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Profit and Loss
1.A shopkeeper earns a profit of 12% on selling a book at 10% discount on the printed price. The ratio of the cost price and the printed price of the book is:

Explanation:

Solution:
$\begin{array}{rl}& \text{Let}\phantom{\rule{thinmathspace}{0ex}}\text{the}\phantom{\rule{thinmathspace}{0ex}}\text{CP}\phantom{\rule{thinmathspace}{0ex}}\text{be}\phantom{\rule{thinmathspace}{0ex}}100\\ & \text{Hence},\\ & \text{SP}=100+12\mathrm{%}\phantom{\rule{thinmathspace}{0ex}}of\phantom{\rule{thinmathspace}{0ex}}100\\ & \phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}=112\\ & \text{If}\phantom{\rule{thinmathspace}{0ex}}\text{the}\phantom{\rule{thinmathspace}{0ex}}\text{marked}\phantom{\rule{thinmathspace}{0ex}}\text{price}\phantom{\rule{thinmathspace}{0ex}}\text{be}\phantom{\rule{thinmathspace}{0ex}}X,\phantom{\rule{thinmathspace}{0ex}}\text{then}\\ & 90\mathrm{%}\phantom{\rule{thinmathspace}{0ex}}of\phantom{\rule{thinmathspace}{0ex}}X=112\\ & ⇒x=\frac{\left(112×100\right)}{90}\\ & ⇒x=Rs.\phantom{\rule{thinmathspace}{0ex}}\frac{1120}{9}\\ & \text{Hence},\\ & \text{Required}\phantom{\rule{thinmathspace}{0ex}}\text{ratio}\\ & =100:\phantom{\rule{thinmathspace}{0ex}}\frac{1120}{9}\\ & =900:1120\\ & =45:56\end{array}$

2.By selling a bicycle for Rs. 2,850, a shopkeeper gains 14%. If the profit is reduced to 8%, then the selling price will be:

Explanation:

Solution:
Let Cost Price was X.
X + 14% of X = 2850
X + 14X/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 = 100/114 * 2850 = Rs. 2500;
SP for a profit of 8% = 108/100 * 2500 = Rs. 2700.

3.A sells an article to B at a profit of 10% B sells the article back to A at a loss of 10%. In this transaction:

Explanation:

Solution:
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 = (11*100)/100 = 10%.

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].

4.If a man were to sell his chair for Rs. 720, he would lose 25%. To gain 25% he should sell it for:

Explanation:

Solution:
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 = (100/75)*720 = Rs. 960;
To gain 25%, SP = (125/100)*960 = Rs. 1200.

5.A man sold two chairs at Rs. 1,200 each. On one he gained 20% and on the other he lost 20%. His gain or loss in the whole transaction is:

Explanation:

Solution:
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,
= (Common loss or gain percentage /10)2 = (20/10)2
= 4%

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).

6.A shopkeeper marks his goods 30% above his cost price but allows a discount of 10% at the time of sale. His gain is:

Explanation:

Solution:
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% 0f 130) = Rs. 117.
Gain = 117-100 = Rs. 17
%gain = (17*100)/100 = 17%.

Short Cut method:

100(CP)==30%↑==>130(MP)==10%↓==>117(SP).
Gain = 17%.

7.If the profit per cent got on selling an article is numerically equal to its cost price in rupees and the selling price is Rs. 39, then cost price (in Rs.) will be:

Explanation:

Solution:
SP = Rs. 39.
CP = x(let)
Profit % = CP
Or, [(39-x)/x] * 100 = x [% profit= (SP-CP)/CP]
3900-100x = x2
X2+100-3900 = 0
X = 30. (we cannot take negative value of x)

8.An article is listed at Rs. 920. A customer pays Rs. 742.90 for it after getting two successive discounts. If the rate of first discount is 15%, the rate of 2nd discount is:

Explanation:

Solution:
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
782x/100 = 39.1
782x = 3910
x = 5%.
Second Discount = 5%.

Short-Cut
920==15%(1st discount))==782==x%↓(2nd discount)==>742.90.
Then, x% = (782-742.90)*100/742.90
= (39.1*100)/742.9
= 5%.

9.A tradesman marks his goods at 25% above the cost price and allows purchasers a discount of 25/2%, his profit is:

Explanation:

Solution:

Let his CP = Rs. 100.
Marked Price = 100 + 25% of 100 = 125.
Now, discount = 25/2% on MP.
So, SP = 125 - (25/2)% of 125 = Rs. 109.375.
%Gain = 9.375%.

Alternatively use graphic change method:

100(CP)==25% Up==>125(MP)==12.5%down ==>109.375.
%Profit = 9.375%.

10.A bicycle marked at Rs. 2,000, is sold with two successive discount of 20% and 10%.An additional discount of 5% is offered for cash payment. The selling price of the bicycle at cash payment is: