[5 marks sum]

Question 15 Marks

A shopkeeper buys an article for ₹ 300. He increases its price by 20% and then gives 10% discount on the new price. Find:
(i) the new price (marked price) of the article.
(ii) the discount is given by the shopkeeper.
(iii) the selling price.
(iv) profit percent made by the shopkeeper.

Answer

C.P. of an article = ₹ 300
Increase in price = 20%
(i)Marked price (M.P.)
$=\frac{\text { C.P. } \times(100+\text { increase } \%)}{100}$
= ₹ $\frac{300(100+20)}{100}$
= ₹ $\frac{300 \times 120}{100}$ = ₹ 360
(ii) Rate of discount = 10%
Amount of discounts
₹ $\frac{360 \times 10}{100}=$ ₹ 36
(iii) Selling price = M.P. discount
= ₹ 360 - ₹ 36 = ₹ 324
(iv) Net profit to the shopkeeper

= S.P. - C.P. = Rs. 324 - 300 = Rs. 24
Gain % = $\frac{\text { gain } \times 100}{\text { C.P. }}=\frac{24 \times 100}{300}=8 \%$

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Question 25 Marks

40 pens are bought at 4 for Rs. 50 and all of them are sold at 5 for Rs. 80 Find
(i) C.P. of one pen.
(ii) S/P. of one pen.
(iii) Profit made by selling one pen.
(iv) Profit percent made by selling one pen.
(v) C.P. of 40 pens
(vi) S.P. of 40 pens.
(vii) Profit made by selling 40 pens.
(viii) Profit percent made by selling 40 pens. Are the results of parts (iv) and (viii) same? What conclusion do you draw from the above result?

Answer

(1) C.P. of 4 pens $=$ RS. 50
$\therefore$ C.P. of 40 pens $=\frac{50 \times 40}{4}=$ Rs. 500
and C.P. of 1 pen $=\frac{500}{40}=$ Rs. $\frac{25}{2}=$ Rs. 12.50
(ii) S.P. of pens $=$ Rs. 80
$\therefore$ S.P. of 1 pen $=$ Rs. $\frac{80}{5}=$ Rs. 16
(iii) Profit on one pen $=$ S.P. - C.P.
= Rs. $16.00-12.50$
$=$ Rs. 3.50
(iv) Profit percent $=\frac{\text { Profit } \times 100}{\text { C.P. }}$
$=\frac{3.50 \times 100}{12.50}=\frac{350 \times 100}{1250}=28 \%$
(v) C.P. of 40 pens $=40 \times 12.50=$ Rs. 500
(vi) S.P. of 40 pens $=40 \times 16=$ Rs. 640
(vii) Profit on 40 pens $=$ S.P. - C.P.
= Rs. $640-500$
$=$ Rs. 140
(viii) Profit on 40 pens $=\frac{\text { Profit } \times 100}{\text { C.P. }}$
$=\frac{140 \times 100}{500}=28 \%$
Yes, the results of (iv) and (viii) are same.
We see that profit of on equal number of articles remains the same.

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Question 35 Marks

By selling two transistors for Rs. 00 each, a shopkeeper gains 20 percent on one transistor and loses 20 percent on the other. Find :
(i) C.P. of each transistor
(ii) total C.P. and total S.P. of both the transistors
(iii) profit or loss percent on the whole.

Answer

S.P. of first transistor $=$ Rs. 600
$ \text { Gain }=20 \% $
$ \begin{aligned} & \text { (i) } \therefore \text { C.P. }=\frac{\text { S.P. } \times 100}{100+\text { gain } \%} \\ & =\frac{600 \times 100}{100+20} \\ & =\frac{600 \times 100}{120}=\text { Rs. } 500 \end{aligned} $
S.P. of the second transistor $=$ Rs. 600
Loss $=20 \%$
$\therefore$ C.P. of the second transistor
$ \begin{aligned} & =\frac{\text { S.P. } \times 100}{100-\text { loss } \%} \\ & =\frac{600 \times 100}{100-20} \\ & =\text { Rs. } \frac{600 \times 100}{80}=\text { Rs. } 750 \end{aligned} $
$\therefore$ C.P. of the two transistors are Rs. 500 and Rs. 750
(ii) Total C.P. of both the transistors
$ \text { = Rs. } 500+\text { Rs. } 750=\text { Rs. } 1250 $
and total S.P. of both the transistors
$ =\text { Rs. } 600+\text { Rs. } 600=\text { Rs. } 1200 $
(iii) Total loss $=$ C.P. - S.P.
$ =1250-1200=\text { Rs. } 50 $
$\therefore$ loss $\%=\frac{\operatorname{loss} \times 100}{\text { C.P. }}$
$ =\frac{50 \times 100}{1250}=4 \% $

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Question 45 Marks

A vendor bought 120 sweets at 20 p each. In his house, 18 were consumed and he sold the remaining at 30 p each. Find his profit or loss as percent.

Answer

Quantity of sweets bought $=120$
$ \therefore \text { C.P. of } 120 \text { sweets }=\frac{120 \times 20}{100}=\text { Rs. } 24 $
No. of sweets consumed $=18$
Balance sweets $=120-18=102$
$\therefore$ S.P. of 102 sweets
$ =\frac{102 \times 30}{100}=\frac{3060}{100}=\text { Rs. } 30.60 $
Gain = S.P. - C.P.
$=$ Rs. $30.60-$ Rs. $24=$ Rs. 6.60
Gain $\%=\frac{\text { gain } \times 100}{\text { C.P }}$
$ =\frac{6.60 \times 100}{24} $
$ =\frac{660 \times 100}{100 \times 24}=\frac{55}{2}=27.5 \% $

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