Profit And Loss - Aptitude MCQ Questions and Solutions with Explanations

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{CP}}\,{\text{be}}\,100 \cr & {\text{Hence}}, \cr & {\text{SP}} = 100 + 12\% \,of\,100 \cr & \,\,\,\,\,\,\, = 112 \cr & {\text{If}}\,{\text{the}}\,{\text{marked}}\,{\text{price}}\,{\text{be}}\,X,\,{\text{then}} \cr & 90\% \,of\,X = 112 \cr & \Rightarrow x = \frac{{ {112 \times 100} }}{{90}} \cr & \Rightarrow x = Rs.\,\frac{{1120}}{9} \cr & {\text{Hence}}, \cr & {\text{Required}}\,{\text{ratio}} \cr & = 100:\,\frac{{1120}}{9} \cr & = 900:1120 \cr & = 45:56 \cr} $$

Let Cost Price was X.
X + 14% of X = 2850
X + $$\frac{{14{\text{X}}}}{{100}}$$ = 2850
X + 0.14X = 2850
1.14X = 2850
X = 2500.
So, Cost Price = Rs. 2500.
Now, Selling Price When profit remains at 8%,
= 2500 + 8% of 2500
= Rs. 2700.

Short-Cut
CP of bicycle = $$\frac{{100}}{{114}}$$ × 2850 = Rs. 2500
SP for a profit of 8% = $$\frac{{108}}{{100}}$$ × 2500 = Rs. 2700

First Method
Let CP was 100 for A originally
A sells article to B at 10% profit,
CP for B = 100 + 10% of 100 = 110
Now, B sells it A again with loss 10%
Now, CP for A this time = 110 - 10% of 110 = 99
A makes Profit = 110 - 99 = 11
%profit for A = $$\frac{{11 \times 100}}{{100}}$$  = 11%

Second Method
It could be easily shown by net percentage change graphic.
100(A) == 10%(Profit) ⇒110(B) == 10%(Loss) ⇒ 99(A)

In this transaction A makes a profit of (110 - 99 = 11%) 11%

[10% on selling to B and 1% profit on buying back from B]

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{original}}\,{\text{CP}} = {\text{Rs}}.\,X \cr & {\text{Hence}}, \cr & {\text{SP}} = X + 15\% \,{\text{of}}\,X \cr & \,\,\,\,\,\,\,\,\, = \frac{{115X}}{{100}} \cr & \,\,\,\,\,\,\,\,\, = Rs.\,\frac{{23x}}{{20}} \cr & {\text{New}}\,{\text{CP}} = x - 25\% \,{\text{of}}\,X \cr & = \frac{{75x}}{{100}} = \frac{{3x}}{4} \cr & {\text{New}}\,{\text{SP}} = \frac{{3x}}{4} + 32\% \,{\text{of}}\,\frac{{3x}}{4} \cr & = Rs.\,\frac{{99x}}{{100}} \cr & \cr & {\text{According}}\,{\text{to}}\,{\text{the}}\,{\text{question,}} \cr & {\frac{{23x}}{{20}}} - {\frac{{99x}}{{100}}} = 600 \cr & {\text{Or}},\,\frac{{ {115x - 99x} }}{{100}} = 600 \cr & 16x = 600 \times 100 \cr & X = 600 \times \frac{{100}}{{16}} \cr & \,\,\,\,\,\, = Rs.\,3750 \cr} $$

Let the Cost price of the Chair is X.
SP = X - 25% of X
720 = 0.75X
X = 960
CP = Rs. 960
So, To gain 25%, SP would be
= 960 + 25% of 960 =Rs. 1200

Short-cut
CP of chair = $$\frac{{100}}{{75}}$$ × 720 = Rs. 960
To gain 25%, SP = $$\frac{{125}}{{100}}$$ × 960 = Rs. 1200

In the case where loss and gain percentage is common on same selling price, always a loss incurs in total deal. And this can be calculated by a short-cut:
Loss on total deal,
$$\eqalign{ & = {\left( {\frac{{{\text{Common loss or gain percentage}}}}{{10}}} \right)^2} \cr & = {\left( {\frac{{20}}{{10}}} \right)^2} \cr & = 4\% \cr} $$

Alternatively, It can be also calculated through Graphic Change Method: This can be given by,
100 == 20% gain ⇒ 120 == 20% loss ⇒ 96
Loss = 4% (As 100 became 96)

