What was the cost price of a pen? - RACE 4 Bank Exams sells an article to B at a gain of 10% and B...
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-≤Ú-´’-¢√®Ωç 1 -V-™„j 2013 Ñ-Ø√-úø’ £j«-ü¿®√-¶«-ü˛ 1 PROFIT & LOSS ★ Cost Price (C.P.): The Price at which the article is bought. ★ Selling Price (S.P.): The price at which the article is sold. ★ Profit = Selling Price − Cost Price ★ Loss = Cost Price − Selling Price Profit ★ Profit % = ⎯⎯⎯⎯⎯ × 100 Cost Price Loss ★ Loss % = ⎯⎯⎯⎯⎯ × 100 Cost Price Ex: A student buys a book for Rs.1,250 and sells for Rs.1,437.50. Find his profit per- cent? 1437.50 − 1250 Sol: Profit % = ⎯⎯⎯⎯⎯⎯⎯ × 100 1250 187.50 ⇒ ⎯⎯⎯⎯ × 100 = 15% 1250 Note: Profit or loss percent is always calculated on Cost Price unless it is asked to be calculated on Selling Price. ★ Cost Price 100 = ⎯⎯⎯⎯⎯⎯⎯⎯ × Selling Price OR 100 + Profit % Cost Price 100 = ⎯⎯⎯⎯⎯⎯⎯⎯ × Selling Price 100 − Loss % ★ Selling Price 100 + Profit % = ⎯⎯⎯⎯⎯⎯⎯⎯ × Cost Price OR 100 100 − Loss % S.P. = ⎯⎯⎯⎯⎯⎯⎯⎯ × Cost Price 100 Ex: The owner of an electronic store charges his customer 11% more than the cost price. If a customer paid Rs.1,33,200 for an LED TV, what was the original price of the TV? (RBI Assts 2012) A) Rs.1,20,000 B) Rs.1,14,500 C) Rs.1,22,500 D) Rs.1,18,000 E) None of these Sol: S.P. = Rs.1,33,200, P% = 11% 100 C.P. = ⎯⎯⎯⎯⎯⎯ × 133200 100 + 11% 100 ⇒ ⎯⎯ × 133200 = Rs.120000 111 Shortcut: Cost price is 100%, Profit = 11% therefore S.P. = 111% If 116% value is 1,33,200 then 100 100% = ⎯⎯ × 133200 111 = Rs.1,20,000 Discounts: ★ The price at which the article is marked above cost price is called the marked price or labelled price or listed price or catalogue price or printed price etc. ★ The discount is allowed on marked price. Discount ★ Discount% = ⎯⎯⎯⎯⎯⎯ × 100 Marked Price Note: Discount percents are always calculated on Marked Price. ★ When discount is deducted from the marked price, the remainder becomes the selling price. Ex: A dealer marked on article at Rs. 2,140 and sells for Rs.1,712. Find the discount percent he has offered? A) 21% B) 25% C) 20% D) 16% E) None of these Sol: Discount% 2140 − 1712 = ⎯⎯⎯⎯⎯⎯ × 100 2140 428 ⇒ ⎯⎯⎯ × 100 = 20% 2140 ★ To find Marked Price from Cost Price, the following formula can be used. ★ Marked Price 100 + Profit% = ⎯⎯⎯⎯⎯⎯⎯⎯ × Cost Price 100 − Discount% Ex: A trader buys an article for Rs.5,160. He allows 14% dis- count on it. If he gains 12% on the article, find the rate at which he marked the article? A) Rs.5,675 B) Rs.6,380 C) Rs.6,720 D) Rs.6,525 E) None of these Sol: C.P. = 5160, Profit% = 12%, Discount% = 14% 100 + 12 M.P. = ⎯⎯⎯⎯⎯ × 5160 100 − 14 112 ⇒ ⎯⎯ × 5160 86 = Rs.6,720 Some More Models 1. The cost of 12 chairs and 15 tables is Rs.58,968. What is the cost of 4 chairs and 5 tables? A) Rs.19,656 B) Rs.29,484 C) Rs.39,312 D) Can't be determined E) None of these Sol: Given, 12 chairs and 15 tables cost price as Rs.58,968. 