Profit And Loss - Aptitude MCQ Questions and Solutions with Explanations

31

Joseph's salary is reduced by 10% . In order to have his salary back to his original amount, it must be raised by = ?

A) 12.5% B) $$11\frac{1}{9}$$% C) 10% D) 11%

Discuss

Answer & Solution

Answer: Option B

Solution:

$$\eqalign{ & {\text{Let}}\,{\text{income}} = 100 \cr & {\text{Reduce}}\,{\text{income}} = 90 \cr & \% {\text{Required}} = \frac{{10}}{{90}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{100}}{9}\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 11\frac{1}{9}\% \cr} $$

32

A shopkeeper sells two watches for Rs. 308 each. On one he gets 12% profit and on the other 12% loss. His profit or loss in the entire transaction was -

A) Neither profit, nor loss B) $$1\frac{{11}}{{25}}$$ % loss C) $$1\frac{{11}}{{25}}$$ % profit D) $$3\frac{2}{{25}}$$ % loss

Discuss

Answer & Solution

Answer: Option B

Solution:

$$\eqalign{ & {\text{loss }}\% \cr & = {\left( {\frac{{{\text{Common Loss and Gain}}\% }}{{10}}} \right)^2}\% \cr & = {\left( {\frac{{12}}{{10}}} \right)^2}\% \cr & = \frac{{36}}{{25}}\% \cr & = {\text{1}}\frac{{11}}{{25}}\% \cr & = {\text{1}}\frac{{11}}{{25}}\% {\text{ loss}}{\text{}} \cr} $$

33

A man sells two flats at the rate of Rs. 1.995 lakhs each. On one he gains 5% and on the other, he loses 5% . His gain or loss percent in the whole transaction is -

A) 0.25% loss B) 0.25% gain C) 2.5% loss D) 25% loss

Discuss

Answer & Solution

Answer: Option A

Solution:

$$\eqalign{ & {\text{Loss }}\% = {\left( {\frac{5}{{10}}} \right)^2}\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\left( {0.5} \right)^2}\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 0.25\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{0}}{\text{.25}}\% {\text{ loss}} \cr} $$

34

The list price of an article is Rs. 900. It is available at two successive discounts of 20% and 10% . The selling price of the article is = ?

A) Rs. 640 B) Rs. 648 C) Rs. 540 D) Rs. 548

Discuss

Answer & Solution

Answer: Option B

Solution:

$$\eqalign{ & 20\% = \frac{1}{5},\,\,10\% = \frac{1}{{10}} \cr & {\text{MP}}\,\,\,\,\,\,{\text{SP}} \cr & \,\,\,{\text{5}}\,\,\,\,\,\,\,\,\,\,\,{\text{4}} \cr & \frac{{10\,\,\,\,\,\,\,\,\,\,9}}{{50\,\,\,:\,\,\,36}} \cr & 50{\text{ units}} = 900 \cr & {\text{36 units}} = \frac{{900}}{{50}} \times 36 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 648 \cr} $$

35

A dishonest grocer sells rice at a profit of 10% and uses weight which are 20% less than the marked weight. The total gain earned by him will be = ?

A) 37.5% B) 32% C) 30.5% D) 35%

Discuss

Answer & Solution

Answer: Option A

Solution:

According to the question,
Grocer use 20% less weight
= 1000 - 200
= 800 gm.
$$\eqalign{ & {\text{The profit }}\% \cr & = \frac{{200}}{{800}} \times 100 \cr & = 25\% \cr & {\text{Then total profit }} \cr & = 10 + 25 + \frac{{25 \times 10}}{{100}} \cr & = 37.5\% \cr} $$

36

A dishonest dealer professes to sell his goods at the cost price but uses a false weight of 850 g. instead of 1 kg. his gain percent is = ?

A) $$17\frac{{12}}{{17}}\% $$ B) $$17\frac{{11}}{{17}}\% $$ C) $$71\frac{{11}}{{17}}\% $$ D) $$11\frac{{11}}{{17}}\% $$

Discuss

Answer & Solution

Answer: Option B

Solution:

According to the question,
Dishonest dealer sold at cost price uses a false weight of 850 gm. instead to 1 kg.
$$\eqalign{ & \therefore {\text{Profit }}\% \cr & = \frac{{150}}{{850}} \times 100 \cr & = 17\frac{{11}}{{17}}\% \,{\text{profit}} \cr} $$

37

A man sells two commodities for Rs. 4000 each, neither losing nor gaining in the deal. If he sold one commodity at a gain of 25%, the other commodity is sold at a loss of = ?

