Comparing Quantities Test - 32

S.P. of each article $$=$$ Rs. $$ \left (\dfrac {37.40}{2}\right )=$$ Rs. $$ 18.70$$
Discount rate $$=15\%$$
$$\therefore$$ M.P. of each article $$=$$ Rs. $$ \dfrac {18.70\times 100}{(100-15)}=$$ Rs. $$ \dfrac {1870}{85}=$$ Rs. $$   22$$.

Let the C.P. of the item be Rs. $$100$$
Then, M.P. $$=$$ Rs. $$140$$, Discount $$= 25\%$$
$$\therefore$$ S.P. $$=$$ Rs. $$ 140 - 25\%$$ of Rs. $$140$$
$$=$$ Rs. $$ 140-\dfrac {25}{100}\times$$ Rs. $$ 140$$

$$=140-35=$$ Rs. $$ 105$$
$$\therefore$$ Profit $$=$$ Rs. $$ 105-$$ Rs. $$ 100=$$ Rs. $$5$$
Profit $$\%$$ $$=\dfrac {5}{100}\times 100=5\%$$.

Given,

Cost price of an article, $$CP=$$ Rs  $$180$$
Profit or gain = $$20$$ %
Discount on the marked price of an article $$=10$$%

Marked price of an article, $$MP=?$$

Let the marked priice of an article be $$x$$.

Discount on the marked price  on an article $$=x-0.10 x$$

                                                                          $$=0.9 x$$

$$\therefore$$ Selling Price of an article is, $$SP=0.9x$$

We know that,

$$\dfrac{SP-CP}{CP}=Gain$$%

Put $$SP=0.9x$$, $$CP=180$$, and $$Gain=20$$ %

$$\dfrac{0.9x-180}{180}=20$$%

$$\dfrac{0.9x-180}{180}=\dfrac{20}{100}$$

$$\dfrac{0.9x-180}{180}=\dfrac{1}{5}$$

$$\dfrac{0.9x-180}{36}=1$$

$$0.9x=36+180$$

$$0.9x=216$$

$$x=\dfrac{216}{0.9}$$

$$x=240$$

$$\therefore$$ Marked Price of an article is Rs 240.

S.P. $$=$$ Rs. $$444$$, Discount $$= 26\%$$
Let M.P. $$=$$ Rs. $$ x$$

Then, M.P. $$-$$ discount $$=$$ S.P,

$$x - 26\% $$ of $$ x = 444$$
$$\Rightarrow x-\dfrac{13x}{50} = 444$$
$$\Rightarrow \dfrac{37x}{50}=444$$

$$\Rightarrow x=\dfrac{444\times 50}{37}=$$ Rs. $$ 600$$

Let the C.P. of the goods $$=Rs 100$$. Then,
Marked price of the goods $$= Rs 140$$
Discount $$=$$ 20%
$$\therefore$$ S.P. of the goods $$=$$ 80% of $$Rs 140=Rs 112$$
$$\therefore$$ Profit % $$=\dfrac {(112-100)}{100}\times 100=12$$%