4 chairs & 5 tables are one-third of given numbers. ∴ Cost price of 4 chairs & 5 tables 58968 = ⎯⎯⎯⎯ = Rs.19,656 3 2. A shopkeeper sold an article for Rs.425, there by losing 15%. At what price should he have sold the article to earn a profit of 10%? A) Rs.580 B) Rs.550 C) Rs.520 D) Can't be determined E) None of these Sol: S.P. = Rs.425, Loss % = 15% 100 ∴ C.P. = ⎯⎯ × 425 = Rs.500 85 Now CP of the article is Rs.500 Profit = 10% 110 ∴ S.P. = ⎯⎯ × 500 = Rs.550. 100 Shortcut: If 85% value (1st S.P.) is Rs.425, then 110% value (2nd S.P.) is 110 = ⎯⎯ × 425 = Rs.550 85 3. A man buys a scooter at Rs.6,250 and spent Rs.1,250 on its repairs. He had to sell it for Rs.6,750. Find his profit or loss percent? A) 10% Profit B) 25% Loss C) 10% Loss D) 15% Profit E) None of these Sol: C.P. = Rs.6,250 + Rs.1,250 = Rs.7,500 S.P. = Rs.6,750 ∴ Loss = Rs.7500 − Rs.6750 = Rs.750 750 Loss% = ⎯⎯⎯ × 100 = 10% 7500 4. A sells an article to B at a gain of 10% and B sells it to C at a gain of 5%. If C pays Rs.4,620 for it, what did it cost to A? A) Rs.4,550 B) Rs.3,250 C) Rs.5,250 D) Rs.4,000 E) None of these Sol: Let the cost price of A be Rs.100, then the selling price = Rs.110. Now, the cost price of B be Rs.110 105 Selling price of B = ⎯⎯ × 110 100 231 = Rs. ⎯⎯ 2 231 ∴ C.P. of C = ⎯⎯ 2 But the cost price of C as given = Rs.4,620 231 If the cost price of C is Rs. ⎯⎯, 2 then the C.P. of A = Rs.100 If the cost price of C is Rs.4,620 then the 100 × 2 × 4620 C.P. of A = ⎯⎯⎯⎯⎯⎯⎯ 231 = Rs.4,000 Shortcut: Let the C.P. of A be Rs. x then 110% of 105% of x = Rs.4,620 110 105 ⇒ ⎯⎯ × ⎯⎯ × x = 4620 100 100 100 100 ⇒ x = 4620 × ⎯⎯ × ⎯⎯ 110 105 = Rs.4,000 5. A dishonest dealer professes to sell his goods at the cost price, but uses only 960 grams in place of a kilogram weight. Find his profit percent? A) 20% B) 25% C) 30% D) 15% E) None of these Sol: Profit % Original Weight − False Weight = ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ × 100 False Weight 1000 − 960 ⇒ P % = ⎯⎯⎯⎯⎯⎯ × 100 960 40 1 ⇒ ⎯⎯ × 100 = 4 ⎯ % 960 6 What was the cost price of a pen? Numerical Ability EXPLANATION 1. C.P. of 10 chairs and 15 tables = Rs.10,625 Dividing by 5, C.P. of 2 chairs and 3 tables = Rs.2,125 Multiplying this by 4 C.P. of 8 chairs and 12 tables = 2125 × 4 = Rs.8,500 2. S.P. = Rs.10,980 P % = 22 % 100 C.P. = ⎯⎯⎯⎯⎯ × 10980 100 + 22 100 ⇒ ⎯ × 10980 = Rs.9,000 122 3. Let the cost price be 100% then for 15% loss the S.P. = 85% and for 15% profit it is 115% If 85% = 136, then 115% 115 = ⎯⎯ × 136 = Rs.184 85 4. Let the C.P. of 5 books be Rs. x, then C.P. of 10 pens = Rs. (1600 − x) ∴ 15% x − 10%(1600 − x) = Rs.90 by solving we get x = Rs.1,000 C.P. of 5 books = Rs.1,000 C.P. of 10 pens = Rs.1600 − Rs.1000 = Rs.600 600 ∴ C.P. of one pen = ⎯ = Rs. 60 10 5. M.P. = Rs.180, Discount = 15% S.P. = 85% of 180 = Rs.153 ∴ articles is available at Rs.153 Number of articles bought for 5202 Rs.5,202 is ⎯ = 34 153 6. Let the C.P. of each article be Rs.100 S.P. of 40 articles (10% profit) = 110 × 40 = Rs.4,400 S.P. of 50 articles (20% profit) = 120 × 50 = Rs.6,000 Total S.P. = Rs.4400 + Rs.6000 = Rs.10,400 By the uniform profit of 15% S.P. of 90 articles = 90 × 115 = Rs.10,350 Difference = Rs.10400 − Rs.10350 = Rs.50 If the difference is Rs.50 then C.P. = Rs.100 If the difference is Rs.40 then C.P. 100 × 40 = ⎯⎯⎯ = Rs.80 50 7. C.P. of 120 litres = Rs.3,360 S.P. of 80 litres at Rs.32 = 80 × 32 = Rs.2,560 S.P. of 40 litres at Rs.24 = 40 × 24 = Rs.960 Total S.P. of 120 litres = 2560 + 960 = Rs.3,520 Profit = 3520 − 3360 = Rs.160 160 ∴ Profit% = ⎯⎯ × 100 = 4.8% 3360 8. C.P. of 20 folders and 15 pen stands = Rs.995 Dividing by 5, C.P. of 4 folders and 3 pen stands = Rs.199 Multiplying this by 3, C.P. of 12 folders and 9 pen stands = 199 × 3 = Rs.597 200 9. Profit % = ⎯ × 100 = 25% 800 100 + 16 10.1,508 = ⎯⎯ × C.P. 100 − 12 88 ⇒ C.P. = ⎯ × 1508 = Rs.1,144 116 G.S. Giridhar Exercise 1. The cost of 10 chairs and 15 tables is Rs.10,625. What is the cost of 8 chairs and 12 tables? a) Rs.9,560 b) Rs.8,500 c) Rs.9,840 d) Can't be determined e) None of these 2. The owner of an electronics shop charges his customer 22% more than the cost price. If a customer paid Rs.10,980 for a TV set, then what was the cost price of the TV set? a) Rs.8,500 b) Rs.8,800 c) Rs.9,500 d) Rs.9,000 e) None of these 3. A man sold an article for Rs.136 at a loss of 15%. At what price should he have sold it to gain 15%? a) Rs.184 b) Rs.174 c) Rs.210 d) Can't be determined e) None of these 4. A shopkeeper buys 5 books and 10 pens for Rs.1,600. He sells books at a profit of 15% and pens at a loss of 10%. If his overall prof- it was Rs.90, what was the cost price of a pen? a) Rs.85 b) Rs.200 c) Rs.70 d) Rs.60 e) None of these 5. An article is marked at Rs.180 and 15% dis- count is offered on it. How many such articles can be bought for Rs.5,202? a) 27 b) 31 c) 34 d) 38 e) None 6. A person purchases 90 articles and sells 40 articles at a gain of 10% and 50 articles at a gain of 20%. Had he sold all of them at a uni- form profit of 15% he would have got Rs.40 less. Find the cost price of each article. a) Rs.70 b) Rs.80 c) Rs.75 d) Rs.90 e) None of these 7. A milkman buys 120 litres of milk for Rs.3,360. He sells 80 litres of milk for Rs.32 per litre and remaining at Rs.24 per litre. Find his overall profit / loss%? a) 4.8% profit b) 3.9% profit c) 4.8% loss d) 2.6% loss e) None of these 8. The cost of 20 folders and 15 pen stands is Rs.995. What is the cost of 12 folders and 9 pen stands? a) Rs.652 b) Rs.597 c) Rs.447 d) Can't be determined e) None of these 9. A dishonest dealer professes to sell his goods at the cost price, but used only 800 grams in place of a kilogram weight. Find his profit percent. a) 20% b) 15% c) 30% d) 25% e) None of these 10. A trader allows 12% discount on the printed price of a certain article and yet makes a profit of 16%. Find the cost price of the arti- cle when printed price is Rs.1,508? a) Rs.1,275 b) Rs.1,144 c) Rs.1,236 d) Rs.1,416 e) None of these Answers 1-b 2-d 3-a 4-d 5-c 6-b 7-a 8-c 9-d 10-b. (Writer - Director, RACE Institute, Hyderabad)
Transcript of What was the cost price of a pen? - RACE 4 Bank Exams sells an article to B at a gain of 10% and B...
