Percentage and Profit & Loss

PrepBank · পাতা ১০ / ১৭ · ৯০১–১,০০০ / ১,৬৯৬

৯০১.

The average calculator price today is Tk.700. If the average calculator price three years ago was 80% of the average calculator price today, what was the percentage increase in the average calculator price over the past three years?

ক
20%
খ
25%
গ
28%
ঘ
30%

ব্যাখ্যা

Question: The average calculator price today is Tk.700. If the average calculator price three years ago was 80% of the average calculator price today, what was the percentage increase in the average calculator price over the past three years?

Solution:
The average computer price three years ago was = 700 × 0.8
= 560 taka

Increase = 700 - 560 taka
= 140 taka

%increase = (140/560) × 100%
= 25%

৯০২.

If both the manufacturer and the retailer sell a product at a profit of 20%, what is the retail price if the product's manufacturing cost is tk 300?

ক
392 tk
খ
432 tk
গ
458 tk
ঘ
494 tk

ব্যাখ্যা

Question: If both the manufacturer and the retailer sell a product at a profit of 20%, what is the retail price if the product's manufacturing cost is tk 300?

Solution:

নির্মাতার ২০% লাভে,

নির্মাণ খরচ ১০০ টাকা হলে বিক্রয়মূল্য = ১২০ টাকা

∴ নির্মাণ খরচ ১ টাকা হলে বিক্রয়মূল্য = ১২০/১০০ টাকা

∴ নির্মাণ খরচ ৩০০ টাকা হলে বিক্রয়মূল্য = (১২০/১০০) × ৩০০ টাকা

= ৩৬০ টাকা

খুচরা বিক্রেতার ২০% লাভে,

ক্রয়মূল্য ৩৬০ টাকা হলে বিক্রয়মূল্য = (১২০/১০০) × ৩৬০ টাকা

= ৪৩২ টাকা

৯০৩.

Profit obtained by selling a watch at Tk. 320 is equal to 7/5th of the profit obtained by selling the same watch at Tk. 300. What is the cost price of the watch?

ক
Tk. 225
খ
Tk. 250
গ
Tk. 275
ঘ
Tk. 265

ব্যাখ্যা

Question: Profit obtained by selling a watch at Tk. 320 is equal to 7/5th of the profit obtained by selling the same watch at Tk. 300. What is the cost price of the watch?

Solution:
Let the cost of a watch be x
∴ (320 - x) = (7/5) × (300 - x).
⇒1600 - 5x = 2100 - 7x
⇒ 2x = 500
⇒ x = 250

৯০৪.

A cloth merchant sold half of his cloth at 20% profit, half of the remaining at 20% loss and the rest was sold at the cost price. Calculate the overall profit% or loss%?

ক
5% loss
খ
7.5% loss
গ
7.5% profit
ঘ
5% profit

ব্যাখ্যা

Question: A cloth merchant sold half of his cloth at 20% profit, half of the remaining at 20% loss and the rest was sold at the cost price. Calculate the overall profit% or loss%?

Solution:

Let the CP of the whole cloth be x

CP of 1/2 cloth = x/2

CP of half of the remaining = x/4

SP of first half of cloth = (120 × x/2) ÷ 100

SP of the half of the remaining cloth = (80 × x/4) ÷ 100

SP of the remaining half = x/4

Total SP = (120 × x/2)/100 + (80 × x/4)/100 + x/4
= 3x/5 + x/5 + x/4
= (12x + 4x + 5x)/20
= 21x/20

Gain = 21x/20 - x = x/20

Gain % = (x/20)/x × 100% = 5%

৯০৫.

If x = 80%, by what percent is x larger than x²?

ক
ক) 8%
খ
খ) 16%
গ
গ) 25%
ঘ
ঘ) 80%

ব্যাখ্যা

x = 80%
⇒ x = 80/100 = 4/5
⇒ x² = 16/25 = 16/25 × 100% = 64%
x is larger than x² (in percentage) = (80% - 64%) = 16%
x is larger than x² = (80% - 64%) = 16%
x is larger than x² (in percentage) = (16/64 ×100) = 25%

৯০৬.

The cost of an article was Tk. 75. The cost was first increased by 20% and later on it was reduced by 20%. The present cost of the article is:

ক
ক) Tk. 90
খ
খ) Tk. 82
গ
গ) Tk. 72
ঘ
ঘ) Tk. 62

ব্যাখ্যা

Question: The cost of an article was Tk. 75. The cost was first increased by 20% and later on it was reduced by 20%. The present cost of the article is:

Solution:
Initial Cost = Tk. 75
After 20% increase in the cost, it becomes,
(75 + 20% of 75)
= 75 + 15
= Tk. 90
Now, Cost is decreased by 20%, So cost will become,
(90 - 20% of 90)
= 90 - 18
=Tk. 72
So, present cost is Tk. 72.

৯০৭.

If x = 63% of y, then y² is approximately what percent of x²?

ক
ক) 125%
খ
খ) 200%
গ
গ) 250%
ঘ
ঘ) 350%

ব্যাখ্যা

প্রশ্ন: If x = 63% of y, then y² is approximately what percent of x²?

সমাধান:
Given that,
x = 63% of y
⇒ x = 63% × y
⇒ x = (63/100)×y
⇒ x = (63×y)/100
⇒ x = 63y/100

On squaring both sides then
x² = (63y/100)²
⇒ x² = (63y)²/(100)²
⇒ x² = 3969y²/10000

Let y² is the A% of x²
∴ y² = A% of x²
⇒ y² = (A/100)×x²
⇒ y² = (A/100)×(3969y²/10000)
⇒ y² = (3969y²A)/(1000000)
⇒ y²×1000000 = 3969y²A
⇒ A = 1000000y²/3969y²
⇒ A = 1000000/3969
⇒ A = 251.95
⇒ A = 252% (correct it to zero decimal)

If the answer is round off the nearest tens then
A = 250%

৯০৮.

In an election between two candidates, the winner got 65% of the total votes cast and won the election by a majority of 2925 votes. What is the total number of votes cast if no vote is declared invalid?

ক
8850
খ
9750
গ
8250
ঘ
9000

ব্যাখ্যা

Question: In an election between two candidates, the winner got 65% of the total votes cast and won the election by a majority of 2925 votes. What is the total number of votes cast if no vote is declared invalid?

Solution:
Winner gets 65% of valid votes and loser gets (100 - 65)% = 35% of votes
Difference between this two = 2925

Now,
(65 - 35)% = 2925
30% = 2925
∴ 1% = 2925/30
∴ 100% = (2925 × 100)/30 = 9750

∴ Total number of voters = 9750

৯০৯.

In one alloy there is 60% gold in its total mass, while in another alloy it is 35%. 12 kg of the first alloy was melted together with 8 kg of the second one to form a third alloy. Find the percentage of gold in the new alloy.

ক
30%
খ
50%
গ
40%
ঘ
25%

ব্যাখ্যা

Question: In one alloy there is 60% gold in its total mass, while in another alloy it is 35%. 12 kg of the first alloy was melted together with 8 kg of the second one to form a third alloy. Find the percentage of gold in the new alloy.

Solution:
Let the mass of the first alloy be m₁ = 12 kg with 60% gold,
and the mass of the second alloy be m₂ = 8 kg with 35% gold.
The total mass of the new alloy, M = m₁ + m₂ = 12 + 8 = 20 kg.

The total mass of gold in the new alloy = (0.6 × m₁) + (0.35 × m₂)
= (0.6 × 12) + (0.35 × 8)
= 7.2 + 2.8
= 10 kg.

The percentage of gold in the new alloy = (Total mass of gold / Total mass of the new alloy) × 100
= (10 kg / 20 kg) × 100
= 50%
Therefore, the percentage of gold in the new alloy is 50%.

৯১০.

In a test, minimum passing percentage for girls and boys are 45% and 60% respectively. A boy scored 767 marks and failed by 313 marks. What are the minimum passing marks for girls?

ক
800
খ
820
গ
790
ঘ
810

ব্যাখ্যা

Question: In a test, minimum passing percentage for girls and boys are 45% and 60% respectively. A boy scored 767 marks and failed by 313 marks. What are the minimum passing marks for girls?

