Profit And Loss - Aptitude MCQ Questions and Solutions with Explanations

21

A man sells a book at a profit of 20% . If he had bought it at 20% less and sold it for Rs. 18 less, he would have gained 25% . The cost price of the book is = ?

A) Rs. 60 B) Rs. 70 C) Rs. 80 D) Rs. 90

Discuss

Answer & Solution

Answer: Option D

Solution:

Let the C.P. be Rs. 100
Then,
Profit = 20%
S.P. = Rs. 120
New C.P. = 20% less = Rs. 80
If he gain is 25% then S.P.
$$\eqalign{ & = {\text{Rs}}\left( {\frac{{125}}{{100}} \times 80} \right) \cr & = {\text{Rs}}.100 \cr} $$
Difference in S.P.
= Rs. (120 - 100)
=Rs. 20
If difference in S.P. is Rs. 20, then C.P. = Rs. 100
If difference in S.P. is Rs. 18, then
$$\eqalign{ & {\text{C}}{\text{.P}}{\text{.}} = {\text{Rs}}.\left( {\frac{{100}}{{20}} \times 18} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}90 \cr} $$

22

A bookseller 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 C.P. of the book be Rs. 100
Profit = 10%. S.P. = Rs. 110
New C.P. = 4% less = Rs. 96
If gain is $$18\frac{3}{4}\%$$
$$\eqalign{ & {\text{Then S}}{\text{.P}}{\text{.}} \cr & = \left( {118\frac{3}{4}\% {\text{ of Rs}}{\text{. }}96} \right) \cr & = {\text{Rs}}.\left( {\frac{{475}}{4} \times \frac{1}{{100}} \times 96} \right) \cr & = {\text{Rs}}{\text{. }}114 \cr} $$
Difference in S.P. = Rs. (114 - 110) = Rs. 4
If difference in S.P. is Rs. 4, C.P. = Rs. 100
If difference in S.P. is Rs. 6,
$$\eqalign{ & {\text{C}}{\text{.P}}{\text{.}} = {\text{Rs}}{\text{.}}\left( {\frac{{100}}{4} \times 6} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}150 \cr} $$

23

A watch is sold at a profit of 20%. If both the cost price and the selling price of the watch are decreased by Rs. 100, the profit would be 5% more. Original cost price of the watch is -

A) Rs. 450 B) Rs. 500 C) Rs. 550 D) Rs. 600

Discuss

Answer & Solution

Answer: Option B

Solution:

$$\eqalign{ & {\text{Let C}}{\text{.P}}{\text{. be Rs}}{\text{. }}x \cr & {\text{Profit}} = 20\% \cr & {\text{S}}{\text{.P}}{\text{.}} = 120\% {\text{ of Rs}}{\text{. }}x \cr & \,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\frac{{6x}}{5} \cr & {\text{New C}}{\text{.P}}{\text{.}} = {\text{Rs}}.\left( {x - 100} \right) \cr & {\text{New S}}{\text{.P}}{\text{.}} = {\text{Rs}}.\left( {\frac{{6x}}{5} - 100} \right) \cr} $$
$$\eqalign{ & {\text{Profit = }} \cr & {\text{Rs}}.\left[ {\left( {\frac{{6x}}{5} - 100} \right) - \left( {x - 100} \right)} \right] \cr & = {\text{Rs}}.\frac{x}{5} \cr & \therefore \frac{x}{5} \times \frac{1}{{\left( {x - 100} \right)}} \times 100 = 25 \cr & \Rightarrow 20x = 25\left( {x - 100} \right) \cr & \Rightarrow 5x = 2500 \cr & \Rightarrow x = 500 \cr} $$

24

A sells a suitcase to B at 10% profit. If B pays Rs. 2860 for it, then the price of which A bought is = ?

A) Rs. 1000 B) Rs. 1600 C) Rs. 2600 D) Rs. 2500

Discuss

Answer & Solution

Answer: Option C

Solution:

$$\eqalign{ & {\text{A}} \times \frac{{110}}{{100}} = 2860 \cr & {\text{A}} = {\text{Rs}}{\text{.}}\,2600 \cr} $$

25

A sells a cycle to B at a profit of 20% and B sells it to C at a loss of 25% . If C bought the cycle for Rs. P, then the cost price of it for A was = ?

A) $${\text{Rs}}{\text{.}}\,\frac{1}{{20}}{\text{P}}$$ B) $${\text{Rs}}{\text{.}}\,\frac{9}{{20}}{\text{P}}$$ C) $${\text{Rs}}{\text{.}}\,\frac{9}{{10}}{\text{P}}$$ D) $${\text{Rs}}{\text{.}}\,\frac{{10}}{9}{\text{P}}$$

Discuss

Answer & Solution

Answer: Option D

Solution:

Let the CP_A = 100x
∴ CP_B = 100x + 20% of 100x = 100x + 20x = 120x
And CP_C = 120x - 25% of 120x = 120x - 30x = 90x
According to question,
90x = P
⇒ x = $$\frac{P}{90}$$
∴ CP_A = $$100 \times \frac{P}{{90}} = \frac{{10P}}{9}$$

26

A man buys a cycle for Rs. 1400 and sells it at a loss of 15% . What is the selling price of the cycle = ?