-≤Ú-´’--¢√®Ωç 1 -V--™„j 2013 Ñ-Ø√-úø’ £j«-ü¿®√-¶«-ü˛ 1
PROFIT & LOSS
★ Cost Price (C.P.): The Price atwhich the article is bought.
★ Selling Price (S.P.): The price atwhich the article is sold.
★ Profit = Selling Price − Cost Price★ Loss = Cost Price − Selling Price
Profit★ Profit % = ⎯⎯⎯⎯⎯ × 100
Cost Price
Loss★ Loss % = ⎯⎯⎯⎯⎯ × 100
Cost PriceEx: A student buys a book for
Rs.1,250 and sells forRs.1,437.50. Find his profit per-cent?
1437.50 − 1250Sol: Profit % = ⎯⎯⎯⎯⎯⎯⎯ × 100
1250187.50
⇒ ⎯⎯⎯⎯ × 100 = 15%1250
Note: Profit or loss percent is alwayscalculated on Cost Price unless it
is asked to be calculated onSelling Price.
★ Cost Price 100
= ⎯⎯⎯⎯⎯⎯⎯⎯ × Selling Price OR100 + Profit %
Cost Price 100
= ⎯⎯⎯⎯⎯⎯⎯⎯ × Selling Price100 − Loss %
★ Selling Price100 + Profit %
= ⎯⎯⎯⎯⎯⎯⎯⎯ × Cost Price OR100
100 − Loss %S.P. = ⎯⎯⎯⎯⎯⎯⎯⎯ × Cost Price
100Ex: The owner of an electronic store
charges his customer 11% morethan the cost price. If a customerpaid Rs.1,33,200 for an LED TV,what was the original price of theTV? (RBI Assts 2012)
A) Rs.1,20,000 B) Rs.1,14,500
C) Rs.1,22,500 D) Rs.1,18,000E) None of these
Sol: S.P. = Rs.1,33,200, P% = 11%100
C.P. = ⎯⎯⎯⎯⎯⎯ × 133200100 + 11%
100⇒ ⎯⎯ × 133200 = Rs.120000
111Shortcut: Cost price is 100%, Profit
= 11% therefore S.P. = 111%If 116% value is 1,33,200 then
100100% = ⎯⎯ × 133200
111= Rs.1,20,000
Discounts:
★ The price at which the article ismarked above cost price is calledthe marked price or labelled priceor listed price or catalogue price orprinted price etc.
★ The discount is allowed on markedprice.
Discount★ Discount% = ⎯⎯⎯⎯⎯⎯ × 100
Marked Price Note: Discount percents are always
calculated on Marked Price.★ When discount is deducted from
the marked price, the remainderbecomes the selling price.
Ex: A dealer marked on article atRs. 2,140 and sells for Rs.1,712.Find the discount percent he hasoffered?
A) 21% B) 25% C) 20% D) 16% E) None of these
Sol: Discount%2140 − 1712
= ⎯⎯⎯⎯ ⎯ ⎯ × 1002140
428⇒ ⎯⎯⎯ × 100 = 20%
2140★ To find Marked Price from Cost
Price, the following formula can beused.
★ Marked Price100 + Profit%
= ⎯⎯⎯⎯⎯⎯⎯⎯ × Cost Price100 − Discount%
Ex: A trader buys an article forRs.5,160. He allows 14% dis-count on it. If he gains 12% onthe article, find the rate at whichhe marked the article?
A) Rs.5,675 B) Rs.6,380C) Rs.6,720 D) Rs.6,525E) None of these
Sol: C.P. = 5160, Profit% = 12%,Discount% = 14%
100 + 12M.P. = ⎯⎯⎯⎯⎯ × 5160
100 − 14112
⇒ ⎯⎯ × 516086
= Rs.6,720
Some MoreModels
1. The cost of 12 chairs and15 tables isRs.58,968.What is the cost
of 4 chairs and 5 tables?
A) Rs.19,656 B) Rs.29,484
C) Rs.39,312
D) Can't be determined
E) None of these
Sol: Given, 12 chairs and 15 tablescost price as Rs.58,968. 4chairs & 5 tables are one-thirdof given numbers.