Solution:
Minimum pass percentage for Boys = 60%
Minimum pass percentage for girls = 45%

A boy gets 767 and failed by 313
Passing marks for boys= 767 + 313 = 1080

Now
60% = 1080
1% = 1080/60
45% = (1080 × 45)/60
= 810

৯১১.

A man made a loss of 20% on his cost by selling a pen at taka 200. What should be his selling price in taka if he wants to make a profit of 10% on cost

ক
ক) 250
খ
খ) 275
গ
গ) 300
ঘ
ঘ) 225

ব্যাখ্যা

According to the question,
At 20% loss, 80 Tk selling price হলে cost = 100 Tk.
∴ 200 Tk. selling price হলে cost = (100 × 200)/80
= 250 Tk.

৯১২.

If a 10% deposit that has been paid toward the purchase of a certain goods is Tk. 110, how much Taka remains to be paid?

ক
ক) 880
খ
খ) 1,100
গ
গ) 1,010
ঘ
ঘ) 990

ব্যাখ্যা

10% টাকা ব্যয় হলে পণ্যটির উপর খরচ = 110 টাকা
1% টাকা ব্যয় হলে পণ্যটির উপর খরচ = 110/10 টাকা
90% টাকা ব্যয় হলে পণ্যটির উপর খরচ = (110 × 90)/10 টাকা
= 990 টাকা

৯১৩.

A student multiplied a number by 3/5 instead of 5/3. what is the percentage error in the calculation?

ক
ক) 32%
খ
খ) 48%
গ
গ) 64%
ঘ
ঘ) 80%

ব্যাখ্যা

Question: A student multiplied a number by 3/5 instead of 5/3. what is the percentage error in the calculation?

Solution:
Let number is x

Error = (5x/3) - (3x/5)
= (25x - 9x)/15
= 16x/15

Error % ={(16x/15) × (3/5x) × 100}% = 64%

৯১৪.

A cuboidal room has its length, breadth, and height increased by 10%, 20%, and 50% respectively. Calculate the percentage change in the volume of the cuboid.

ক
98% increase
খ
91% increase
গ
90% increase
ঘ
95% increase
ঙ
none

ব্যাখ্যা

Question: A cuboidal room has its length, breadth, and height increased by 10%, 20%, and 50% respectively. Calculate the percentage change in the volume of the cuboid.

Solution:
Let,
Each side of the cuboid be 10 unit initially.
Initial Volume of the cuboid,
= length × breadth × height
= 10 × 10 × 10
= 1000 cubic unit.

After increment dimensions become,
Length = (10 + 10% of 10) = 11 unit.
Breadth = (10 + 20% of 10) = 12 unit.
Height = (10 + 50% of 10) = 15 unit.

Now, present volume = 11 × 12 × 15 = 1980 cubic unit.
Increase in volume = 1980 - 1000 = 980 cubic unit.
∴ percentage increase in volume = (980/1000) × 100 = 98%

৯১৫.

Oranges are bought at 5 for Tk. 10 and sold at 6 for Tk. 15. The gain percent is

ক
ক) 50%
খ
খ) 40%
গ
গ) 25%
ঘ
ঘ) 35%

ব্যাখ্যা

Question: Oranges are bought at 5 for Tk. 10 and sold at 6 for Tk.15. The gain percent is-

Solution:
CP of 1 oranges=(10/5) =Tk. 2
CP of 1 oranges=(15/6) =Tk. 5/2

Profit = Tk. (5/2 - 2)
= Tk. (5 - 4)/2
= 1/2

∴Profit percent = [{(1/2)/2} × 100]%
= {(1/2) × (1/2) × 100}%
= 25%

৯১৬.

An employee's annual salary was increased Tk.15,000. If her new annual salary now equals Tk. 90,000 what was the percent increase?

ক
ক) 15%
খ
খ) 22%
গ
গ) 24%
ঘ
ঘ) 20%

ব্যাখ্যা

New annual salary = 90,000
Salary increase = 15,000.
Original salary = 90,000 - 15,000.
= 75,000

% Increase = (15,000/ 75,000 )×100
=20%

৯১৭.

A trader purchases an item for Tk. 540 and sets it marked price at 30% above the cost price. He then sells it at a discount of 20% on the marked price. What is his profit percentage?

ক
8%
খ
16%
গ
4%
ঘ
12%

ব্যাখ্যা

Question: A trader purchases an item for Tk. 540 and sets it marked price at 30% above the cost price. He then sells it at a discount of 20% on the marked price. What is his profit percentage?

Solution:
Let
the cost price be Tk. 100
Therefore the marked price is Tk. 130 (30% above CP)
Discount is Tk. 26 (20% of marked price)
Selling price is = (Tk. 130 - Tk. 26) = Tk. 104

Therefore, profit percentage is 4%.

The given cost price of Tk. 540 is unnecessary and is only for creating confusion.

৯১৮.

Kiron invests Tk. 500 in a Bank of Bangladesh at a simple interest rate of 8%. How much will be in his account after 5 years?

ক
Tk. 650
খ
Tk. 660
গ
Tk. 750
ঘ
Tk. 700

ব্যাখ্যা

Question: Kiron invests Tk. 500 in a Bank of Bangladesh at a simple interest rate of 8%. How much will be in his account after 5 years?

Solution:
Let,
P = Tk. 500
r = 8% = 8/100
n = 5 years

∴ I = Pnr
= 500 × 5 × (8/100)
= 200

∴ total amount after 5 years will be = (500 + 200)
= Tk. 700

৯১৯.

If an article was sold at 18% profit on cost price then the selling price of the article was Tk. 9,381. What would have been the selling price of the article if it was sold at 25% profit?

ক
ক) Tk. 9,984.5
খ
খ) Tk. 9,927.5
গ
গ) Tk. 9,937.5
ঘ
ঘ) None of these

ব্যাখ্যা

ধরি,
পণ্যটির ক্রয়মূল্য x টাকা
প্রশ্নমতে,
18 % of x = 9,381 - x
⇒ 18x/100 + x = 9,381
⇒118x/100 = 9,381
⇒ x = (9,381×100)/118
∴ x = 7,950
পণ্যটির ক্রয়মূল্য 7,950 টাকা

25% লাভে,
পণ্যটির বিক্রয়মূল্য= 25% of 7,950
= (125 × 7,950)/100
= 9,937.5

৯২০.

A number is decreased by 10% and then increased by 10%. The number of obtained is 10 less than the original number. What was the original number?

ক
ক) 4,000
খ
খ) 3,000
গ
গ) 2,000
ঘ
ঘ) 1,000

ব্যাখ্যা

ধরি,
মূল সংখ্যা = 100x
10% কমলে দাঁড়ায় = 100x - 100x এর 10%
= 90x
90x সংখ্যাটি 10% বাড়ালে নতুন সংখ্যা = 90x + 90x এর 10%
= 99x
প্রশ্নমতে,
100x - 99x = 10
x = 10

নির্ণেয় সংখ্যা = 100x
=100 × 10 = 1000

৯২১.

What is 200% of 0.010?

ক
0.0002
খ
0.002
গ
0.2
ঘ
0.02

ব্যাখ্যা

Question: What is 200% of 0.010?

Solution:
200% of 0.010
= (200/100) × 10/1000
= 2/100
= 1/50
= 0.02

৯২২.

The cost price of 40 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is-

ক
30
খ
32
গ
36
ঘ
50
ঙ
None of these

ব্যাখ্যা

Question: The cost price of 40 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is-

Solution:
Let,
Cost price of each article be Tk. 1
Cost price of x articles = Tk. x
Selling price of x articles = Tk. 40

∴ Profit = Tk. (40 - x)

ATQ,
(40 - x)/x = 25%
Or, 100(40 - x)/x = 25
Or, 4000 - 100x = 25x
Or, 125x = 4000
∴ x = 32

৯২৩.

A collection of books went on sale and 2/3 of them was sold for Tk 3.20 each. If none of the 41 remaining books were sold, what was the total amount received for the books that were sold?

ক
ক) 162.6 Tk
খ
খ) 198.4 Tk
গ
গ) 200 Tk
ঘ
ঘ) 262.4 Tk

ব্যাখ্যা

Remaining books = 1 - 2/3 = 1/3
1/3 of the books = 41 books
So, 2/3 of the books = 41×(2/3) / (1/3) = 82

∴ Total amount received for the sold books = 82 × 3.20 = 262.4 TK

৯২৪.

