Profit And Loss - Aptitude MCQ Questions and Solutions with Explanations

Let the C.P. of 1 kg goods be Rs. 1
Then,
He buys 1100 g goods for Rs. 1 and sells 900 g goods for Rs. 1
∴ C.P. of 1100 g goods = Rs. 1
⇒ C.P. of 900 g goods
$$\eqalign{ & = {\text{Rs}}.\left( {\frac{1}{{1100}} \times 900} \right) \cr & = {\text{Rs}}.\frac{9}{{11}} \cr} $$
S.P. of 900 g goods = Rs. 1
$$\eqalign{ & {\text{Gain = Rs}}.\left( {1 - \frac{9}{{11}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\frac{2}{{11}} \cr & \therefore {\text{Gain }}\% \cr & = \left( {\frac{2}{{11}} \times \frac{{11}}{9} \times 100} \right)\% \cr & = \frac{{200}}{9}\% \cr} $$

$$\eqalign{ & {\text{Gain/loss }}\% \cr & = \left\{ {\left( {\frac{{y - x}}{{100 - y}}} \right) \times 100} \right\}\% \cr & = \left\{ {\left( {\frac{{15 - 20}}{{100 - 15}}} \right) \times 100} \right\}\% \cr & = \left( {\frac{{ - 5}}{{85}} \times 100} \right)\% \cr & = - \frac{{100}}{{17}}\% \cr & = - 5\frac{{15}}{{17}}\% \cr} $$
Since it is -ve, hence it is a loss.

Let the marked price = 100 units
According to the question,
\[{\text{100(MP)}}\xrightarrow{{30\% {\text{ discount}}}}{\text{70(SP)}}\]      \[ \to \] CP of retailer
Cost price of retailer = 70
Retailer sold at Marked price = 100
Profit = Marked price - Cost price
= 100 - 70
= 30 units profit
$$\eqalign{ & \therefore {\text{Profit }}\% = \frac{{30}}{{70}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 42\frac{6}{7}\% \cr} $$

Let CP be Rs. 100. Then, marked price = Rs. 125
$$\eqalign{ & {\text{SP}} = 84\% \,{\text{of}}\,{\text{Rs}}{\text{.}}\,125 \cr & \,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,\left( {\frac{{84}}{{100}} \times 125} \right) \cr & \,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,105 \cr} $$
∴ Profit = (105 - 100)% = 5%

$$\eqalign{ & {\text{CP}} = {\text{Rs}}{\text{.}}\,\left( {\frac{{100}}{{125}} \times 8750} \right) \cr & \,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,7000 \cr} $$
Let the labelled price be Rs. x
Then,
$$\eqalign{ & \frac{{70}}{{100}} \times x = 7000 \cr & \therefore x = {\text{Rs}}{\text{.}}\,\left( {\frac{{7000 \times 100}}{{70}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,10000 \cr} $$

Let the percentage deduction in weight be y%
Then,
$$\eqalign{ & \frac{{y - 4}}{{100 - y}} \times 100 = 20 \cr & \Rightarrow \frac{{y - 4}}{{100 - y}} = \frac{1}{5} \cr & \Rightarrow 5y - 20 = 100 - y \cr & \Rightarrow 6y = 120 \cr & \Rightarrow y = 20 \cr} $$
Hence, for a meter, length used = (100 - 20)% of 1 m
= 80% of 100 cm = 80 cm

Let the required gain be x%
Percentage deduction in weight
$$\eqalign{ & = \left( {\frac{{200}}{{1000}} \times 100} \right)\% \cr & = 20\% \cr & \therefore \frac{{20 + x}}{{100 - 20}} \times 100 = 37\frac{1}{2} \cr & \Rightarrow \frac{{20 + x}}{{80}} = \frac{3}{8} \cr & \Rightarrow 20 + x = 30 \cr & \Rightarrow x = 10 \cr} $$
Hence, nominal gain percentage = 10%

We find the net profit in each case :
1 → In this case, profit = 10%
$$\eqalign{ & 2 \to {\text{Profit}} = \left( {\frac{{100}}{{900}} \times 100} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 11\frac{1}{9}\% \cr} $$
3 → Let C.P. of sugar be Rs. 1 per kg

Then, he mixes 100 gm impurities and realizes the C.P. of 1.1 kg sugar by selling 1 kg of sugar.
S.P. of sugar = Rs. 1.10 per kg.
$$\eqalign{ & \therefore {\text{Profit}} = \left( {\frac{{0.1}}{1} \times 100} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 10\% \cr} $$
4 → Let C.P. of sugar be Rs. 1 per kg.
Since he weighs 950 gm instead of a kg, his actual
C.P. = Rs. 0.95
S.P. = 105% of Rs. 1 = Rs. 1.05
$$\eqalign{ & \therefore {\text{Profit}} = \left( {\frac{{0.10}}{{0.95}} \times 100} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 10\frac{{10}}{{19}}\% \cr} $$
Clearly, the maximum profit is earned when he used a 900 gm weight for a kg.

Let the cost price be Rs. 100
then the mark up price which is 15% above the cost price,
Mark price = (100 + 15% of 100) = Rs. 115
Shopkeeper gives a discount of 20% on mark up price, then the
Selling Price = (115 - 20% of 115) = Rs. 92
loss = 92 - 100 = Rs. -8
$$\eqalign{ & \% {\text{loss}} = \frac{{ - 8 \times 100}}{{100}} = - 8\% \cr & \therefore {\text{loss}} = 8\% \cr} $$

Let the Marked price = Rs. 100
10% discount price will be = Rs. 90
$$17\% {\text{ of }}90 = \frac{{17 \times 100}}{{90}} \approx 20$$
∴ Cost price ≈ 90 - 20 ≈ 70
If the product is sell on marked price , then profit will be ≈ 30%