Profit and Loss Test

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Profit and Loss Test - 15

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Question 1
1 / -0

Two successive discounts of 10% and 20% are equivalent to a single discount of

A
30%

B
28%

C
15%

D
10%

Solution

Short Cut: In case of successive discounts of a% and b%, the effective discount is.
Given, two successive discounts are 10% and 20%,
So, effective discount = (10 + 20 - ) %
= (30 - 2) % = 28%
Question 2
1 / -0

Ankit made a pen. He spent Rs. 5 on the body and Rs. 3 on the refill. At what price must he sell the pen to gain 25%?

A
Rs. 6

B
Rs. 6.40

C
Rs. 4

D
Rs. 10

Solution

Total CP of pen = CP of body of pen + CP of refill of pen
= Rs. 5 + Rs. 3
= Rs. 8
Given that gain% = 25%
To find: SP of pen
Now, CP =
8 = S.P of pen = Rs. = Rs. 10
Question 3
1 / -0

Sneha wanted to buy a pair of trousers. The list price of the trousers is Rs. 450, but Sneha has only Rs. 300 in her pocket. What percent discount must she get to buy the trousers?

A
60%

B
33.3%

C
40.37%

D
50%

Solution

MP of trousers = Rs. 450
SP of trousers = Rs. 300
To find: percentage discount
Discount = MP - SP = Rs. (450 - 300) = Rs. 150
Percentage discount = = = 33.3%
Question 4
1 / -0

Umesh purchased a watch from a shop. He purchased the watch at 10% discount. The shopkeeper had marked up the watch by 20%. If the cost price of watch to shopkeeper is Rs. x, at what price did Umesh purchase the watch?

A
1.2x

B
1.08x

C
1.32x

D
1.1x

Solution

CP of watch for shopkeeper = Rs. x
Discount percent for Umesh = 10%
Percentage of mark up by shopkeeper = 20%
To find: CP of watch for Umesh
Mark up = 20% of CP of watch for shopkeeper
=
MP of watch = CP of watch for shopkeeper + Mark up
= Rs. = Rs.
Discount = 10% of MP of watch
= Rs. = Rs.
CP of watch for Umesh = MP of watch - Discount
= Rs. = Rs.
= =
Question 5
1 / -0

Rajesh and Kamal purchase a horse for Rs. 10,000. Rajesh contributes Rs. 4000 and Kamal contributes Rs. 6000. They sell the horse for Rs. 12,000. Now, they want to share the profit in the proportion of their contributions. What percentages of the profit do Rajesh and Kamal get, respectively?

A
20% and 80%

B
60% and 40%

C
40% and 60%

D
70% and 30%

Solution

Given: Total C.P. of horse = Rs. 10,000
Investment by Rajesh = Rs. 4,000
Investment by Kamal = Rs. 6,000
S.P. of horse = Rs. 12,000
To find the percentage shares of profit of Rajesh and Kamal,
concept to be used:

Solution:
Amount of profit made = Rs. (S.P. of horse - C.P. of horse)
= Rs. (12,000 - 10,000)
= Rs. 2,000
So, =

Now, percentage of profit made by Rajesh = = 40%
Percentage of profit made by Kamal = = 60%
Question 6
1 / -0

The price of an article was increased by P% and then decreased by P%. If the final price was Re. 1, the original price was

A
Re. 1

B
Rs.

C
Rs.

D
Rs.

Solution

Let the original price of the article be Rs. o.
After an increase in price by P%, price = Rs. (o + (P/100)o) = Rs. (o(1 + P/100))
After a further decrease in price by P%, price = Rs. (((100 + P)/100)o - (P/100)((100 + P)/100)o)
= Rs. (((100 + P)/100)o(1 - P/100))
= Rs. (o((100 + P)/100)((100 - P)/100))
= Rs. ((100² - P²)/10000)
= Re. 1
Or o = (10000/(10000 - P²))
Thus, answer option 3 is correct.
Question 7
1 / -0

An article is marked at a price of Rs. 200. In case 1, a discount of 40% is offered on it. In case 2, two successive discounts of 36% and 4% are offered on the same article. What is the difference between the discounts offered in the two cases?