Jamal has 160 chocolates. He gave 5% chocolates to Rana, 15% to Amit and one - fourth of the chocolates to Galib. How many chocolates are left with Jamal after distribution?

ক
56
খ
72
গ
88
ঘ
None of these

ব্যাখ্যা

Question: Jamal has 160 chocolates. He gave 5% chocolates to Rana, 15% to Amit and one - fourth of the chocolates to Galib. How many chocolates are left with Jamal after distribution?

Solution:
Rana gets = 160 × 5/100 = 8 chocolates
Amit gets = 160 × 15/100 = 24 chocolates
Galib gets = 160/4 = 40 chocolates

chocolates are left with Jamal after distribution = 160 - 8 - 24 - 40 = 88 chocolates

৯২৫.

A shopkeeper sold an article at a loss of 20%. If he had sold it for Tk. 150 more, he would have made a profit of 10%. The cost price of the article is.

ক
Tk. 480
খ
Tk. 600
গ
Tk. 750
ঘ
Tk. 500

ব্যাখ্যা

Question: A shopkeeper sold an article at a loss of 20%. If he had sold it for Tk. 150 more, he would have made a profit of 10%. The cost price of the article is.

Solution:
Given that,
Loss = 20%
If sold for Tk. 150 more, profit = 10%

Now, Let cost price = Tk. x
Then,
Selling price at 20% loss = x - x of 20% = 0.80x
Selling price at 10% profit = x + x of 10% = 1.10x

According to the question,
⇒ 1.10x - 0.80x = 150
⇒ 0.30x = 150
⇒ x = 150/0.30
∴ x = 500

So, the cost price of the article is Tk. 500.

৯২৬.

The ratio of cost price and selling price is 4 : 5. The profit percentage is

ক
20%
খ
25%
গ
35%
ঘ
30%
ঙ
None

ব্যাখ্যা

Question: The ratio of cost price and selling price is 4 : 5. The profit percentage is

Solution:
Given,
The ratio of cost price (C.P.) to selling price (S.P.) is 4:5.

Let,
The cost price be 4x and the selling price be 5x.

∴ Profit = S.P - C.P. = 5x - 4x = x
∴ Profit percent = (Profit/CP) × 100
= (x/4x) × 100
= (1/4) × 100
= 25%

৯২৭.

Out of total expenditure for a month, a man spends 8% on petrol, 15% on his son's education and 52% on his family and the remaining Tk. 2500 for savings. What is the total expenditure?

ক
Tk.15000
খ
Tk.18000
গ
Tk.10000
ঘ
Tk.20000

ব্যাখ্যা

Let the total expenditure = Tk.X
He spends for petrol = 8X/100
For his son's education = 15X/100
For his family = 52X/100
Therefore the remaining amount for savings = Tk. 2500 = X - (8X/100 + 15X/100 + 52X/100)
⇒ X - (8X/100 + 15X/100 + 52X/100) = Tk. 2500
⇒ X - 75X/100 = Tk. 2500
⇒ 25X/100 = Tk. 2500
⇒ 25X = Tk. 2500 × 100
⇒ X = (Tk. 2500 × 100)/25
⇒ X = Tk. 10000
Hence, the total expenditure = Tk. 10000.

৯২৮.

Ratul gets 55% of total valid votes in an election. If the total votes were 9000, what is the number of valid votes that the other candidate Sami gets if 30% of the total votes were declared invalid?

ক
6300
খ
4950
গ
3465
ঘ
2835

ব্যাখ্যা

Question: Ratul gets 55% of total valid votes in an election. If the total votes were 9000, what is the number of valid votes that the other candidate Sami gets if 30% of the total votes were declared invalid?

Solution:
Total votes = 9000
Total valid votes = 70% of 9000 = 6300
Shyam gets 45% of 6300 = (45/100) × 6300 = 2835 votes

৯২৯.

After decreasing 24% in the price of an article the discounted price becomes $1368. Find the actual price of the article?

ক
ক) 1800
খ
খ) 1600
গ
গ) 1200
ঘ
ঘ) 1000

ব্যাখ্যা

Let the products actual price be x
ATQ, 76% of x = 1368
Or, 76x/100 = 1368
Or, x = (1368 × 100) / 76
= 1800

৯৩০.

Fresh grapes contain 80 percent water while dry grapes contain 10 percent water. If the weight of the dry grapes is 250 kg what is total weight when it was fresh?

ক
1000 kg
খ
1100 kg
গ
1125 kg
ঘ
1225 kg

ব্যাখ্যা

Question: Fresh grapes contain 80 percent water while dry grapes contain 10 percent water. If the weight of the dry grapes is 250 kg what is total weight when it was fresh?

Solution:
Quantity of water in 250 kg dry grapes = 250 × (10/100)
= 25 kg
Then, pulp of grapes = (250 - 25) kg = 225 kg.

We get 20 kg pulp in 100 kg fresh grapes
To get 225 kg pulp, we need fresh grapes = (100 × 225)/20 kg
= 1125 kg.

৯৩১.

A student erroneously multiplied a number by 7/10 instead of 7/5. What is the percentage error in the calculation?

ক
60%
খ
50%
গ
45%
ঘ
40%

ব্যাখ্যা

Question: A student erroneously multiplied a number by 7/10 instead of 7/5. What is the percentage error in the calculation?

Solution:
Let
the number be 100.

ATQ,
Actual calculation be: (7/5) × 100 = 140
and error calculation be: (7/10) × 100 = 70

∴ Difference = 140 - 70 = 70

∴ Percentage error = (70/140) × 100 = 50%

৯৩২.

If 20% of x is the same as the 10% of y, then x : y is equal to

ক
ক) 1 : 4
খ
খ) 1 : 3
গ
গ) 5 : 2
ঘ
ঘ) 1 : 2

ব্যাখ্যা

Question: If 20% of x is the same as the 10% of y, then x : y is equal to

Solution:
20% of x = 10% of y
⇒ (20/100) × x = (10/100) × y
⇒ 20 x = 10 y
⇒ x/b = 10/20
∴ x : y = 1 : 2

৯৩৩.

Ankita deposited Tk. 750 into her savings account. If the interest rate of the account is 4% per year, how much interest will she have made after 5 years?

ক
ক) Tk. 131
খ
খ) Tk. 142
গ
গ) Tk. 150
ঘ
ঘ) Tk. 168

ব্যাখ্যা

We know, I = pnr
= 750 × 5/100 × 4
= 150

৯৩৪.

The population of a city grows by 10% every year. If the current population is 50,000, what will the population be after 2 years?

ক
59400
খ
60500
গ
61600
ঘ
63600
ঙ
None

ব্যাখ্যা

Question: The population of a city grows by 10% every year. If the current population is 50,000, what will the population be after 2 years?

Solution:
Here we can use the compound interest based formula,
Population after n years
= P × [1 + (r/100)]n
∴ Population after 2 years = 50000 × [1 + (10/100)]²
= 50000 × (110/100)²
= 50000 × 1.21
= 60,500

৯৩৫.

If 40% of all women are voters and 52% of the population is women, what percent of the population are women voters?

ক
20.8
খ
19.2
গ
26.4
ঘ
40.0
ঙ
None of these

ব্যাখ্যা

Question: If 40% of all women are voters and 52% of the population is women, what percent of the population are women voters?

Solution:
Let,
There are 100 number of population

∴ The number of women is 52
∴ Women voters in number 40% of 52 = 20.8

∴ 20.8% of the population are women voters.

৯৩৬.

A vendor purchased 200 books for Taka 150 each and sold them for Taka 200 each. Calculate the total profit.

ক
Taka 15,000
খ
Taka 20,000
গ
Taka 10,000
ঘ
Taka 11,000

ব্যাখ্যা

Question: A vendor purchased 200 books for Taka 150 each and sold them for Taka 200 each. Calculate the total profit.

Solution:
Cost Price of 200 books = 200 × Taka 150 = Taka 30,000
Selling Price of 200 books = 200 × Taka 200 = Taka 40,000
Total Profit = Selling Price - Cost Price = Taka 40,000 - Taka 30,000 = Taka 10,000

৯৩৭.

