Profit And Loss - Aptitude MCQ Questions and Solutions with Explanations

$$\eqalign{ & {\text{S}}{\text{.P}}{\text{.}} = {\text{Rs}}{\text{.340}}{\text{}} \cr & {\text{Let marked price be Rs}}{\text{. }}x{\text{.}} \cr & {\text{Then,}} \cr & {\text{ = 85}}\% {\text{ of }}x = {\text{340}} \cr & \Rightarrow x{\text{ = }}\left( {\frac{{340 \times 100}}{{85}}} \right) = 400 \cr & {\text{Cost Price}} \cr & = {\text{Rs}}{\text{.}}\left( {100 \times \frac{3}{{340}} \times 340} \right) \cr & = {\text{Rs}}{\text{. 300}}{\text{.}} \cr & {\text{Now, C}}{\text{.P}}{\text{. = Rs}}{\text{. 300}}{\text{}} \cr & {\text{S}}{\text{.P}}{\text{.}} = {\text{Rs}}{\text{. 400}}{\text{}} \cr & \therefore {\text{ Required profit }}\% \cr & = \left( {\frac{{100}}{{300}} \times 100} \right)\% \cr & = 33\frac{1}{3}\% \cr} $$

Step - 1. Start with the assumption that the shopkeeper has Rs. 10000 in his cash (this is just for making it simple).

Step - 2. The lady comes in and shops for Rs. 350 and gives the shopkeeper Rs. 2000. Then, the shopkeeper now has Rs. 10000 + 2000 = Rs. 12000 in cash.

Step - 3. The shopkeeper takes the Rs. 2000 Note to another shopkeeper and gets Rs. 2000 in change - therefore he still has Rs. 12000 in cash as in step 2.

Step - 4. Now the shopkeeper gives Rs. 1650 back to the lady. So the shopkeeper is now left with 12000 - 1650 = Rs. 10350 in cash.

Step - 5. Now the other shopkeeper comes in with the duplicate note and takes his money back. The duplicate note has zero value. So basically now the shopkeeper is down to 10350 - 2000 =Rs. 8350

Step - 6. He originally had Rs. 10000 in cash. Now has Rs. 8350, So Rs. 1650 loss, plus 350 lost in the grocery that the lady took.

Step - 7. Total loss Rs. 1650 + 350 = Rs. 2000.

Let us assume that the shopkeeper has Rs. 1000 currency Extra with his Rs. 200 worth Goods.
Step - 1. Shopkeeper → Rs. 200 worth goods + Rs. 1000 Original Currency.
Lady → Rs. 1000 fake currency.
Neighbor → Rs. 1000 as changes.

Step - 2. Shopkeeper → Rs. 1000 fake currency + Rs. 1000 Original Currency.
Lady → Rs. 200 worth goods.
Neighbor → Rs. 1000 as changes

Step - 3. Shopkeeper → Rs. 1000 as changes + Rs. 1000 Original Currency.
Lady → Rs. 200 worth goods.
Neighbor → Rs. 1000 fake currency

Step - 4. Shopkeeper → Rs. 200 + Rs.1000 Original Currency
Lady → Rs. 200 worth goods + Rs. 800
Neighbor → Rs. 1000 fake currency

Step - 5. Shopkeeper → Rs. 200 + Rs. 1000 fake currency
Lady → Rs. 200 worth goods + Rs. 800
Neighbor → Rs. 1000 Original Currency

Compare Step 1 and Step 5 now. Lady changed her Rs. 1000 fake currency into goods and currency of total worth Rs. 1000 The shopkeeper changed his Original Rs. 1000 currency into a fake currency. So the loss for the shopkeeper is Rs. 1000.

$$\eqalign{ & \frac{{MP}}{{CP}} = \frac{{115}}{{100}} \cr & \frac{{MP}}{{CP}} = \frac{{100 + P}}{{100 - d}}\,\,\,\,\left( {d\% = 10\% } \right) \cr & \Rightarrow \frac{{115}}{{100}} = \frac{{100 + P}}{{100 - 10}} \cr & \Rightarrow \frac{{23}}{{20}} = \frac{{100 + P}}{{90}} \cr & \Rightarrow P\% = 3.5\% \cr & {\text{Now, According to the question he weights }}25\% {\text{ less}} \cr & 25\% = \frac{1}{4} \cr & \frac{{SP}}{{CP}} = \frac{4}{3} \times \frac{{103.5}}{{100}} = \frac{{69}}{{50}} \cr & {\text{Profit }}\% = \frac{{19}}{{50}} \times 100 = 38\% \cr} $$

Let the part sold at 5% loss be = a kg
a × -5% + (640 - a) × 20% = 640 × $$\frac{{15}}{{100}}$$
⇒ -5a + 640 × 20 - 20a = 640 × 15
⇒ 640 × 20 - 640 × 15 = 25a
⇒ 640 × $$\frac{{\left( {20 - 15} \right)}}{{25}}$$  = a
⇒ a = 128 = Loss portion
So, Profit portion = 640 - 128
⇒ 512
Ratio = 128 : 512
⇒ 1 : 4
∴ Required ratio is 1 : 4

$${\text{Loss}} = \frac{4}{{80}} \times 100 = 10\% $$

$$\eqalign{ & {\text{Profit}} = \frac{{200}}{{800}} \times 100 = 25\% \cr & {\text{Over all profit}} \cr & = 25 - 10 - \frac{{25 \times 10}}{{100}} \cr & = 12.5\% {\text{ Answer}} \cr} $$

$$8\% = \frac{2}{{25}}$$

$$\eqalign{ & \to 25x \times \frac{{23}}{{20}} = 27x + 714 \cr & 115x = 108x + 2856 \cr & 7x = 2856 \cr & x = 408 \cr & {\text{Cost price}} = 25x = 25 \times 408 \cr & {\text{So, required answer}} \cr & = 25 \times 408 \times \frac{{59}}{{50}} \cr & = 12036{\text{ Answer}} \cr} $$

\[\begin{array}{*{20}{c}} {}&{ + 16\% }&{ - 12\% } \\ {}&{\text{I}}&{{\text{II}}} \\ {{\text{Cost Price}}}&{{{25}_{ \times 22}}}&{{{25}_{ \times 29}}} \\ {{\text{Profit/Loss}}}&{{4_{ \times 22}}}&{ - {3_{ \times 29}}} \\ {{\text{Sale Price}}}&{{{29}_{ \times 22}}}&{{{22}_{ \times 29}}} \end{array}\]
Cost Price = 25(29 + 22) = 25 × 51
Profit/Loss = 88 - 87 = +1
Profit % $$ = \frac{1}{{25 \times 51}} \times 100 = 0.08\% $$

$$\eqalign{ & 25x + \frac{{108}}{{100}} = 21x + 660 \cr & 6x = 660 \cr & x = 110 \cr & {\text{Cost price}} = 25 \times 11 = 2750 \cr & {\text{Selling price}} = 3080 \cr & {\text{Profit}} = 3080 - 2750 = 330 \cr & {\text{Profit }}\% = \frac{{330 \times 100}}{{2750}} = 12\% \cr} $$

2 SP = 48640
SP = 24320
28% profit on A
$$\frac{{128{\text{A}}}}{{100}} = 24320$$
A = 190 × 100 = 19000
24% loss on B
$$\frac{{76{\text{B}}}}{{100}} = 24320$$
B = 320 × 100 = 32000