A
Rs. 77.12

B
Rs. 0

C
Rs. 2.88

D
Rs..88

Solution

Case I:
Discount of 40% on Rs. 200
= Rs. = Rs. 80
Case II:
Since there are successive discounts of 36% and 4% on Rs. 200, this is equivalent to discount of (36 + 4 - )% on Rs. 200.
= Discount of (36 + 4 - 1.44)% on Rs. 200
= Discount of 38.56% on Rs. 200
= Rs. 77.12
Now, (Discount in case I) - (Discount in case II) = Rs. (80 - 77.12)
= Rs. 2.88
Hence, answer option 3 is correct.
Question 8
1 / -0

Rashmi purchased a mobile at th of its list price and sold it at 8% profit. Her gain percent is

A
8%

B
%

C
–8%

D
7.4%

Solution

Let the cost price of mobile = Rs. x
So, C.P of mobile for Rashmi = Rs.
Profit made = 8% of cost price = Rs.
= Rs.
So, S.P of mobile = C.P of mobile + profit made
= Rs. = Rs.
= Rs.
Now, C.P =

100 + Gain% = = 108
Gain% = (108 – 100) % = 8%
Question 9
1 / -0

Ravi marks his goods at 20% above the cost price; he then allows some discount on it and makes a profit of 8%. The rate of discount is

A
12%

B
8%

C
10%

D
11.11%

Solution

Let cost price = Rs. x
Since, Ravi marks his goods at 20% above cost price.
M.P. of goods = Rs. (x + 20% of x)
= Rs. = Rs.
Profit percent = 8%
Profit = 8% of C.P = 8% of x = Rs. = Rs.
Now, S.P of goods = C.P + Profit
= Rs. = Rs.
Discount = M.P. of goods - S.P of goods
= Rs. = Rs.
So, rate of discount =
=
= 10%
Question 10
1 / -0

Profit obtained by selling a mixer for Rs. 56 is the same as the loss incurred by selling it for Rs. 42. What is the cost of the mixer?

A
Rs. 49

B
Rs. 7

C
Rs. 50

D
Rs. 54

Solution

Let C.P. of the mixer be Rs. x.
Concept to be used:
S.P. - C.P. = Profit
And, C.P. - S.P. = Loss
Given: When S.P. = Rs. 56, a profit is made.
Profit = Rs. (S.P. - C.P.) = Rs. (56 - x)
And when S.P. = Rs. 42, a loss is incurred.
Loss = C.P. - S.P. = Rs. (x - 42)
Since Profit made = Loss incurred, therefore
56 - x = x - 42
56 + 42 = 2x 98 = 2x
x = 49
So, C.P. of the mixer = Rs. 49
Question 11
1 / -0

On selling an article for Rs. 240, a trader loses 4%. In order to gain 10%, he must sell that article for

A
Rs. 225

B
Rs. 253.83

C
Rs. 275

D
Rs. 207.68

Solution

Selling price of the article = Rs. 240 (Given)
Loss percent = 4%
To find: Selling price of article when gain percent is 10%
Concept to be used: Cost price (C.P) =
Cost price (C.P) =
Solution: Firstly, we find the cost price of the article as:
C.P = = Rs. 250
Now, we find S.P of article when gain percent is 10% as:
C.P =
S.P =
S.P = Rs. 275
Question 12
1 / -0

A dishonest dealer professes to sell his goods at cost price but uses a weight of 960 grams for 1 kg. Then his gain percentage is

A
6%

B
4%

C
4%

D
96%

Solution

Short cut: By using false weight, if a substance is sold at cost price, the overall gain percent is gain by:
Gain% =
Solution:
Here, true weight = 1 kg = 1000 gm
False weight = 960 gm
So, gain% =
=
= =
= %
Question 13
1 / -0

Find the C.P. of an article if it is sold at a gain of 6% instead of a loss of 6% so that the seller gets Rs. 6 more.

A
Rs. 50

B
Rs. 100

C
Rs. 3

D
Rs. 300

Solution

Let SP₁ = selling price of article if it is sold at a gain of 6%
SP₂ = selling price of article if it is sold at a loss of 6%
Gain that: SP₁ - SP₂ = Rs. 6
To find: C.P of article
Concept used:
C.P =
Solution:
C.P of article, when it is sold at gain of 6%, is given by:
C.P =
SP₁ = (C.P) = (C.P) ....(1)
Now,
C.P of article, when it is sold at a loss of 6%, is given by:
C.P =
C.P =
S.P₂ = or S.P₂ = (C.P) ......(2)
SP₁ - SP₂ = 6,
Putting in values from (1) and (2),
(C.P) = 6
C.P = Rs. = Rs. 50
Question 14
1 / -0

A businessman mixes 3 kg of cashew which costs Rs. 200 per kg with 2 kg of cashew which costs Rs. 300 per kg and sells the mixture at Rs. 250 per kg. What is the profit percentage on his outlay?