A person who spends (200/3)% of his income is able to save Tk.1500 per month. His monthly expenses ( in Tk.) are-

ক
ক) Tk. 2600
খ
খ) Tk. 3200
গ
গ) Tk. 3000
ঘ
ঘ) Tk. 4500

ব্যাখ্যা

Let
The monthly income be Tk. x
Now
{100 - (200/3)}% of x = 1500
{(300 - 200)/3}% of x = 1500
(100/3) % of x = 1500
(100/3) × (1/100) × x = 1500
x/3 = Tk.1500
x = Tk.4500

His monthly expense = Tk. (4500 - 1500)
= Tk. 3000

৯৩৮.

A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of 784 Tk, what was his profit?

ক
72 Tk.
খ
144 Tk.
গ
148 Tk.
ঘ
164 Tk.

ব্যাখ্যা

Question: A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of 784 Tk, what was his profit?

Solution:
Given,
Selling price = 784 Tk.

For a gain of 22.5%,
The cost price can be = 122.5

Cost price = (100/122.5) × 784 Tk.
= (1000/1225) × 784 Tk.
= 640 Tk

Therefore, Profit = 784 - 640 Tk.
= 144 Tk.

৯৩৯.

Two persons contested an election of Parliament. The winning candidate secured 57% of the total votes polled and won by a majority of 42000 votes. The number of total votes polled is :

ক
700000
খ
400000
গ
300000
ঘ
200000

ব্যাখ্যা

Question: Two persons contested an election of Parliament. The winning candidate secured 57% of the total votes polled and won by a majority of 42000 votes. The number of total votes polled is :

Solution:
Winning candidates secured 0.57x votes and other gets 0.43x votes.

ATQ,
0.57x - 0.43x = 42000
⇒ 0.14x = 42000
⇒ x = 42000/0.14
= 300000

৯৪০.

If a shopkeeper sells a bat for Tk. 600, he incurs a loss of 20%. At what price should he sell it to make a profit of 20%?

ক
Tk. 850
খ
Tk. 900
গ
Tk. 800
ঘ
Tk. 950
ঙ
None

ব্যাখ্যা

Question: If a shopkeeper sells a bat for Tk. 600, he incurs a loss of 20%. At what price should he sell it to make a profit of 20%?

Solution:
Let the cost price (CP) of the bat be x.
Selling price = x - 20% of x
⇒ 600 = x - (20x/100)
⇒ 600 = 80x/100
⇒ 80x = 60000
⇒ x = 750 (This is the CP)

To gain,
20% = 750 + 20% of 750
= 750 + (20 × 750)/100
= 750 + 150
= Tk. 900

৯৪১.

If three fifth of a number is 40 more than 40 % of the same number, what is the number?

ক
ক) 120
খ
খ) 160
গ
গ) 180
ঘ
ঘ) 200

ব্যাখ্যা

Let be assume the number is x
According to the question
x × 3/5 = 40 + 40% of x
⇒ x × (3/5) = 40 + x × (40/100)
⇒ x × (3/5) = 40 + x × (2/5)
⇒ (3x/5) - (2x/5) = 40
⇒(3x - 2x)/5 = 40
⇒ x/5 = 40
⇒ x = 200

∴ The required result will be 200.

৯৪২.

There were two friends appearing for the examination. One of those friends scored 6 marks more than the other and his marks were 52% of the sum of the total marks. How many marks did better on the two friends' scores?

ক
70
খ
72
গ
78
ঘ
84

ব্যাখ্যা

Question: There were two friends appearing for the examination. One of those friends scored 6 marks more than the other and his marks were 52% of the sum of the total marks. How many marks did better on the two friends' scores?

Solution:
Let, better on the two friends' score x

another friend scores x - 6

ATQ,
x/(x + x - 6) = 52/100 = 13/25
⇒ 25x = 26x - 78
∴ x = 78

৯৪৩.

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 = ?

ক
ক) 99 : 56
খ
খ) 25 : 56
গ
গ) 45 : 61
ঘ
ঘ) 45 : 56

ব্যাখ্যা

According to the question,
Cost Price : Marked Price
(100 - Discount) : (100 + Profit)
100 - 10 : 100 + 12
90 : 112
45 : 56

৯৪৪.

A trader sells a bag for Tk. 2,400 at a loss of 20%. If his regular profit is 10%, find the regular selling price.

ক
2,400 Taka
খ
3,000 Taka
গ
3,200 Taka
ঘ
3,300 Taka

ব্যাখ্যা

Question: A trader sells a bag for Tk. 2,400 at a loss of 20%. If his regular profit is 10%, find the regular selling price.

Solution:
Selling price = 2,400 Taka
Loss % = 20%

Original cost price = 2400 / 0.8 = 3000 Taka

Regular profit = 10%
Regular Selling price = 3000 × 1.1 = 3300 Taka

∴ Regular Selling price = 3300 Taka

৯৪৫.

As the price of mango has reduced 20%, it is now possible to buy 2 more mangoes at Tk. 12. What is the correct price of 50 mangoes?

ক
ক) Tk. 50
খ
খ) Tk. 60
গ
গ) Tk. 70
ঘ
ঘ) Tk. 80

ব্যাখ্যা

As the price of mango has reduced 20% that means
mango of Tk. 100 will be available for Tk. 80
Therefore, mango of Tk. 12 will be available for Tk. (80 × 12/100) or Tk. 9.6
So, cost price of 2 mangoes = (12 - 9.6) = Tk. 2.4
cost price of 50 mangoes = Tk. 2.4 × 50/2 = Tk. 60
---------------------------------------------------------------------------
short-cut
20% of Tk. 12 = Tk. 2.4
The price of 2 mangoes is Tk. 2.4
The price of 50 mangoes is Tk. 2.4 × 50/2 = Tk. 60

৯৪৬.

A shopkeeper suffers a loss of 20% upon selling a shirt for Tk 4000. If he wants to make 15% profit after giving an 8% discount on the marked price, what is the marked of the shirt in tk?

ক
5000
খ
5750
গ
6000
ঘ
6250
ঙ
None

ব্যাখ্যা

Question: A shopkeeper suffers a loss of 20% upon selling a shirt for Tk 4000. If he wants to make 15% profit after giving an 8% discount on the marked price, what is the marked of the shirt in tk?

Solution:
At 20% loss,
Selling price Tk. 80 when cost price Tk. 100
Selling price Tk. 1 when cost price Tk. 100/80
Selling price Tk. 4000 when cost price Tk. (100 × 4000)/80
= Tk. 5000

At 15% profit,
cost price Tk. 100 when selling price Tk. 115
cost price Tk. 1 when selling price Tk. 115/100
cost price Tk. 5000 when selling price Tk. (115 × 5000)/100
= Tk. 5750

At 8% discount,
Selling price Tk. 92 when marked price Tk. 100
Selling price Tk. 1 when marked price Tk. 100/92
Selling price Tk. 5750 when marked price Tk. (100 × 5750)/92
= Tk. 6250

৯৪৭.

What would be the value of 20% of m as a percentage of p, if 8% of m = 4% of p?

ক
80%
খ
16%
গ
10%
ঘ
None

ব্যাখ্যা

Question: What would be the value of 20% of m as a percentage of p, if 8% of m = 4% of p?

Solution:
8% of m = 4% of p
⇒ 8m/100 = 4p/100
⇒ m = p/2
⇒ 20% of m = (p/2) × 20%
⇒ 20% of m = 10% of p

৯৪৮.

A lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/6 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?

ক
1/16
খ
3/16
গ
7/16
ঘ
9/16

ব্যাখ্যা

Question: A lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/6 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?

Solution:
lets, the total cups sold 15
small cups = (3/5) × 15 = 9
large cups = 15 - 9 = 6

let, small cups were sold 6 taka each, then large cups were sold 7 taka each.

large cup's revenue = 7 × 6 = 42 taka
small cup's revenue = 6 × 9 = 54 taka

fraction of Tuesday's total revenue was from the sale of large cups = 42/(42 + 54)
= 42/96
= 7/16

৯৪৯.

P is 6 times greater than Q then by what percent is Q smaller than P?

ক
87%
খ
79.67%
গ
83.33%
ঘ
71%
ঙ
None

ব্যাখ্যা

Question: P is 6 times greater than Q then by what percent is Q smaller than P?

