Practice MCQ Questions and Answer on Profit and Loss

Solution: $$\eqalign{ & {\text{S}}{\text{.P}}{\text{. of 90 ball pens}} \cr & = {\text{Rs}}{\text{. 160, loss}} = 20\% \cr & {\text{C}}{\text{.P}}{\text{.of 90 ball pens}} \cr & = {\text{Rs}}.\left( {\frac{{100}}{{80}} \times 160} \right) \cr & = {\text{Rs}}{\text{. }}200 \cr} $$ ∴ Desired S.P. of 90 ball pens $$\eqalign{ & = {\text{Rs}}.\left( {\frac{{120}}{{100}} \times 200} \right) \cr & = {\text{Rs}}{\text{. }}240 \cr} $$ For Rs. 240, ball pens sold = 90 For Rs. 96, ball pens sold $$\eqalign{ & = \left( {\frac{{90}}{{240}} \times 96} \right) \cr & = 36 \cr} $$

Solution: Let marked price be Rs. 100 Then, S.P. = (100 - q)% of (100 - p)% of Rs. 100 $$\eqalign{ & = {\text{Rs}}{\text{.}}\left[ {\frac{{100 - {\text{q}}}}{{100}} \times \frac{{100 - {\text{p}}}}{{100}} \times 100} \right] \cr & = {\text{Rs}}.\left[ {\frac{{\left( {100 - {\text{q}}} \right)\left( {100 - {\text{p}}} \right)}}{{100}}} \right] \cr & \therefore {\text{Single discount }} \cr & = \left\{ {100 - \left[ {\frac{{\left( {100 - {\text{q}}} \right)\left( {100 - {\text{p}}} \right)}}{{100}}} \right]} \right\}\% \cr & = \left( {{\text{p}} + {\text{q}} - \frac{{{\text{pq}}}}{{100}}} \right)\% \cr} $$

Solution: In this type of question we can find the profit % by $$\eqalign{ & {\text{ = }}\frac{{{\text{Less quantity}}}}{{{\text{Quantity given to customer}}}} \cr & {\text{According to the question,}} \cr & {\text{Less quantity}} = \left( {1000 - 950} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 50 \cr & {\text{Quantity given to customer}} = 950 \cr & {\text{Profit }}\% = \frac{{50}}{{950}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{100}}{{19}}\% \cr} $$

Solution: According to the question, Cost price of pen = Rs. 50 Cost price of 50 pen = Rs. 50 × 50 = Rs. 2500 To gain 10% overall sold at = Rs. 2750 Now, 40 pen sold at 5% loss ∴ Selling price of 40 pens = 40 × 47.5 = Rs. 1900 Remaining 10 pens sold to get overall profit of 10% at = Rs. 850 selling price of 1 (remaining pens) $$ = \frac{{850}}{{10}} = {\text{Rs}}{\text{. 85}}$$ Cost price of 1 pen = Rs. 50 Profit % of remaining pens $$\eqalign{ & {\text{ = }}\frac{{35}}{{50}} \times 100 \cr & = 70\% \cr} $$

Solution: $$\eqalign{ & {\text{S}}{\text{.P}}{\text{.}} = {\text{Rs}}{\text{. }}100 \cr & {\text{Gain}} = {\text{Rs}}{\text{. }}15. \cr & \therefore {\text{C}}{\text{.P}}{\text{.}} = {\text{Rs}}.\left( {100 - 15} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}85 \cr & {\text{Gain }}\% = \left( {\frac{{15}}{{85}} \times 100} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{300}}{{17}}\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 17\frac{{11}}{{17}}\% \cr} $$

Solution: $$\eqalign{ & {\text{Total discount }}\% \cr & {\text{ = }}\left( {20 + 15 - \frac{{20 \times 15}}{{100}}} \right)\% \cr & = 35 - 3 \cr & = 32\% \cr & = \frac{{32 \to {\text{Discount}}}}{{100 \to {\text{MRP}}}} \cr} $$ MRP → Discount → Selling Price 100 → 32 → 68 68 units → 3060 1 units → 45 ⇒ then MRP = 100 units = 45 × 100 = Rs. 4500

Solution: $${\text{Let Cost price}} = 100$$ \[\begin{gathered} {\text{CP }}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{SP}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ MP}} \hfill \\ 100\,\,\xrightarrow[{{\text{Profit}}}]{}\,\,125\,\,\xleftarrow[{ - 25\% }]{}x \hfill \\ \end{gathered} \] $$\eqalign{ & {\text{Profit}} = 125 - 100 = 25{\text{ units}} \cr & {\text{MP}} = x = \frac{{75}}{{100}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 125 \cr & {\text{MP}} = x = \frac{{500}}{3}{\text{ units}} \cr & \because {\text{ 25 units}} = 6000 \cr & \therefore {\text{MP}} = \frac{{500}}{3}{\text{ units}} \cr & {\text{ = }}\frac{{500}}{3} \times \frac{{6000}}{{25}} \cr & = {\text{Rs}}{\text{.}}\,40000 \cr} $$

Solution: Total S.P. = Rs. 8000 and Total C.P. = Rs. 8000 S.P. of 1st commodity = Rs. 4000 Gain on it = 25% ∴ C.P. of 1st commodity $$\eqalign{ & = {\text{Rs}}.\left( {\frac{{100}}{{125}} \times 4000} \right) \cr & = {\text{Rs}}.3200 \cr & {\text{C}}{\text{.P}}{\text{. of }}{{\text{2}}^{{\text{nd}}}}{\text{ commodity}} \cr & = {\text{Rs}}{\text{.}}\left( {8000 - 3200} \right) \cr & = {\text{Rs}}.4800 \cr & {\text{S}}{\text{.P}}{\text{. of }}{{\text{2}}^{{\text{nd}}}}{\text{ commodity}} \cr & = {\text{Rs}}.4000 \cr & \therefore {\text{loss on }}{{\text{2}}^{{\text{nd}}}}{\text{ commodity}} \cr & = \left( {\frac{{800}}{{4800}} \times 100} \right)\% \cr & = 16\frac{2}{3}\% \cr} $$

Solution: $$\eqalign{ & {\text{Profit}}\% = 25 \cr & 25\% = \frac{1}{4} \cr & {\text{CP}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{SP}} \cr & \,\,\,4\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,5 \cr & \,\,\,\,1 - - - 210 \cr & \therefore {\text{SP}} = 210 \times 5 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1050 \cr} $$ Alternate Solution : Let Cost price is 100x Then Selling price is 125x According to the question, Selling price - Cost Price = 210 ⇒ 125x - 100x = 210 ⇒ x = $$\eqalign{ \frac{210}{25} \cr }$$ So the Selling price → 125x = 125 × $$\eqalign{ \frac{210}{25} \cr }$$ = Rs. 1050

Solution: Let C.P. of whole stock = Rs. 100 Then, Marked price of whole stock = Rs. 120 $$\eqalign{ & {\text{M}}{\text{.P}}{\text{. of }}\frac{1}{2}{\text{ stock}} \cr & {\text{ = Rs}}{\text{. 60,}} \cr & {\text{M}}{\text{.P}}{\text{. of }}\frac{1}{4}{\text{ stock}} \cr & {\text{ = Rs}}{\text{. 30}} \cr} $$ ∴ Total S.P. = Rs. [60 + (80% of 30) + (60% of 30)] = Rs. (60 + 24 + 18) = Rs. 102 Hence, gain% = (102 - 100)% = 2%