Profit And Loss - Aptitude MCQ Questions and Solutions with Explanations

Ratio of selling price and Cost Price,
SP : CP = 12 : 9 =4 : 3
Profit of 3 oranges = Rs. 1 (Let CP = Rs. 1)
Profit = $$\frac{1}{3}$$ = 33.33%
and, Discount = 11.11%
Since,
CP : SP : MP = 3 : 4 : 4.5
Profit doubles that of discount.
So, % point discount = 33.33% - 11.11% = 22.22% point.

Detail Explanation:
12 C.P = 9 S.P,
So profit % = $$\frac{{12\,{\text{C}}{\text{.P}}{\text{.}} - 9\,{\text{C}}{\text{.P}}{\text{.}}}}{{9\,{\text{C}}{\text{.P}}{\text{.}}}}$$     = 33.33.
Then it is said that,
5 SP - 5 CP = 10 MP -10 SP
From that we get relation between MP and SP, that is,
27 SP = 24 MP(With help of 12 CP = 9 SP)
THEN DISCOUNT % = $$\frac{{{\text{MP}} - {\text{SP}}}}{{{\text{MP}}}}$$   = 11.11%
So, % point discount = 33.33% - 11.11% = 22.22%

Candle - - - - - - - - Bulb
CP . . . . A - - - - - - - - B
SP . . . . C - - - - - - - - D
$$\eqalign{ & and.\,C = 2A \cr & {\text{Profit}} = 10\left( {B - A} \right) = 3D \cr & {\text{Loss}} = 10\left( {C - D} \right) = 4B \cr & {\text{Profit}}\% = \frac{{ {3D \times 100} }}{{10A}} \cr & {\text{Loss}}\% = \frac{{ {4B \times 100} }}{{10C}} \cr & {\text{Now,}}\,{\text{By}}\,{\text{the}}\,{\text{questions}}, \cr & \frac{{ {3D \times 100} }}{{10A}} = \frac{{ {4B \times 100} }}{{10C}} \cr & \frac{B}{D} = \frac{3}{2} = 3:2 \cr} $$

$$\eqalign{ & {\text{CP of one egg in }}{{\text{1}}^{st}}{\text{ case}} \cr & = \frac{1}{3} = 33.33\,{\text{paise}} \cr & {\text{CP of one egg in}}\,{2^{nd}}{\text{ case}} \cr & = \frac{1}{6} = 16.66\,{\text{paise}} \cr & {\text{Average}}\,{\text{CP}} \cr & = \frac{{ {33.33 + 16.66} }}{2} \cr & = 25\,{\text{paise}} \cr & {\text{Selling}}\,{\text{price}}\,{\text{of}}\,{\text{9}}\,{\text{eggs}} \cr & = Rs.\,2 \cr & {\text{SP}}\,{\text{of}}\,{\text{one}}\,{\text{egg}} \cr & = \frac{{200}}{9} \cr & {\text{Profit}}\,{\text{or}}\,{\text{loss}} \cr & = \frac{{ {\left( {25 - {\frac{{200}}{9}} } \right) \times 100} }}{{25}} \cr & {\text{Profit}}\,{\text{or}}\,{\text{loss}} \cr & = 11.11\,({\text{loss}}) \cr} $$

Let CP's be Rs. 1000 each, their respective SP will be,
1000 == 25%↑ ⇒ 1250 [person calculating profit on the CP]
1000 == 33.33%↑ ⇒ 1333.33 [The person calculating his profit on SP: 25% of SP = 33.33% of CP]
The difference turned out to be = 83.33. This has occured when we have assumed the CP as 1000. But, we are given difference of Rs. 100
So, on comparing,
83.33 = 1000
1 = $$\frac{{1000}}{{83.33}}$$
100 = $$\frac{{1000}}{{83.33}} \times 100$$   = Rs. 1200

For 20% profit on selling price means $$\frac{1}{5}$$ of 3000 i.e. Rs. 600
Now, let the CP = Rs. 100, Then,
SP with 20% profit = Rs. 120
For 20% profit on selling price means cost is 100 + profit is 20 = selling price is 120.
Means selling price is 120% of cost price.
Now selling price is 120% ie 3000 then find 100% amount which will be cost.
Cost = $$\frac{{3000}}{{120}}\% $$
= $$\frac{{3000}}{{\frac{6}{5}}}$$
Because, 120% = $$\frac{6}{5}$$
= 3000 x $$\frac{5}{6}$$
= 2500
Cost is 2500
Thus profit is 20% i.e. $$\frac{1}{5}$$ x 2500 = 500
Thus,
Difference is 600 - 500 = Rs.100

Total sales revenue (Old) = 2000 × 3.25 × 0.75 = 4875 [0.75 as 25% discount was allowed]
Profit_old = Total sales revenue - 4800
= 4875 - 4800 = 75
Total sales revenue (New) = 3000 × 4.25 × 0.75 = 9562.5 [New price is calculated on doctors samples as well.]
Profit_new = 9562.5 - 4800 = 4762.5
Ratio,
$$\frac{{{\text{Profi}}{{\text{t}}_{{\text{new}}}}}}{{{\text{Profi}}{{\text{t}}_{{\text{old}}}}}} = \frac{{4762.5}}{{75}} = 63.5$$

The successive discounts must have been of 10% each As
20 (CP) == 25%↑ ⇒ 25(MP) == 10↓ ⇒ 22.5 == 10%↓ ⇒ 20.25(SP)

Profit = 20.25 - 20 = 0.25
Increased percentage if price have been increased twice successively instead of reducing it,
20(MP) == 10%↑ ⇒ 27.5 == 10%↑ ⇒ 30.25
Profit = 30.25 - 20 = 10.25.
Profit Change = 10.25 - 0.25 = 10
Percentage Profit change,
= $$\frac{{10 \times 100}}{{0.25}}$$
= 4000%

The company is able to deliver 90% of the manufactured pens. Means to produce 7200 pens they must have to produce 8000 pens as 10% are defectives.
So, let K be the manufacturing price of each pen.
Total income (including 25% profit) = 8000 × K × 1.25
This same income is obtained by selling 90% manufactured pens at Rs. 10 which is equal to 7200 × 10
Thus,
8000 × K × 1.25 = 7200 × 10
K = Rs. 7.2 [90% of 8000 = 7200]

$$\eqalign{ & {\text{Charge per call in February}} \cr & = \frac{{350}}{{150}} = \frac{7}{3} = 2.33 \cr & {\text{Charge per call in March}} \cr & = \frac{{ {350 + \left( {50 \times 1.4} \right)} }}{{250}} \cr & = \frac{{420}}{{250}} = \frac{{42}}{{25}} = 1.68 \cr & \% {\text{ Cheaper call rate in March}}. \cr & = {\frac{{ {2.33 - 1.68} }}{{2.33}}} \times 100 \cr & = 28\% \cr} $$

$$\eqalign{ & {\text{MP}} = M \cr & {\text{SP}} = \frac{M}{2} \cr & \% \,{\text{Discount}} \cr & = {\frac{{ {\frac{M}{2}} }}{M}} \times 100 \cr & = 50\% \cr} $$