Profit And Loss - Aptitude MCQ Questions and Solutions with Explanations

41

When a plot is sold for Rs. 18700, the owner loses 15% . At what price must the plot be sold in order to gain 15% ?

A) Rs. 21,000 B) Rs. 22,500 C) Rs. 25,300 D) Rs. 25,800

Discuss

Answer & Solution

Answer: Option C

Solution:

Let the new S.P. be Rs. x
Then, 85 : 18700 = 115 : x
$$\eqalign{ & \Rightarrow x = \left( {\frac{{18700 \times 115}}{{85}}} \right) \cr & \Rightarrow x = 25300 \cr} $$

42

A book seller sells a book at a profit of 10% . If he had bought it at 4% less and sold it for Rs. 6 more. He would have gained $$18\frac{3}{4}$$% . The cost price of the book is = ?

A) Rs. 130 B) Rs. 140 C) Rs. 150 D) Rs. 160

Discuss

Answer & Solution

Answer: Option C

Solution:

Let the CP of the book = x
Gain = 10%
SP = $$\frac{{110{\text{x}}}}{{100}}$$
If he had bought it at 4% less and sold it for Rs 6 more,
$$\eqalign{ & {\text{CP}} = \frac{{96x}}{{100}} \cr & {\text{SP}} = \frac{{110x}}{{100}} + 6 \cr & {\text{Gain}} = \left( {\frac{{110x}}{{100}} + 6} \right) - \frac{{96x}}{{100}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \left( {\frac{{14x}}{{100}}} \right) + 6 \cr} $$
Now, the gain =$$18\frac{3}{4}\% = \frac{{75}}{4}\% $$
Therefore,
$$\eqalign{ & \Rightarrow \frac{{14x}}{{100}} + 6 = \frac{{96x}}{{100}} \times \frac{{75}}{{400}} \cr & \Rightarrow \frac{{14x}}{{100}} + 6 = \frac{{96x}}{4} \times \frac{3}{{400}} \cr & \Rightarrow 14x + 600 = \frac{{96x}}{4} \times \frac{3}{4} \cr & \Rightarrow 14x + 600 = 6x \times 3 \cr & \Rightarrow 14x + 600 = 18x \cr & \Rightarrow 18x - 14x = 600 \cr & \Rightarrow 4x = 600 \cr & \therefore x = 150 \cr} $$

43

A businessman sells a commodity at 10% profit. If he had bought it at 10% less and sold it for Rs. 2 less, then he would have gained $$16\frac{2}{3}$$% . The cost price of the commodity is = ?

A) Rs. 32 B) Rs. 36 C) Rs. 40 D) Rs. 48

Discuss

Answer & Solution

Answer: Option C

Solution:

Let the CP₁ of commodity = 100x
Initial SP₁ = 100x + 10% of 100x = 100x + 10x = 110x
Now, If He brought table at 10% discount. Therefore CP₂ = 90x
Now SP₂ = 90x + $$16\frac{2}{3}$$% of 90x = 90x + 15x =105x
According to question
SP₁ - SP₂ = 2
⇒ 110x - 105x = 2
⇒ 5x = 2
⇒ x = $$\frac{2}{5}$$
Initial Cost of commodity = 100 × $$\frac{2}{5}$$ = Rs. 40

44

A fruit seller sells mangoes at the rate of Rs. 9 per kg and thereby loses 20% . At what price per kg, he should have sold, them to make a profit of 5% ?

A) Rs. 11.81 B) Rs. 12 C) Rs. 12.25 D) Rs. 12.31

Discuss

Answer & Solution

Answer: Option A

Solution:

Let the new S.P. be Rs. x
$$\eqalign{ & {\text{Then,}} \cr & 80:9 = 105:x \cr & \Rightarrow x = \left( {\frac{{9 \times 105}}{{80}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\, = 11.81 \cr} $$

45

Raju purchased an item for Rs. 8200 and sold it at a gain of 25% . From that amount he purchased another item and sold it at a loss of 20% . What is his overall gain loss ?

A) Loss of Rs. 120 B) Gain of Rs. 120 C) Loss of Rs. 140 D) Neither loss nor gain

Discuss

Answer & Solution

Answer: Option D

Solution:

$$\eqalign{ & {\text{Initial investment}} \cr & = {\text{Rs}}.8200 \cr & {\text{S}}{\text{.P}}{\text{.of }}{{\text{1}}^{{\text{st}}}}{\text{ term}} \cr & = {\text{Rs}}.\left( {\frac{{125}}{{100}} \times 8200} \right) \cr & = {\text{Rs}}{\text{. }}10250 \cr & {\text{C}}{\text{.P}}{\text{.of }}{{\text{2}}^{{\text{nd}}}}{\text{ term}} \cr & = {\text{Rs}}{\text{. }}10250 \cr & {\text{loss}} = 20\% \cr & {\text{Final receipt}} \cr & = {\text{S}}{\text{.P}}{\text{.of }}{{\text{2}}^{{\text{nd}}}}{\text{ term}} \cr & = {\text{Rs}}.\left( {\frac{{80}}{{100}} \times 10250} \right) \cr & = {\text{Rs}}{\text{. }}8200 \cr} $$
Since initial investment = final receipt, there was neither gain nor loss.