∴ Cost price of 4 chairs & 5 tables
58968= ⎯⎯⎯⎯ = Rs.19,656
3
2. A shopkeeper sold an article forRs.425, there by losing 15%. Atwhat price should he have sold thearticle to earn a profit of 10%?A) Rs.580 B) Rs.550 C) Rs.520D) Can't be determinedE) None of these
Sol: S.P. = Rs.425, Loss % = 15%100
∴ C.P. = ⎯⎯ × 425 = Rs.50085
Now CP of the article is Rs.500Profit = 10%
110∴ S.P. = ⎯⎯ × 500 = Rs.550.
100Shortcut: If 85% value (1st S.P.) is
Rs.425, then 110% value (2ndS.P.) is
110= ⎯⎯ × 425 = Rs.550
853. A man buys a scooter at Rs.6,250
and spent Rs.1,250 on its repairs.He had to sell it for Rs.6,750. Findhis profit or loss percent?A) 10% Profit B) 25% LossC) 10% Loss D) 15% ProfitE) None of these
Sol: C.P. = Rs.6,250 + Rs.1,250= Rs.7,500S.P. = Rs.6,750
∴ Loss = Rs.7500 − Rs.6750= Rs.750
750Loss% = ⎯⎯⎯ × 100 = 10%
75004. A sells an article to B at a gain of
10% and B sells it to C at a gain of5%. If C pays Rs.4,620 for it, whatdid it cost to A?A) Rs.4,550 B) Rs.3,250C) Rs.5,250 D) Rs.4,000E) None of these
Sol: Let the cost price of A beRs.100, then the selling price =Rs.110. Now, the cost price of Bbe Rs.110
105Selling price of B = ⎯⎯ × 110
100231
= Rs. ⎯⎯2
231∴ C.P. of C = ⎯⎯
2But the cost price ofC as given = Rs.4,620
231If the cost price of C is Rs. ⎯⎯,
2then the C.P. of A = Rs.100If the cost price of C isRs.4,620 then the
100 × 2 × 4620C.P. of A = ⎯⎯⎯⎯⎯⎯⎯
231= Rs.4,000
Shortcut:Let the C.P. of A be Rs. x then110% of 105% of x = Rs.4,620
110 105⇒ ⎯⎯ × ⎯⎯ × x = 4620
100 100100 100
⇒ x = 4620 × ⎯⎯ × ⎯⎯ 110 105
= Rs.4,0005. A dishonest dealer professes to
sell his goods at the cost price, butuses only 960 grams in place of akilogram weight. Find his profitpercent?A) 20% B) 25% C) 30%D) 15% E) None of these
Sol: Profit % Original Weight − False Weight
= ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ × 100False Weight
1000 − 960⇒ P % = ⎯⎯⎯⎯⎯⎯ × 100
960
40 1⇒ ⎯⎯ × 100 = 4 ⎯ %
960 6
What was the cost price of a pen?
Numerical Ability
EXPLANATION
1. C.P. of 10 chairs and 15 tables = Rs.10,625Dividing by 5,C.P. of 2 chairs and 3 tables = Rs.2,125Multiplying this by 4C.P. of 8 chairs and 12 tables= 2125 × 4 = Rs.8,500