Solution:
Let Q = 10.
Then, P = 60.
Q is 50 less than P.
Q, % less than P = (50/60) × 100
= 83.33%

৯৫০.

A dishonest dealer sells the goods at 6(1/4)% loss on cost price but uses 12(1/2)% less weight. What is the percentage profit or loss?

ক
7(1/2)%
খ
7(5/7)%
গ
7(1/7)%
ঘ
7(2/5)%

ব্যাখ্যা

Let,
The C.P (cost price) of 1 kg goods be 1 tk
Then, S.P. of {100 - (25/2)% of 1 kg}
Or, 875 gm goods = .9375 tk
S.P of 1 kg goods = (.9375/875 × 1000) tk
= 1 (1/14) tk
∴ Profit % = (1/14 × 100)% = 7(1/7)%
Answer: 7(1/7)%

৯৫১.

If a pen is sold at taka 55 it makes a profit of 10%. What is its purchase cost?

ক
ক) 50
খ
খ) 110
গ
গ) 45
ঘ
ঘ) 60

ব্যাখ্যা

Question: If a pen is sold at taka 55 it makes a profit of 10%. What is its purchase cost?

Solution:
10% লাভে
ক্রয়মূল্য 100 টাকা হলে বিক্রয়মূল্য = 100 + 10 = 110 টাকা

বিক্রয়মূল্য 110 টাকা হলে ক্রয়মূল্য = 100 টাকা
বিক্রয়মূল্য 1 টাকা হলে ক্রয়মূল্য = 100/110 টাকা
বিক্রয়মূল্য 55 টাকা হলে ক্রয়মূল্য = 100 × 55/110 টাকা
= 50 টাকা

৯৫২.

In a shipment of 120 machine parts, 5 percent were defective. In a shipment of 80 machine parts, 10 percent were defective. For the two shipments combined, what percent of the machine parts were defective?

ক
6.5%
খ
7.0%
গ
7.5%
ঘ
8.0%
ঙ
8.5%

ব্যাখ্যা

Question: In a shipment of 120 machine parts, 5 percent were defective. In a shipment of 80 machine parts, 10 percent were defective. For the two shipments combined, what percent of the machine parts were defective?

Solution:
Defective machine in 1st shipment = 5% of 120 = 6

Defective machine in 2nd shipment = 10% of 80 = 8

Total Defective machine = (6 + 8) = 14

Percentage of combined defective machine = (14/200) × 100% = 7%

৯৫৩.

605 sweets were distributed equally among children in such a way that the number of sweets received by each child is 20% of the total number of children. How many sweets did each child receive?

ক
9
খ
11
গ
15
ঘ
Data inadequate

ব্যাখ্যা

Question: 605 sweets were distributed equally among children in such a way that the number of sweets received by each child is 20% of the total number of children. How many sweets did each child receive?

Solution:
Let Children = X
A/Q,
605/X = 20% of X
⇒ 605/X = X/5
⇒, X² =5 × 605
⇒ X²= 5² × 11²
X = 55

So each children receive = 605/55
= 11

৯৫৪.

A fruit salad is made by mixing 3 kgs of mango costing Tk 120 per kg and 2 kgs of papaya costing Tk 100 per kg and 2 kgs of grapes costing Tk 140 per kg. At what price (in Taka) per kg should the mixture be sold to make profit of 25 percent?

ক
125
খ
150
গ
175
ঘ
None of these

ব্যাখ্যা

Question: A fruit salad is made by mixing 3 kgs of mango costing Tk 120 per kg and 2 kgs of papaya costing Tk 100 per kg and 2 kgs of grapes costing Tk 140 per kg. At what price (in Taka) per kg should the mixture be sold to make profit of 25 percent?

Solution:
3 কেজি আমের মূল্য = 120 × 3 = 360 টাকা
2 কেজি পেঁপের মূল্য = 100 × 2 = 200 টাকা
2 কেজি আঙ্গুরের মূল্য = 140 × 2 = 280 টাকা

মোট = 360 + 200 + 280 = 840 টাকা

25% লাভে
বিক্রয়মূল্য = 840 + 840 এর 25%
= 840 + 840 এর 25/100
= 840 + 210
= 1,050

7 কেজি বিক্রয় করতে হবে = 1050 টাকা
1 কেজি বিক্রয় করতে হবে = 1050/7 টাকা
= 150 টাকা

৯৫৫.

Hasan sold an article for 56 taka which cost him x taka. If he had gained x% on his outlay, what was his cost?

ক
ক) 40 taka
খ
খ) 45 taka
গ
গ) 36 taka
ঘ
ঘ) 25 taka
ঙ
ঙ) None of these

ব্যাখ্যা

Question: Hasan sold an article for 56 taka which cost him x taka. If he had gained x% on his outlay, what was his cost?

Solution:
ক্রয়মূল্য x টাকা
x% লাভে, বিক্রয়মূল্য = x + x × x/100
= (100x + x²)/100

প্রশ্নমতে,
(100x + x²)/100 = 56
⇒ 100x + x² = 5600
⇒ x² + 100x - 5600 = 0
⇒ x² + 140x - 40x - 5600 = 0
⇒ x(x + 140) - 40 (x + 140) = 0
⇒ (x + 140) (x - 40) = 0
∴ x = - 140; যা গ্রহণযোগ্য নয়।
অতএব, x = 40
∴ ক্রয়মূল্য ৪০ টাকা

৯৫৬.

If 20% of a = b, then b% of 20 is the same as-

ক
4% of a
খ
6% of a
গ
8% of a
ঘ
10% of a

ব্যাখ্যা

Question: If 20% of a = b, then b% of 20 is the same as-

Solution:
20% of a = b
⇒ (20/100) × a = b
∴ b = (20a)/100

Now,
b% of 20
=(b/100) × 20
= b/5
= [{(20a)/100}/5]
= {(20a)/(100 × 5)}
= (4a)/100
= 4% of a.

৯৫৭.

'Buy Three get One Free' what is the percentage of discount being offered here?

ক
ক) 25%
খ
খ) 48.78%
গ
গ) 21%
ঘ
ঘ) 33.33%

ব্যাখ্যা

Question: 'Buy Three get One Free' what is the percentage of discount being offered here?

Solution:

'Buy Three get One Free' এর অর্থ হলো - ৩টি পণ্য ক্রয় করলে ১টি পণ্য ফ্রী।

ধরি, প্রতিটি পণ্যের ক্রয়মূল্য X টাকা
⇒ ৩টি পণ্যের ক্রয়মূল্য = 3X টাকা

সুতরাং, ডিসকাউন্ট হার = (X/3X) × 100 = 33.33%

৯৫৮.

An article has a marked price of Tk. 500. If two successive discounts of x% and 5% reduce the selling price to Tk. 427.50, determine the value of x.

ক
7%
খ
10%
গ
14%
ঘ
19%

ব্যাখ্যা

Question: An article has a marked price of Tk. 500. If two successive discounts of x% and 5% reduce the selling price to Tk. 427.50, determine the value of x.

Solution:
Marked Price = Tk. 500
Final Selling Price after two successive discounts = Tk. 427.50
Let the first discount = x%
Second discount = 5%

First discount be:
500 × (1 - x/100) × (1 - 0.05) = 427.50
⇒ 500 × (1 - x/100) × 0.95 = 427.50
⇒ 475 × (1 - x/100) = 427.50
⇒ (1 - x/100) = 427.50 / 475
⇒ 1 - x/100 = 0.9
⇒ - x/100 = 0.9 - 1
⇒ - x/100 = - 0.1
⇒ x = 0.1 × 100
⇒ x = 10%

∴ First discount = 10%

৯৫৯.

A started a business with Tk. 2100 and is joined afterwards by B with Tk. 3600. After how many months did B join if the profits at the end of the year are divided equally?

ক
5 months
খ
7 months
গ
10 months
ঘ
1 year

ব্যাখ্যা

Question: A started a business with Tk. 2100 and is joined afterwards by B with Tk. 3600. After how many months did B join if the profits at the end of the year are divided equally?

Solution:
Suppose,
B joined after x months.

Then,
2100 × 12 = 3600 × (12 - x)
⇒ 252 = 432 - 36x
⇒ 36x = 180
∴ x = 5

∴ B joined after 5 months

৯৬০.