Let the cost price be Rs. 100
then the mark up price which is 30% above the cost price,
Mark price = (100 + 30% of 100) = Rs. 130
Shopkeeper gives a discount of 10% on mark up price, then the
Selling Price = (130 - 10% of 130) = Rs. 117
Gain = 117 - 100 = Rs. 17
$$\% {\text{gain}} = \frac{{17 \times 100}}{{100}} = 17\% $$

Short Cut method:
100(CP) == 30%↑ ⇒ 130(MP) == 10%↓ ⇒ 117(SP)
Gain = 17%

SP = Rs. 39
CP = x(let)
Profit % = CP
$${\text{or,}}\,\frac{{39 - x}}{x} \times 100 = x$$       $$\left[ {\% \,{\text{profit}} = \frac{{{\text{SP}} - {\text{CP}}}}{{{\text{CP}}}}} \right]$$
$$\eqalign{ & 3900 - 100x = {x^2} \cr & {x^2} + 100 - 3900 = 0 \cr } $$  
$$x=30$$   (we cannot take negative value of x)

$$\eqalign{ & {\text{First}}\,{\text{Method}}: \cr & {\text{CP}} = 360000 \cr & {\text{To}}\,{\text{gain}}\,10\% \,{\text{on}}\,{\text{whole}}\,{\text{land}}, \cr & SP = 360000 + 10\% \,\text{of}\,360000 \cr & \,\,\,\,\,\,\,\, = Rs.\,396000 \cr & \frac{1}{3}\,{\text{of}}\,{\text{the}}\,{\text{land}}\,{\text{sold}}\,{\text{on}}\,20\% \,{\text{loss}}. \cr & {\text{SP}}\,{\text{of}}\,\frac{1}{3}\,{\text{land}} \cr & = {\frac{{360000}}{3}} - 20\% \,{\text{of}}\,\, {\frac{{360000}}{3}} \cr & = Rs.\,96000 \cr & {\text{SP}}\,{\text{of}}\,\frac{2}{5}\,{\text{of}}\,{\text{the}}\,{\text{land}} \cr & = \frac{{ {360000 \times 2} }}{5} + 25\% \,{\text{of}}\,\,\frac{{ {360000 \times 2} }}{5} \cr & = Rs.\,180000 \cr & {\text{Thus}}, \cr & {\text{SP}}\,{\text{of}}\,{\text{the}}\,{\text{remaining}}\,{\text{land}} \cr & = 396000 - 96000 - 180000 \cr & = Rs.\,120000 \cr & \cr & {\text{Second}}\,{\text{Method:}} \cr & {\text{SP of total agricultural }} \cr & {\text{field at a profit of}} \cr & 10\% = \frac{{ {360000 \times 110} )}}{{100}} \cr & \,\,\,\,\,\,\,\,\,\,\, = Rs.\,396000 \cr & {\text{So,}}\,{\text{SP}}\,{\text{of}}\,\frac{1}{3}\,{\text{of}}\,{\text{field}} \cr & = {\frac{{360000}}{3}} \times {\frac{{80}}{{100}}} \cr & = Rs.\,96000 \cr & {\text{SP}}\,{\text{of}}\,\frac{2}{5}th\,{\text{of}}\,{\text{the}}\,{\text{field}} \cr & = \frac{{ {2 \times 360000 \times 125} }}{{ {5 \times 100} }} \cr & = Rs.\,180000 \cr & {\text{Hence}}, \cr & {\text{SP}}\,{\text{of}}\,{\text{the}}\,{\text{remaining}}\,{\text{field}} \cr & = Rs.\,\left( {396000 - 96000 - 180000} \right) \cr & = Rs.\,120000 \cr} $$

MP = 920
After first discount Marked Price (MP) become,
= 920 - 15% of 920 = 782
The Selling Price (SP) = 742.90
Let second discount was x% on 782
782 - x% of 782 = 742.90
$$\frac{{782x}}{{100}}$$ = 39.1
782x = 3910
x = 5%
Second Discount = 5%

Short-Cut
920 == 15%(1^st discount)) == 782 == x%↓(2^nd discount) ⇒ 742.90
Then,
$$\eqalign{ & x\% = \frac{{\left( {782 - 742.90} \right) \times 100}}{{742.90}} \cr & \,\,\,\,\,\,\,\,\,\,\, = \frac{{39.1 \times 100}}{{742.90}} \cr & \,\,\,\,\,\,\,\,\,\,\, = 5\% \cr} $$