A
6%

B
4%

C
4%

D
None

Solution

Firstly, we find the cost of mixture per kg.
Cost of mixture per kg =
=
= Rs. = Rs. = Rs. = Rs. 240
SP of the mixture = Rs. 250 per kg
Profit = Rs. (250 - 240) = Rs. 10
Profit percentage = × 100 = % = 4%
Hence, answer option 3 is correct.
Question 15
1 / -0

1 kg tea and 3 kg sugar cost Rs. 61.20. If the cost of tea rose by 50% and cost of sugar by 10% they would cost Rs. 77.40. The prices of tea and sugar per kg respectively are

A
Rs. 12, Rs. 25.20

B
Rs. 25.20, Rs. 12

C
Rs. 10, Rs. 31.2

D
Rs. 31.2, Rs. 10

Solution

Let the price of 1 kg of tea = Rs. x
Let the price of 1 kg of sugar = Rs. y
Since, total cost of 1 kg of tea and 3 kg of sugar = Rs. 61.20
x + 3y = 61.20 .....(I)
On raising the cost of tea by 50%, the new cost of 1 kg tea becomes = Rs. = Rs. = Rs.
On raising the cost of sugar by 10%, the new cost of 1 kg sugar becomes = Rs. = Rs. = Rs.
According to the question,
New cost of 1 kg of tea and 3 kg of sugar in total = Rs. (77.40)

15x + 33y = 774
3(5x + 11y) = 3 258
5x + 11y = 258 .....(2)
Now, we solve equations (1) and (2) for x and y:
1 5 - (2)
+ 5x + 15y = + 306
+ 5x + 11y = + 258
- - -
4y = 48
y =
So, (1) implies x = 61.20 - 3y = 61.20 - 3 12 = 61.20 - 36
= Rs. 25.20
So, cost of tea per kg = Rs. 25.20
Cost of sugar per kg = Rs. 12
Question 16
1 / -0

Neha purchased an article for of the listed price and sold it for of the list price. What is her % age gain?

A
46.67%

B
70%

C
87.5%

D
-46.67%

Solution

Let the list price of article = Rs. x
So, C.P of article = of list price = Rs.
And S.P of article = of list price = Rs.
To find: Percentage gain
Concept used: C.P =
Solution: Putting values of C.P and S.P in the above formula,

100 + gain% =
Gain% = (187.5 - 100) % = 87.5%
Question 17
1 / -0

By selling salt at Re.1 per kg, a man gains 10%. By how much must he raise the price so as to gain 21%?

A
10 paise rise

B
13 paise fall

C
10 paise fall

D
11 paise rise

Solution

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Now, we find S.P of salt per kg so that the gain percent is 21%.
C.P of salt per kg =

S.P of salt per kg = Rs. = Rs. 1.1
So, rise in S.P of salt per kg = Rs. 1.1 - Rs. 0.1 = 0.1 100 paisa = 10 paisa
Question 18
1 / -0

Swati buys 8 oranges for Rs. 10. At what price should she sell a dozen oragnes if she wishes to make a profit of 15%?

A
Rs. 12.75

B
Rs. 13.04

C
Rs. 17.64

D
Rs. 17.25

Solution

CP of 8 oranges = Rs. 10
CP of 1 orange = Rs. = Rs.
Profit percent = 15%
Concept to be used: CP =
Now, CP of 1 orange =
Rs.
SP of 1 orange = Rs.
So, SP of 12 oranges = Rs. = Rs. 17.25
Question 19
1 / -0

By selling a bucket for 30% of the marked price Samindhi makes a loss of 20%, what will be her percentage profit, it she sells the bucket at 80% of the marked price

A
113.33%

B
220%

C
313.33%

D
233.33%

Solution

Let the cost price of bucket = Rs. x
So, selling price of bucket = Rs. (30% of x)
= Rs. = Rs.
Loss percent = 20%
Firstly, we find the C.P of bucket using:
= Rs. = Rs.
= Rs.
New selling price of bucket = 80% of marked price
= Rs. = Rs.
Profit% =
=
=
= 113.33%
Question 20
1 / -0

What is the maximum percentage discount Mike can offer on his bike so that he ends up selling with no profit no loss, if he had initially marked his bike up by 50%?

A
50%

B
75%

C
%

D
33.33%

E
25%

Solution

Let C.P. of bike = $x
So, M.P. of bike = $(x + 50% of x) = $ = $
There is no profit and no loss.

C.P. of bike = S.P. of bike = $x
So, discount = M.P. of bike - S.P. of bike = $= $
Percentage discount = = = 33.33%