Comparing Quantities Test - 64

Let the cost price of one good be $$ Rs  100 $$ 
Then, Marked Price to get $$ 20 $$ % profit   $$ =100+\dfrac{20}{100}\times 100 =  Rs  120 $$

Let $$ x $$ goods be there, then total C.P. $$ = 100 x $$

When he sells $$ \dfrac {3}{5} $$ the of the goods at $$ Rs 120$$, selling price for this amount of goods will be $$ SP_1 = \dfrac {3}{5} \times 120 \times x = Rs 72x $$

Now, Selling price of remaining $$ \dfrac {2x}{5} $$ goods at $$80\%$$ discount $$  = \dfrac {(100-20)}{100} \times 120 = Rs 96 $$ 

Selling price for this $$ \dfrac {2}{5}x$$ amount of goods will be $$ SP_2= \dfrac {2}{5} \times 96 \times x = Rs 38.4x $$


So, Total S.P. $$ = Rs 72x + Rs 38.4x = Rs 110.4x $$


Profit % on the whole transaction $$ = \dfrac {S.P - C.P.}{C.P.} \times 100$$

                                                        $$ =\dfrac {110.4x - 100x}{100x} \times 100 = 10.4  $$  %

Selling price of article $$A, B$$ and $$C$$ is in ratio $$8 : 9 : 5$$
Let Selling price is $$8y, 9y$$ and $$5y$$
Profit percentage in ratio $$ = 8 : 7 : 14$$
Let their profit percentage is,
$$8x\%, 7x\%$$ and $$14\ x%$$
A's profit percent $$= 14.28\%$$
$$8x\% = 14.28\%$$
$$x = \dfrac{14.28}{8 }= 1.78$$
$$B's$$ Profit percent,
$$= 7x\% = 7 \times 1.78 = 12.50\%$$ (approx)
$$C's$$ profit percentage $$= 14x = 14 \times 1.78 = 25\%$$
Cost price of $$B =$$ Rs. $$400$$
$$\therefore$$ Selling price of$$ $$B = $$400 + \dfrac{12.50}{100}\times  400 =$$ Rs. $$450$$
$$\therefore 9y = 450$$
$$y = 50$$
Selling price of $$A$$ $$= 8y = 8 \times 50 =$$ Rs. $$400$$
SP of $$C$$ $$= 5y = 5 \times 50 =$$ Rs. $$250$$
Total SP $$= 450 + 400 + 250 =$$ Rs. $$1100$$
Let CP of $$A = a$$
$$a = 400 - 14.28\%$$ of $$a$$
$$a=400-\dfrac{14.28a}{100}$$

$$100a = 40000 - 14.28a$$
$$114.28a = 40000$$
$$a =$$ Rs. $$350$$
Let CP of $$C = c$$
$$c + 25\%$$ of $$c = 250$$
$$125c = 25000$$
$$c =$$ Rs. $$200$$
Total CP $$ = 400 + 350 + 200 =$$ Rs. $$950$$
Profit $$= 1100 - 950 = 150$$
Overall $$\%$$ profit $$=\dfrac{150}{950}\times 100= 15.78\%$$