Jasim's weight is 140% of Masum's weight. Bashir's weight is 90% of Limon's Weight. Limon weights twice as much as Masum. What percentage of Jasim's weight is Bashir's weight?

ক
ক) 452/7%
খ
খ) 695/9%
গ
গ) 900/7%
ঘ
ঘ) 410/9%

ব্যাখ্যা

Masum : Jasim = 100 : 140 = 5 : 7
Limon : Bashir = 100 : 90 = 10 : 9
Limon: Masum = 2 : 1 = 10 : 5 [5 দ্বারা গুণ করে পাই]

Masum : Jasim : Limon : Bashir = 5 : 7 : 10 : 9

ধরি
Jasim এর ওজন = 7x কেজি
Bashir এর ওজন = 9x কেজি

নির্ণেয় শতাংশ = (9x/7x) × 100%
= 900/7%

৯৬১.

Three shirts and five ties cost Tk 23. Five shirts and one tie cost Tk 20. What is the price of one shirt?

ক
ক) Tk. 2.50
খ
খ) Tk. 3.00
গ
গ) Tk. 3.50
ঘ
ঘ) Tk. 6.00

ব্যাখ্যা

Let s=shirt and t=tie
Need to solve:
3s + 5t = 23 and 5s + 1t = 20
Look for a multiple of one (or both) formula that will match the quantity of the second. One option is to multiply the second equation by 5:
5x (5s + 1t) = 5x 20
Or, 25s + 5t = 100
Subtract the first formula :
25s + 5t - 3s - 5t = 100 - 23
Or, 22s = 77

So shirts are 77 / 22 = Tk. 3.50 each

৯৬২.

What percentage should be added to 40 to make it 70?

ক
10
খ
75
গ
25
ঘ
50

ব্যাখ্যা

Let, x% should be added.
Therefore, 40 + x% of 40 = 70
⇒ 40 + 40x/100 = 70
⇒ 40x/100 = 30
2x/5 = 30
2x = 150
x = 75
Therefore, 75% should be added to 40 to make it 50

৯৬৩.

A milkman purchases the milk at Tk. x per liter and sells it at Tk. 2x per liter still he mixes 2 liters of water with every 6 liters of pure milk. What is the profit percentage?

ক
ক) 116%
খ
খ) 166.66%
গ
গ) 60%
ঘ
ঘ) 100%

ব্যাখ্যা

Let,
He purchases 6 liters milk.
So, cost of 6 liters = 6x tk.
After mixing 2 liters waters, he sells , (6 + 2) = 8 liters
Now, selling price of 8 liters = 8 × 2x = 16x tk
Profit = 16x – 6x = 10x tk.
∴ Profit percentage = (10x/6x) × 100 = 166.66%

৯৬৪.

In a club, 60% members are male and 70% members are graduates. Also 50% of the graduate members are male. What percentage of the club members are female and non-graduate?

ক
ক) 5%
খ
খ) 10%
গ
গ) 15%
ঘ
ঘ) 20%

ব্যাখ্যা

Question: In a club, 60% members are male and 70% members are graduates. Also 50% of the graduate members are male. What percentage of the club members are female and non-graduate?

Solution:
ধরি
x জন সদস্য নারী ও নন-গ্র্যাজুয়েট

প্রশ্নমতে,
100 = 70 + (60 - 35) + x
x + 25 = 30
x = 30 - 25
x = 5

৯৬৫.

A retailer buys pens in packs of 24 for Tk.336/pack and then resells them in packs of 5 for Tk.80/pack. If the retailer sold all the pens it purchased and made a profit of Tk.960. How many packs of pens did the retailer purchase?

ক
ক) 10
খ
খ) 20
গ
গ) 25
ঘ
ঘ) None

ব্যাখ্যা

No explanation added.

৯৬৬.

Manoj sold an article for TK.15,000. Had he offered a discount of 10% on the selling price he would have earned a profit of 8%. What is the cost price?

ক
ক) TK.12,500
খ
খ) TK.13,500
গ
গ) TK.12,250
ঘ
ঘ) TK.13,250
ঙ
ঙ) Tk. 14,250

ব্যাখ্যা

Let the cost price x.
Therefore, 90% of 15000 = 108% of x .
Or, x = 90 × 15000108
Or, x = Tk. 12500

৯৬৭.

Aslam bought 5 apples at taka 10 and sold 4 apples at taka 10. What will be the rate of profit?

ক
ক) 25%
খ
খ) 20%
গ
গ) 30%
ঘ
ঘ) 33.33%

ব্যাখ্যা

5টি আপেলের ক্রয়মূল্য 10 টাকা
1টি আপেলের ক্রয়মূল্য 10/5 টাকা
= 2 টাকা

4টি আপেলের বিক্রয়মূল্য 10 টাকা
1টি আপেলের বিক্রয়মূল্য 10/4 টাকা
= 2.5 টাকা
লাভ = (2.5 - 2)টাকা = 0.5

শতকরা লাভ = {(0.5/2) × 100}%
= 25%

৯৬৮.

Sixty-five percent of a number is 42 less than four-fifth of that number. What is the number?

ক
320
খ
280
গ
260
ঘ
240

ব্যাখ্যা

Question: Sixty-five percent of a number is 42 less than four-fifth of that number. What is the number?

Solution:
Let, the number = x.

ATQ,
65% of x = (4/5) of x - 42
⇒ 65x/100 = (4x/5) - 42
⇒ 13x/20 = (4x/5) - 42
⇒ (4x/5) - (13x/20) = 42
⇒ (16x - 13x)/20 = 42
⇒ 3x/20 = 42
⇒ 3x = 840
⇒ x = 840/3
∴ x = 280

So, the number is 280

৯৬৯.

If the value of XYZ Company stock drops from Tk. 25 per share to Tk. 21 per share, what is the percent of the decrease?

ক
4%
খ
8%
গ
12%
ঘ
16%
ঙ
None of these

ব্যাখ্যা

Question: If the value of XYZ Company stock drops from Tk. 25 per share to Tk. 21 per share, what is the percent of the decrease?

Solution:
Decrease = 25 - 21 = 4

Percentage of decrease = (4/25) × 100% = 16%

৯৭০.

Zayed sold an article at 6% loss. Had he sold it for Tk. 32 more, he would have made a profit of 10%. Then the cost of the article is =?

ক
Tk. 380
খ
Tk. 220
গ
Tk. 400
ঘ
Tk. 200

ব্যাখ্যা

Question: Zayed sold an article at 6% loss. Had he sold it for Tk. 32 more, he would have made a profit of 10%. Then the cost of the article is =?

Solution:
Let, the cost of the article is x taka

Selling price = 0.94x

According to the question,
0.94x + 64 = 1.1x
⇒ 1.1x - 0.94x = 32
⇒ 0.16x = 32
⇒ x = 32/0.16
∴ x = 200 taka

৯৭১.

Tanvir purchased an item for Tk. 8200 and sold it at a gain of 25%. From that amount, he purchased another item and sold it at a loss of 20%. What is his overall gain or loss?

ক
ক) Loss of Tk. 120
খ
খ) Loss of Tk. 180
গ
গ) Gain of Tk. 80
ঘ
ঘ) Neither gain nor loss.

ব্যাখ্যা

Question: Tanvir purchased an item for Tk. 8200 and sold it at a gain of 25%. From that amount, he purchased another item and sold it at a loss of 20%. What is his overall gain or loss?

Solution:
Initial investment=Tk.8200

S.P.of 1st term=Tk. {(125/100) × 8200} = Tk. 10250

C.P. of 2nd term = Tk. 10250
loss = 20%

S.P.of 2nd term = Tk. {(80/100) × 10250}
=Tk. 8200

Since initial investment = final receipt,
so, there was neither gain nor loss.

৯৭২.

A student scores 55% marks in 8 papers of 100 marks each. He scores 15% of his total marks in English. How much does he score in English?

ক
ক) 44
খ
খ) 45
গ
গ) 66
ঘ
ঘ) 77

ব্যাখ্যা

Total marks obtained by the student = 55% of 800
= {(55/100) × 800}
= 440
∴ Marks scored in English
= 15% of 440
= {(15/100) × 440}
= 66

৯৭৩.