A) $$16\frac{2}{3}\% $$ B) $$18\frac{2}{9}\% $$ C) 25% D) None of these

Discuss

Answer & Solution

Answer: Option A

Solution:

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

38

A house and a shop were sold for Rs. 1 lakh each. In this transaction, the house sale resulted into 20% loss whereas the shop sale resulted into 20% profit. The entire transaction resulted in -

A) No loss, no gain B) Loss of Rs. $$\frac{1}{12}$$ lakh C) Loss of Rs. $$\frac{1}{18}$$ lakh D) Gain of Rs. $$\frac{1}{24}$$ lakh

Discuss

Answer & Solution

Answer: Option B

Solution:

$$\eqalign{ & {\text{Total S}}{\text{.P}}{\text{.}} = {\text{Rs}}{\text{. 2 lakh}} \cr & {\text{C}}{\text{.P}}{\text{. of house}} \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{100}}{{80}} \times 1} \right){\text{lakh}} \cr & = {\text{Rs}}.\frac{5}{4}{\text{lakh}}{\text{}} \cr & {\text{C}}{\text{.P}}{\text{.of shop}} \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{100}}{{120}} \times 1} \right){\text{lakh}} \cr & = {\text{Rs}}{\text{.}}\frac{5}{6}{\text{lakh}}{\text{}} \cr & {\text{Total C}}{\text{.P}}. \cr & = {\text{Rs}}{\text{.}}\left( {\frac{5}{4} + \frac{5}{6}} \right){\text{lakh}} \cr & = {\text{Rs}}.\frac{{25}}{{12}}{\text{lakh}}{\text{}} \cr & \therefore {\text{Loss}} \cr & = {\text{Rs}}.\left( {\frac{{25}}{{12}} - 2} \right){\text{lakh}} \cr & = {\text{Rs}}.\frac{1}{{12}}{\text{ lakh}} \cr} $$

39

A man bought two goats for Rs. 1008. He sold one at a loss of 20% and other at a profit of 44% if each goat was sold for the same price the cost price of the goat which was sold at loss, was = ?

A) Rs. 648 B) Rs. 360 C) Rs. 568 D) Rs. 440

Discuss

Answer & Solution

Answer: Option A

Solution:

Let the CP of two goats be → x & y
$$\eqalign{ & x \times \frac{{80}}{{100}} = y \times \frac{{144}}{{100}} \cr & \frac{x}{y} = \frac{{144}}{{80}} \cr & \,\,\,\,\,\,\, = \frac{{18}}{{10}} \cr & \,\,\,\,\,\,\,\, = \frac{9}{5} \cr & {\text{CP of goats sold at loss}} \cr & \Rightarrow {\text{1008}} \times \frac{9}{{14}} \cr & \Rightarrow 72 \times 9 \cr & = {\text{Rs}}{\text{.}}\,648 \cr} $$

40

One trader calculates the percentage of profit on the buying price and another calculates on the selling price. When their selling price are the same then the difference of their actual profits is Rs. 85 and both claim to have made 20% profit, what is the selling price of each ?

A) Rs. 1700 B) Rs. 2100 C) Rs. 2550 D) Rs. 2750

Discuss

Answer & Solution

Answer: Option C

Solution:

For the first trader,
Let the CP of the article = Rs. 100
⇒ SP = Rs. 120
Now, For the second trader,
SP of the article = Rs. 120
& Gain = 20%
Let the CP be Rs. x
$$\eqalign{ & \therefore \frac{{120 - x}}{{120}} \times 100 = 20 \cr & \therefore 120 - x = 20 \times \frac{6}{5} = 24 \cr & \therefore x = 120 - 24 = {\text{Rs}}{\text{.}}\,96 \cr & \therefore {\text{Gain}} = {\text{Rs}}{\text{.}}\,24 \cr} $$
Now when difference of gain = Rs. 4
Then SP = Rs. 120
So, When the difference = Rs. 85
Then
$$\eqalign{ & {\text{SP}} = \frac{{120}}{4} \times 85 \cr & \,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,2550 \cr} $$