Profit And Loss - Aptitude MCQ Questions and Solutions with Explanations

Discount on one shirt,
= 25% of 320 = $$\frac{{320 \times 25}}{{100}}$$  = Rs. 80
Hence, number of shirt he must buy to get a rebate of Rs. 400 = $$\frac{{400}}{{80}}$$ = 5

$$\eqalign{ & {1^{st}}\,{\text{Method}}: \cr & {\text{Let}}\,{\text{the}}\,{\text{original}}\,{\text{prine}}\,{\text{of}}\,{\text{tea}}\,{\text{be}}\,{\text{Rs}}.\,x\,\text{kg} \cr & {\text{After reduction the price becomes}} \cr & = x - 10\% \,\text{of}\,x = \frac{{9x}}{{10}}\,\text{per kg} \cr & {\text{Now}}, \cr & {\frac{{22500}}{{ {\frac{{9x}}{{10}}} }}} - \frac{{22500}}{x} = 25 \cr & {\text{or}},\,22500\left[ {\frac{{10}}{{9x}} - \frac{1}{x}} \right] = 25 \cr & {\text{or}},\,25 \times 9x = 22500 \cr & {\text{or}},\,x = {\frac{{22500}}{{25\times9}}} = \text{Rs.}\,100 \cr & {\text{Hence,}}\,{\text{new}}\,{\text{price}} \cr & = 90\,{\text{per}}\,{\text{kg}}{\text{}} \cr }$$

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$$\eqalign{ & {\text{Thought}}\,{\text{process}}\,{\text{method:}} \cr & {\text{Let the original price be Rs}}{\text{. 100 per kg}}, \cr & {\text{He get tea}} = \frac{{22500}}{{100}} \cr & = 225\,\text{kg} \cr & {\text{After reduction the price becomes}} \cr & = {\text{ }}90{\text{ per kg}} \cr & {\text{He}}\,{\text{get}}\,{\text{tea}} = \frac{{22500}}{{90}} \cr & = 250\,\text{kg} \cr & {\text{So, reduction price is }}{\text{ Rs. }}90{\text{ per kg}} \cr & {\text{As it enables him to buy 25 kg of more tea}}{\text{.}} \cr} $$

First Method
Let Cost Price for A was 100
Then CP for B = 100 + 25% of 100 = 125
CP for C = 125 + 20% of 125 = 150
CP for D = 150 + 10% of 150 = 165
But, D pay Rs. 330, Then it must be equal to
165 = 330
1 = $$\frac{{330}}{{165}}$$
100 = $$\frac{{330 \times 100}}{{165}} = 200$$
Thus, CP for A = Rs. 200

Short-cut
A's CP = $$330 \times \frac{{100}}{{125}} \times \frac{{100}}{{120}} \times \frac{{100}}{{110}}$$     = Rs. 200

In such cases, always loss occurs. It can be calculated by this formula,
$$ = \frac{{{{\left( {{\text{loss or gain percentage}}} \right)}^2}}}{{100}} = 4$$
That is 4% of loss

Graphic Change method
100 == 20%(loss) ⇒ 120 == 20%(gain) ⇒ 96
% Loss = 4%

CP = Rs. 95.
Then SP = 95 + 10% of 95 = Rs. 104.5
Let MP = X. He gives 5% commission on MP.
So,
SP = X - 5% of X
SP = 0.95X
104.5 = 0.95X
X = $$\frac{{104.5}}{{0.95}} = 100$$
Thus, MP = Rs. 110

Short-cut
95 == 10%(gain) ⇒ 104.5 == 5%(Commission) ⇒ 109.72 (= 110)

Use Formula,
Equivalent Discount = (A + B) - $$\frac{{{\text{AB}}}}{{100}}$$ where A = First Discount, B =Second Discount.
Equivalent Discount = (20 + 10) - $$\frac{{20 \times 10}}{{100}}$$
Equivalent Discount = 30 - 2 = 28%

Graphic Change Method
100 == 20%(disc.) ⇒ 80 == 10%(disc.) ⇒ 72
Equivalent discount = 28%

Let MP = X
CP = 1440
SP = 1440 + 25% of 1440 = Rs. 1800
SP = MP - 25% of MP
SP = X - 25% of 100
SP = X - 0.25X
1800 = 0.75X
X = 2400
MP = Rs. 2400

Short-Cut
Let the marked price = Rs. x
Hence,
$$\frac{{{\text{75}} \times {\text{x}}}}{{100}} = 1440 \times \frac{{125}}{{100}}$$
⇒ $$\frac{{1440 \times 125}}{{75}}$$  = Rs. 2400

Equivalent Discount,
=(A + B) - $$ {\frac{{{\text{AB}}}}{{100}}} $$
= (10 + 5) - $$ {\frac{{10 \times 5}}{{100}}} $$
= 14.5%
Let MP = X
Now,
X - 14.5% of X = 171(Selling Price)
0.855X = 171
X = 200
Hence, MP = Rs. 200

Going through options,
200(MP) == 10%(disc.) ⇒ 180 == 5%(disc.) ⇒ 171(CP)

To get 20% profit on whole,
1000(CP) ⇒ 20%(gain) ⇒ 1200(SP)
Total Profit = 1200 - 1000 = Rs. 200
400 ⇒ 10%(gain) ⇒ 440
He gets Rs. 40 profit on 400
Rest Profit = 200 - 40 = 160
Then he must get Rs. 160 as profit on Rs. 600
Hence, % profit
= $$\frac{{160 \times 100}}{{600}}$$
= $$\frac{{80}}{3}$$
= $$26\frac{2}{3}$$%

Let the CP of the article be Rs. x, since he earns a profit of 20%, hence SP = X + 20% of X = 1.2x
It is given that he incurs loss by selling 16 articles at the cost of 12 articles [loss = $$\frac{{16 - 12}}{{16}}$$  = 25%]
His selling price = SP - 25% of SP = SP × 0.75
Hence, SP × 0.75 = 1.2X
Or, SP = $$\frac{{1.2 \times {\text{x}}}}{{0.75}}$$  = 1.6X
This SP is arrived after giving a discount of 20% on MP.
Let MP = Y
Y - 20% of Y = SP
0.80Y = 1.6X
Y = 2X
It means that the article has been marked 100% above the cost price. Or Marked Price was twice of cost price.