The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is -

ক
ক) Tk. 18
খ
খ) Tk. 16
গ
গ) Tk. 15
ঘ
ঘ) Tk. 14

ব্যাখ্যা

Question: The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is -

Solution:
Let,
Cost price of each article be Tk. 1
Cost price of x articles = Tk. x
Selling price of x articles = Tk. 20

∴ Profit = Tk. (20 - x)

ATQ,
(20 - x)/x = 25%
Or, 100(20 - x)/x = 25
Or, 2000 - 100x = 25x
Or, 125x = 2000
∴ x = 16

৯৭৪.

Of the students in a school, 20 percent are in the science club and 30 percent are in the band. If 25 percent of the students in the school are in the band but are not in the science club, what percent of the students who are in the science club are not in the band?

ক
ক) 5%
খ
খ) 20%
গ
গ) 75%
ঘ
ঘ) 60%

ব্যাখ্যা

প্রশ্ন : Of the students in a school, 20 percent are in the science club and 30 percent are in the band. If 25 percent of the students in the school are in the band but are not in the science club, what percent of the students who are in the science club are not in the band?

সমাধান :

ধরি, মোট ছাত্রসংখ্যা ১০০ জন

৩০ জন ছাত্র ব্যান্ড এর সদস্য, এর মধ্যে ২৫ জন ছাত্র বিজ্ঞানের নয়।

সুতরাং, বিজ্ঞান ও ব্যান্ড উভয়ের সদস্য = ৩০ - ২৫ = ৫ জন।

অপরদিকে, বিজ্ঞানের ছাত্র ২০ জন, এর মধ্যে ৫ জন উভয়ের মধ্যে অন্তর্ভুক্ত।

আমরা বলতে পারি, বিজ্ঞানে রয়েছে কিন্তু ব্যান্ড দলে নয় এরূপ ছাত্র সংখ্যা = ২০ - ৫ = ১৫ জন
বিজ্ঞানে রয়েছে কিন্তু ব্যান্ড দলে নয় এরূপ ছাত্রসংখ্যার হার = 15 / 20 = 75 / 100 = 75%

৯৭৫.

Anis, who owns (200/3)% of a factory, sells half of his share for Tk. 33,333. The value of the entire factory is-

ক
ক) Tk. 9,999
খ
খ) Tk. 66,666
গ
গ) Tk. 99,999
ঘ
ঘ) Tk. 133,332

ব্যাখ্যা

Question: Anis, who owns (200/3)% of a factory, sells half of his share for Tk. 33,333. The value of the entire factory is-

Solution:
(200/3)% = 200/(3 × 100)
= 2/3 of factory

1/2 of 2/3 or 1/3 of factory = 33,333 tk
∴ value of entire factory = 33,333 × 3 tk
= 99,999 tk.

৯৭৬.

A fruit seller buys lemons at a rate of 2 lemons for a Taka and sells them at a rate of 5 lemons for 3 Taka. What is her profit margin (based on cost price)?

ক
10%
খ
15%
গ
20%
ঘ
30%

ব্যাখ্যা

Question: A fruit seller buys lemons at a rate of 2 lemons for a Taka and sells them at a rate of 5 lemons for 3 Taka. What is her profit margin (based on cost price)?

Solution:
The cost price of 2 lemons = 1 Tk
The cost price of 1 lemon = 1/2 Tk

Then,
The selling price of 5 lemons = 3 Tk
The selling price of 1 lemon = 3/5 Tk

So, profit = 3/5 - 1/2 = 1/10 Tk

Hence, profit percentage = {(1/10)/(1/2)} × 100 = 20%

৯৭৭.

Shihab sells his goods 25% cheaper than Fahim and 25% dearer than Aftab. How much of the goods of Aftab are cheaper than Fahim's?

ক
33.33%
খ
66.66%
গ
40%
ঘ
50%

ব্যাখ্যা

Question: Shihab sells his goods 25% cheaper than Fahim and 25% dearer than Aftab. How much of the goods of Aftab are cheaper than Fahim's?

Solution:
Let, Fahim sells at 100 taka
Shihab sells at 75 taka

Aftab sells at 75/1.25
= 60 tka

the goods of Aftab are cheaper than Fahim's = (100 - 60)
= 40%

৯৭৮.

The selling price of 40 apples is equal to cost price of 35 apples. Find the profit or loss obtained.

ক
ক) Gain of 5.5%
খ
খ) Gain of 12.5%
গ
গ) Loss of 5.5%
ঘ
ঘ) Loss of 12.5%

ব্যাখ্যা

Question: The selling price of 40 apples is equal to cost price of 35 apples. Find the profit or loss obtained.

Solution:
Let,
C.P. of each apple be Tk. 1

Therefore,
C.P. of 40 apples = Tk. 40
S.P. of 40 apples = Tk. 35

C.P. of 40 apples > S.P. of 40 apples

∴ Loss = 40 - 35 = 5 Taka

Loss % = {(5 × 100)/40}% = 12.5%

৯৭৯.

After getting two successive discount, a shirt with a list price of Tk.150 is available at Tk.105. If the second discount is 12.5%, find the first discount.

ক
ক) 15%
খ
খ) 20%
গ
গ) 22%
ঘ
ঘ) 25%

ব্যাখ্যা

Let the first discount be x%.
Now
87.5% of (100 - x)% of 150 = 105
(87.5/100) × {(100 - x)/100} × 150 = 105
100 - x = (105 × 100 × 100)/(150 × 87.5)
100 - x = 80
100 - 80 = x
x = 20

The first discount be 20%

৯৮০.

In an examination, 36% are pass marks. If an examine gets 17 marks and fails by 10 marks, what are the maximum marks?

ক
45
খ
50
গ
60
ঘ
75

ব্যাখ্যা

• Question: In an examination, 36% are pass marks. If an examine gets 17 marks and fails by 10 marks, what is the maximum mark?

Solution:
Pass mark = (17 + 10) = 27

Let maximum marks be x

Then 36% of x = 27
Or, 36x/100 = 27
Or, 36x = 2700

Hence, x = 75

∴ The maximum mark is 75

৯৮১.

Moni and Mimi are partners in a business. Moni invests 36000 for 8 months and Mimi invests Tk 48000 for 10 months. Out of a profit of 7200, Moni's share is -

ক
Tk. 4500
খ
Tk. 2500
গ
Tk. 2700
ঘ
Tk. 3000

ব্যাখ্যা

Question: Moni and Mimi are partners in a business. Moni invests 36000 for 8 months and Mimi invests Tk 48000 for 10 months. Out of a profit of 7200, Moni's share is -

Solution:
Ratio of their shares = (36000 × 8) : (48000 × 10)
= 288 : 480
= 3 : 5

Moni's share = 7200 × (3/8) = Tk. 2700

৯৮২.

In company there are 75% skilled workers and reaming are unskilled. 80% of skilled workers and 20% of unskilled workers are permanent. If number of temporary workers is 126, then what is the number of total workers?

ক
446
খ
420
গ
396
ঘ
360

ব্যাখ্যা

Question: In company there are 75% skilled workers and reaming are unskilled. 80% of skilled workers and 20% of unskilled workers are permanent. If number of temporary workers is 126, then what is the number of total workers?

Solution:
Let, the number of total workers = x
Number of skilled worker = 75% of x = 75x/100 = 3x/4
No. of unskilled workers = 25% of x = 25x/100 = x/4

∴ No. of permanent workers = {(80/100) × (3x/4) + (20/100) × (x/4)}
= (3x/5) + (x/20)
= 13x/20

∴ No .of temporary workers = {x - (13x/20)}
= 7x/20

ATQ,
7x/20 = 126
⇒ 7x = 2520
∴ x = 360

৯৮৩.

One-fifth of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and 1/20 of the non defective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?

ক
4%
খ
5%
গ
6.25%
ঘ
11%
ঙ
16%

ব্যাখ্যা

Question: One-fifth of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and 1/20 of the non defective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?

Solution:
Assume x as the number of switches and that x =100
Defective Switches = (1/5) × 100 = 20
Defective Switches that are rejected = (4/5) × 20 = 16
Defective Switches that are sold = 20 - 16 = 4

Non-defective Switches = 100 - 20 = 80
Non-defective Switches mistakenly rejected = 80 × (1/20) = 4
Non-defective Switches that are sold = 80 - 4 = 76

Total sold in the market = 76 + 4 = 80
% of defective = (4/80) × 100 = 5%

৯৮৪.