46

If the selling price of an article is doubled, then its loss profit percent is converted into equal profit percent. The loss percent on the article is = ?

A) $$26\frac{2}{3}$$ % B) 33 % C) $$33\frac{1}{3}$$ % D) 34 %

Discuss

Answer & Solution

Answer: Option C

Solution:

Let SP = Rs. x
According to question,
$$\eqalign{ & \left( {\frac{{CP - x}}{{CP}}} \right) \times 100 = \left( {\frac{{2x - CP}}{{CP}}} \right) \times 100 \cr & CP - x = 2x - CP \cr & 3x = 2CP \cr & x = \frac{2}{3}CP \cr & SP = \frac{2}{3}CP \cr & \frac{{SP}}{{CP}} = \frac{2}{3} > 1{\text{ unit loss}} \cr & {\text{Loss}}\% = \frac{1}{3} \times 100 = 33\frac{1}{3}\% \cr} $$

47

If an article sold at 200% profit then the ratio of its cost price to his selling price will be = ?

A) 1 : 2 B) 2 : 1 C) 1 : 3 D) 3 : 1

Discuss

Answer & Solution

Answer: Option C

Solution:

Let the cost price of the article is = Rs. 100
According to the question,
\[{\text{100 (cp)}}\xrightarrow{{200\% {\text{ profit}}}}{\text{300 (sp)}}\]
\[{\text{Ratio of }}\frac{{{\text{CP}}}}{{{\text{SP}}}} = \frac{{100}}{{300}} = \frac{1}{3}\]

48

A fruit seller makes a profit of 20% by selling mangoes at a certain price. If he charges Rs. 1 more for each mango, he can make a profit of 40% . Find the selling price of a mango in the first case = ?

A) Rs. 6 B) Rs. 5 C) Rs. 5.50 D) Rs. 7

Discuss

Answer & Solution

Answer: Option A

Solution:

Let CP of 1 mango → 100

CP		SP
100	→	120	[Profit→20]
100	→	140	[Profit→40]

Difference in SP = 140 - 120 = 20
20 unit = Rs. 1
1 unit = $$\frac{1}{{20}}$$
120 unit = $$\frac{120}{{20}}$$ = Rs. 6

49

If selling price of an article is $$\frac{4}{3}$$ of its cost price, the profit in the transaction is -

A) $$16\frac{2}{3}$$ % B) $$20\frac{1}{2}$$ % C) $$25\frac{1}{2}$$ % D) $$33\frac{1}{3}$$ %

Discuss

Answer & Solution

Answer: Option D

Solution:

$$\eqalign{ & {\text{Let C}}{\text{.P}}{\text{.}} = {\text{Rs}}{\text{. }}x. \cr & Then,S.P. = {\text{Rs}}.\frac{{4x}}{3} \cr & Gain = {\text{Rs}}.\left( {\frac{{4x}}{3} - x} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}\frac{x}{3} \cr & \therefore {\text{Gain }}\% \cr & = \left( {\frac{x}{3} \times \frac{1}{x} \times 100} \right)\% \cr & = 33\frac{1}{3}\% \cr} $$

50

If an article is sold for Rs. x, there is a loss of 15%. If the same article is sold for Rs. y, there is a profit of 15%. The ratio of left (y - x) to (y + x) is -

A) 3 : 20 B) 20 : 3 C) 17 : 23 D) 20 : 23

Discuss

Answer & Solution

Answer: Option A

Solution:

$$\eqalign{ & {\text{Let C}}{\text{.P}}{\text{. of the article be Rs}}.p. \cr & Then, \cr & x = 85\% {\text{ of Rs}}{\text{. }}p = {\text{Rs}}.\frac{{85}}{{100}}p. \cr & {\text{and,}} \cr & y = 115\% {\text{ of Rs}}{\text{. }}p = {\text{Rs}}.\frac{{115}}{{100}}p. \cr & \therefore \left( {y - x} \right):\left( {y + x} \right) \cr & = \left( {\frac{{115}}{{100}}p - \frac{{85}}{{100}}p} \right):\left( {\frac{{115}}{{100}}p + \frac{{85}}{{100}}p} \right) \cr & = \frac{{30}}{{100}}p:\frac{{200}}{{100}}p \cr & = \frac{3}{{10}}:2 \cr & = 3:20 \cr} $$