: (i) C.P.of each transistor. (ii) total C P and total S.P. of both the transistors (iii) profit or loss percent on the whole.

Solution

## Let $$CP_{1}$$ & $$CP_{2}$$  be the cost price of $$1 ^{st}$$ transistors and $$2^{nd}$$ transistors respectivelyselling price of each transistors, $$SP_{1} = RS 600$$Gain of one transistors = 20%$$\Rightarrow \frac{SP_{1}-CP_{1}}{CP_{1}}\times 100 =20.$$$$\Rightarrow \frac{600-CP_{1}}{CP_{1}}\times 100 = 20.$$$$\Rightarrow 600 - CP_{1} = \frac{20}{100}CP_{1}$$$$\Rightarrow 600 = \frac{20}{100} CP_{1}+CP_{1}$$$$\Rightarrow \frac{120}{100}CP_{1}=600$$$$\Rightarrow CP_{1} = \frac{600\times 100}{120}$$$$\Rightarrow CP_{1} = Rs 500$$and loss of other transistors = 20 %$$\Rightarrow \frac{CP_{2}-SP_{1}}{CP^{1}} \times 100 = 20$$$$\Rightarrow CP_{2}-600 = \frac{20}{100}CP_{2}$$$$\Rightarrow CP_{2}\frac{-20}{100}CP_{2}=600$$$$\Rightarrow \frac{80}{100}CP_{2}=600$$$$\Rightarrow CP_{2}= \frac{600\times 100}{80}$$=RS 750cost price of $$1^{st}$$ transistors = Rs 1350Cost price of $$2^{nd}$$  transistors = Rs 750.Total cost price ,CP = Rs (600+750) = 1350Total selling price SP = Rs (600+600) = Rs 1200.loss on the whole = $$\frac{CP-SP}{CP}\times 100$$$$\frac{1350-1200}{1350}\times 100$$$$\frac{150}{1350}\times 100$$= 11.11 % (approx.)Mathematics

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