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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:

A. 45 : 56

B. 45 : 51

C. 47 : 56

D. 47 : 51

Discuss

Solution:

\begin{aligned} Let the CP be 100 \\ Hence, \\ SP = 100 + 12 % o f 100 \\ = 112 \\ If the marked price be X, then \\ 90 % o f X = 112 \\ \Rightarrow x = \frac{112 \times 100}{90} \\ \Rightarrow x = R s . \frac{1120}{9} \\ Hence, \\ Required ratio \\ = 100 : \frac{1120}{9} \\ = 900 : 1120 \\ = 45 : 56 \end{aligned}

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:

A. Rs. 2600

B. Rs. 2700

C. Rs. 2800

D. Rs. 3000

Discuss

Solution:

Let Cost Price was X.
X + 14% of X = 2850
X +

\frac{14 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

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:

A. A neither losses nor gains

B. A makes a profit of 11%

C. A makes a profit of 20%

D. B loses 20%

Discuss

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 =

\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]

4. A person sold a horse at a gain of 15%. Had he bought it for 25% less and sold it for Rs. 600 less, he would have made a profit of 32%. The cost price of the horse was:

A. Rs. 3,750

B. Rs. 3,250

C. Rs. 2,750

D. Rs. 2,250

Discuss

Solution:

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

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

A. Rs. 1,200

B. Rs. 1,000

C. Rs. 960

D. Rs. 900

Discuss

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 =

\frac{100}{75}

× 720 = Rs. 960
To gain 25%, SP =

\frac{125}{100}

× 960 = Rs. 1200

6. A man sold two chairs at Rs. 1200 each. On one he gained 20% and on the other he loss 20%. His gain or loss in the whole transaction is:

A. 1% loss

B. 2% loss

C. 4% loss

D. 15 gain

Discuss

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,

\begin{aligned} = {(\frac{Common loss or gain percentage}{10})}^{2} \\ = {(\frac{20}{10})}^{2} \\ = 4 % \end{aligned}

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)

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

A. 21%

B. 20%

C. 18%

D. 17%

Discuss

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% of 130) = Rs. 117
Gain = 117 - 100 = Rs. 17

% gain = \frac{17 \times 100}{100} = 17 %

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

8. 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:

A. 20

B. 22

C. 28

D. 30

Discuss

Solution:

SP = Rs. 39
CP = x(let)
Profit % = CP

or, \frac{39 - x}{x} \times 100 = x

[% profit = \frac{SP - CP}{CP}]

\begin{aligned} 3900 - 100 x = x^{2} \\ x^{2} + 100 - 3900 = 0 \end{aligned}

x = 30

(we cannot take negative value of x)

9. A man buys a field of agricultural land for Rs. 3,60,000. He sells one-third at a loss of 20% and two-fifths at a gain of 25%. At what price must he sell the remaining field so as to make an overall profit of 10%?

A. Rs.1,00,000

B. Rs. 1,15,000

C. Rs. 1,20,000

D. Rs. 1,25,000

Discuss

Solution:

\begin{aligned} First Method : \\ CP = 360000 \\ To gain 10 % on whole land, \\ S P = 360000 + 10 % of 360000 \\ = R s . 396000 \\ \frac{1}{3} of the land sold on 20 % loss . \\ SP of \frac{1}{3} land \\ = \frac{360000}{3} - 20 % of \frac{360000}{3} \\ = R s . 96000 \\ SP of \frac{2}{5} of the land \\ = \frac{360000 \times 2}{5} + 25 % of \frac{360000 \times 2}{5} \\ = R s . 180000 \\ Thus, \\ SP of the remaining land \\ = 396000 - 96000 - 180000 \\ = R s . 120000 \\ Second Method: \\ SP of total agricultural \\ field at a profit of \\ 10 % = \frac{360000 \times 110)}{100} \\ = R s . 396000 \\ So, SP of \frac{1}{3} of field \\ = \frac{360000}{3} \times \frac{80}{100} \\ = R s . 96000 \\ SP of \frac{2}{5} t h of the field \\ = \frac{2 \times 360000 \times 125}{5 \times 100} \\ = R s . 180000 \\ Hence, \\ SP of the remaining field \\ = R s . (396000 - 96000 - 180000) \\ = R s . 120000 \end{aligned}

10. 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:

A. 3%

B. 5%

C. 8%

D. 12%

Discuss

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

\frac{782 x}{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,

\begin{aligned} x % = \frac{(782 - 742.90) \times 100}{742.90} \\ = \frac{39.1 \times 100}{742.90} \\ = 5 % \end{aligned}

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