2. S.P. = Rs.10,980 P % = 22 %100
C.P. = ⎯⎯⎯⎯⎯ × 10980 100 + 22
100 ⇒ ⎯ × 10980 = Rs.9,000
1223. Let the cost price be 100% then for 15%
loss the S.P. = 85% and for 15% profit it is115%If 85% = 136, then 115%
115= ⎯⎯ × 136 = Rs.184
854. Let the C.P. of 5 books be Rs. x, then C.P.
of 10 pens = Rs. (1600 − x)∴ 15% x − 10%(1600 − x) = Rs.90by solving we get x = Rs.1,000C.P. of 5 books = Rs.1,000C.P. of 10 pens= Rs.1600 − Rs.1000 = Rs.600
600∴ C.P. of one pen = ⎯ = Rs. 60
105. M.P. = Rs.180, Discount = 15%
S.P. = 85% of 180 = Rs.153∴ articles is available at Rs.153Number of articles bought for
5202 Rs.5,202 is ⎯ = 34
153
6. Let the C.P. of each article be Rs.100S.P. of 40 articles (10% profit)= 110 × 40 = Rs.4,400
S.P. of 50 articles (20% profit)= 120 × 50 = Rs.6,000
Total S.P. = Rs.4400 + Rs.6000 = Rs.10,400By the uniform profit of 15% S.P. of 90 articles
= 90 × 115 = Rs.10,350Difference = Rs.10400 − Rs.10350 = Rs.50 If the difference is Rs.50 then C.P. = Rs.100
If the difference is Rs.40 then C.P.100 × 40= ⎯⎯⎯ = Rs.80
507. C.P. of 120 litres = Rs.3,360S.P. of 80 litres at Rs.32 = 80 × 32 = Rs.2,560S.P. of 40 litres at Rs.24 = 40 × 24 = Rs.960Total S.P. of 120 litres = 2560 + 960
= Rs.3,520Profit = 3520 − 3360 = Rs.160
160 ∴ Profit% = ⎯⎯ × 100 = 4.8%
33608. C.P. of 20 folders and 15 pen stands
= Rs.995 Dividing by 5,C.P. of 4 folders and 3 penstands = Rs.199 Multiplying this by 3,C.P. of 12 folders and 9 pen stands= 199 × 3 = Rs.597
2009. Profit % = ⎯ × 100 = 25%
800
100 + 16 10.1,508 = ⎯⎯ × C.P.
100 − 12 88
⇒ C.P. = ⎯ × 1508 = Rs.1,144116
G.S. Giridhar
Exercise
1. The cost of 10 chairs and 15 tables isRs.10,625. What is the cost of 8 chairs and12 tables?a) Rs.9,560 b) Rs.8,500 c) Rs.9,840d) Can't be determined e) None of these
2. The owner of an electronics shop charges hiscustomer 22% more than the cost price. If acustomer paid Rs.10,980 for a TV set, thenwhat was the cost price of the TV set?a) Rs.8,500 b) Rs.8,800c) Rs.9,500 d) Rs.9,000e) None of these
3. A man sold an article for Rs.136 at a loss of15%. At what price should he have sold it to
gain 15%?a) Rs.184 b) Rs.174 c) Rs.210d) Can't be determined e) None of these
4. A shopkeeper buys 5 books and 10 pens forRs.1,600. He sells books at a profit of 15%and pens at a loss of 10%. If his overall prof-it was Rs.90, what was the cost price of apen?
a) Rs.85 b) Rs.200 c) Rs.70
d) Rs.60 e) None of these
5. An article is marked at Rs.180 and 15% dis-count is offered on it. How many such articlescan be bought for Rs.5,202?
a) 27 b) 31 c) 34 d) 38 e) None
6. A person purchases 90 articles and sells 40articles at a gain of 10% and 50 articles at again of 20%. Had he sold all of them at a uni-form profit of 15% he would have got Rs.40
less. Find the cost price of each article.
a) Rs.70 b) Rs.80 c) Rs.75
d) Rs.90 e) None of these
7. A milkman buys 120 litres of milk forRs.3,360. He sells 80 litres of milk for Rs.32per litre and remaining at Rs.24 per litre. Findhis overall profit / loss%?
a) 4.8% profit b) 3.9% profit
c) 4.8% loss d) 2.6% loss
e) None of these
8. The cost of 20 folders and 15 pen stands isRs.995. What is the cost of 12 folders and 9pen stands?
a) Rs.652 b) Rs.597 c) Rs.447
d) Can't be determined e) None of these
9. A dishonest dealer professes to sell hisgoods at the cost price, but used only 800grams in place of a kilogram weight. Find hisprofit percent.
a) 20% b) 15% c) 30%
d) 25% e) None of these
10. A trader allows 12% discount on the printedprice of a certain article and yet makes aprofit of 16%. Find the cost price of the arti-cle when printed price is Rs.1,508?
a) Rs.1,275 b) Rs.1,144
c) Rs.1,236 d) Rs.1,416
e) None of these
Answers1-b 2-d
3-a 4-d
5-c 6-b
7-a 8-c
9-d10-b.
(Writer - Director, RACE Institute, Hyderabad)