A) Rs. 1202 B) Rs. 1190 C) Rs. 1160 D) Rs. 1000

Discuss

Answer & Solution

Answer: Option B

Solution:

According to the question 15% loss,
$$\eqalign{ & \,\,\,\,{\text{CP}}\,\,\,\,\,\,\,\,{\text{Loss}}\,\,\,\,\,\,\,\,\,{\text{SP}} \cr & \mathop { \downarrow \times 14}\limits_{1400}^{100} \,\,\,\,\,\,\,\,15\,\,\,\,\,\,\mathop { \downarrow \times 14}\limits_{1190 \to {\text{Answer}}}^{85} \cr} $$

27

An article is sold at a profit of 20% . If the cost price is increased by 10% and the sale price by Rs. 26, then the percentage of profit reduces by 5% . Determine the cost price = ?

A) Rs. 300 B) Rs. 400 C) Rs. 500 D) Rs. 600

Discuss

Answer & Solution

Answer: Option B

Solution:

$$\eqalign{ & {\text{Let the C}}{\text{.P}}{\text{. be Rs}}{\text{. }}x \cr & {\text{Profit}} = 20\% \cr & {\text{S}}{\text{.P}}{\text{.}} = {\text{Rs}}.\left( {\frac{{120}}{{100}} \times x} \right) \cr & \,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\frac{{6x}}{5} \cr & {\text{New C}}{\text{.P}}{\text{.}} = {\text{Rs}}{\text{.}}\left( {\frac{{110}}{{100}} \times x} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\frac{{11x}}{{10}} \cr & {\text{New S}}{\text{.P}}{\text{.}} = {\text{Rs}}.\left( {\frac{{6x}}{5} + 26} \right) \cr & {\text{New profit}} \cr & = {\text{Rs}}.\left[ {\left( {\frac{{6x}}{5} + 26} \right) - \frac{{11x}}{{10}}} \right] \cr & = {\text{Rs}}.\left( {\frac{x}{{10}} + 26} \right) \cr & \therefore \left( {\frac{x}{{10}} + 26} \right) \times \frac{{10}}{{11x}} \times 100 = 15 \cr & \Rightarrow 100\left( {x + 260} \right) = 165x \cr & \Rightarrow 65x = 26000 \cr & \Rightarrow x = 400 \cr} $$

28

Shailja earns 15 percent on an investment but loses 10 percent on another investment. If the ratio of the two investments is 3 : 5, then the combined loss percent is -

A) $$\frac{5}{8}$$ B) $$\frac{8}{5}$$ C) $$\frac{4}{5}$$ D) $$\frac{5}{4}$$

Discuss

Answer & Solution

Answer: Option A

Solution:

Let the two investments be Rs. 3x and Rs. 5x respectively.
Then,
Total investment = Rs. (3x + 5x) = Rs. 8x
Total output = Rs. (115% of 3x + 90% of 5x)
= Rs. (3.45x + 4.5x) = Rs. 7.95x
Loss = Rs. (8x - 7.95x) = Rs. 0.05x
$$\eqalign{ & \therefore {\text{Loss percent}} \cr & = \left( {\frac{{0.05x}}{{8x}} \times 100} \right)\% \cr & = \frac{5}{8}\% \cr} $$

29

On selling an article for Rs. 651, there is a loss of 7%. The cost price of that article is = ?

A) Rs. 744 B) Rs. 751 C) Rs. 793 D) Rs. 700

Discuss

Answer & Solution

Answer: Option D

Solution:

According to the question 7% loss
$$\eqalign{ & \,\,\,{\text{CP}}\,\,\,\,\,\,\,\,{\text{Loss}}\,\,\,\,\,\,\,\,\,{\text{SP}} \cr & \mathop { \downarrow \times 7}\limits_{\mathop {700}\limits_{\left( {{\text{Answer }}} \right)} }^{100} \,\,\,\,\,\,\,\,\,\,\,7\,\,\,\,\,\,\,\mathop {\,\,\,\,\,\,\, \downarrow \times 7}\limits_{651}^{93} \cr} $$

30

A reduction of 20% in the price of salt enabled a purchaser to obtain 4 kg, more for Rs. 100. The reduced price of salt per kg. is = ?

A) Rs. 4/kg. B) Rs. 5/kg. C) Rs. 6.25/kg. D) Rs. 6.50/kg.

Discuss

Answer & Solution

Answer: Option B

Solution:

Let the original price of salt per kg. is Rs. x
So, purchaser can buy $$\frac{{100}}{x}$$ kg.
Now, reduction price is 20%
Salt per kg. $$ = x \times \frac{{80}}{{100}} = {\text{Rs}}{\text{.}}\,\frac{{4x}}{5}$$
Now purchaser can buy
$$\eqalign{ & \frac{{100}}{{\frac{{4x}}{5}}} = \frac{{125}}{x}\,{\text{kg}} \cr & \therefore \frac{{125}}{x} - \frac{{100}}{x} = 4\,{\text{kg}} \cr & \Rightarrow \frac{{25}}{x} = 4 \cr & \Rightarrow x = {\text{Rs}}{\text{.}}\,6.25 \cr} $$
Hence the reduced price of salt per kg.
$$\eqalign{ & = {\text{Rs}}{\text{.}}\,6.25 \times \frac{{80}}{{100}} \cr & = {\text{Rs}}{\text{.}}\,5/{\text{kg.}} \cr} $$

Alternate:
$$\eqalign{ & {\text{Trick}} = \frac{a}{x} \times \frac{{{\text{reduction}}}}{{100}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{100}}{4} \times \frac{{20}}{{100}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,5/{\text{kg.}} \cr} $$