Income of A is 25% less than B. How much percent of B's income would be more than that of A?

ক
23.5%
খ
33.3%
গ
32.5%
ঘ
25%
ঙ
29%

ব্যাখ্যা

Let's say that B makes $100.
Then A makes $75. So,
Question then becomes 100 is what percent of 75
This can be solved by setting up the proportion
100 / 75 = x / 100
75x = 10000
x = 133.3
So, B's income is 33.3% more than A's income.

৯৮৫.

Mr. Ali is a trader. He mixes 26 kg of rice at Tk. 20 per kg with 30 kg of rice of other variety at Tk. 36 per kg and sells the mixture at Tk. 32 per kg. His profit percent is-

ক
12%
খ
7%
গ
9%
ঘ
6%

ব্যাখ্যা

Question: Mr. Ali is a trader. He mixes 26 kg of rice at Tk. 20 per kg with 30 kg of rice of other variety at Tk. 36 per kg and sells the mixture at Tk. 32 per kg. His profit percent is-

Solution:
Cost Price of 56 kg rice = {(26 × 20) + (30 × 36)}
= (520 + 1080)
= 1600 taka

Selling Price of 56 kg rice = (56 × 32)
= 1792 taka

∴ Profit = 1792 - 1600
= 192 taka

∴ Profit percentage = (192/1600) × 100%
= 12%

৯৮৬.

A batsman scored 86 runs which included 8 boundaries and 3 sixes. What percent of his total score did he make by running between the wickets?

ক
38.86%
খ
54.86%
গ
34.86%
ঘ
41.86%

ব্যাখ্যা

Question: A batsman scored 86 runs which included 8 boundaries and 3 sixes. What percent of his total score did he make by running between the wickets?

Solution:
Total score of batsman = 86 runs
runs from boundaries = 4 × 8 = 32
runs from sixes = 6 × 3 = 18
∴ Total runs from boundaries and sixes = 32 + 18 = 50 runs
Scores by running between the wickets = 86 - 50 = 36 runs

percentage of his score made by running between wickets = (36/86) × 100% = 41.86%

৯৮৭.

After receiving a 25% discount, Sue paid $180 for a lawnmower. What is the original price of the lawnmower before the discount?

ক
ক) 215
খ
খ) 220
গ
গ) 225
ঘ
ঘ) 240

ব্যাখ্যা

At 25% discount, 75% = 180
So, 100% = (180×100)/75 = 240

৯৮৮.

Kiran purchased a scooter for Tk. 52000. He sold it at loss of 10%. With that money be purchased another scooter and sold it at profit of 20%. What is his overall loss/profit?

ক
ক) Tk. 2060 profit
খ
খ) Tk. 2560 loss
গ
গ) Tk. 1340 loss
ঘ
ঘ) Tk. 4160 profit

ব্যাখ্যা

At 10% loss, He got = (52000×90) / 100 = 46800 tk
His loss is = 52000 - 46800 = 5200

At 20% profit, He receives = (46800×120)/100 = 56160
Profit, 56160 - 46800 = 9360

∴ His net profit = 9360 - 5200 = 4160

৯৮৯.

What is the original price of a t - shirt, if the sale price after 15% discount is 272?

ক
ক) 300
খ
খ) 280
গ
গ) 320
ঘ
ঘ) 314

ব্যাখ্যা

15% discount - এ T - shirt টির বিক্রয়মূল্য 85 টাকা হলে প্রকৃত মূল্য 100 টাকা
∴ বিক্রয়মূল্য 272 টাকা হলে প্রকৃত মূল্য = (100 × 272) / 85 = 320 টাকা

৯৯০.

The cost of an article was 75 taka. The cost was first increased by 20% and later on it was reduced by 20%. The present cost of the article is:

ক
52
খ
64
গ
72
ঘ
84
ঙ
96

ব্যাখ্যা

Initial Cost = 75 taka
After 20% increase in the cost, it becomes (75 + 20% of 75) or 90 taka
Now, Cost is decreased by 20%, So cost will become (90 - 20% of 90) or 72 taka
So, present cost is 72 taka

৯৯১.

A worker union contract specifies a 6% salary increase plus a Tk. 450 bonus for each worker. For a worker, this is equivalent to an 8% salary increase. What was this worker's salary before the new contract?

ক
Tk. 22,000
খ
Tk. 22500
গ
Tk. 24000
ঘ
Tk. 25400

ব্যাখ্যা

Question: A worker union contract specifies a 6% salary increase plus a Tk. 450 bonus for each worker. For a worker, this is equivalent to an 8% salary increase. What was this worker's salary before the new contract?

Solution:
ধরি, কর্মীর পূর্বের বেতন = x টাকা।

6% বৃদ্ধিতে বেতন = x + x এর 6%
= x + (6x/100) = 106x/100

বোনাস হিসেবে 450 টাকা যোগ করলে মোট বেতন = (106x/100) + 450

8% বৃদ্ধিতে বেতন = x + x এর 8%
= x + (8x/100) = (108x/100)

প্রশ্নমতে,
(106x/100) + 450 = (108x/100)
⇒ 450 = (108x/100) - (106x/100)
⇒ 450 = (2x/100)
⇒ x = (450 × 100)/2
∴ x = 22500

অর্থাৎ, কর্মীর পূর্ববর্তী বেতন ছিল 22500 টাকা।

৯৯২.

A boy bought a camel and carriage for Tk 5000. He sells the camel at a gain of 20% and the carriage at a loss of 10%. If he gains 3% on the whole, then find the cost of the camel.

ক
ক) Tk. 2166.67
খ
খ) Tk. 2400.38
গ
গ) Tk. 2315.25
ঘ
ঘ) Tk. 2600.45

ব্যাখ্যা

Now, in this numerical, there is no common loss and gain %.
Hence, solve it by making equations.

Let the cost price of the camel be x.
As the cost of camel and carriage = Tk 5000
Cost of carriage = Tk (5000 – x)
After selling the camel he gains 20% and on carriage a loss of 10%. But on the whole, he gains 3%.

Therefore,
20% of x – 10% of (5000 – x) = 3% of 5000
⇒ (20/100) × x - (10/100) × (5000 – x) = (3/100) × 5000
⇒ x/5 - (5000 – x)/10 = 150
⇒ 10x/5 - {(5000 – x) × 10}/10 = 150 × 10
⇒ 10x/5 - (5000 – x) = 1500
⇒ 2x - 5000 + x = 1500
⇒ 3x=1500 + 5000
⇒ x = 2166.67.
The cost of camel = Tk. 2166.67

৯৯৩.

A stock increases in value by 25%. By what percent must the stock decrease to reach back to its former value?

ক
30%
খ
25%
গ
22%
ঘ
20%
ঙ
None

ব্যাখ্যা

Question: A stock increases in value by 25%. By what percent must the stock decrease to reach back to its former value?

Solution:
এখানে,
২৫% বৃদ্ধিতে মূল্য = (১০০ + ২৫) টাকা
= ১২৫ টাকা

১২৫ টাকায় মূল্য কমাতে হবে ২৫ টাকা
∴ ১ টাকায় মূল্য কমাতে হবে ২৫/১২৫ টাকা
∴ ১০০ টাকায় মূল্য কমাতে হবে (২৫ × ১০০)/১২৫ টাকা
= ২০ টাকা

৯৯৪.

The selling price of 15 items equals the cost of 20 items. What is the percentage of profit earned by the seller?

ক
23.54%
খ
30.87%
গ
23.33%
ঘ
33.3%
ঙ
56.4%

ব্যাখ্যা

Let cost price per item be 1.
cp of 15 items = 15
sp of 15 items = cost price of 20 items= 20

So, profit = 20 - 15 = 5.
∴ required profit % = (5/15) × 100 = 33.3%

৯৯৫.

Selling 12 pen at a price of Tk. 10 yields a loss a%. Selling 12 pen at a price of Tk. 12 yields a profit of a %, what is the value of a?

ক
ক) 10
খ
খ) 11
গ
গ) 100/11
ঘ
ঘ) 11/100

ব্যাখ্যা

a% ক্ষতিতে,
ক্রয়মূল্য 100 টাকা হলে বিক্রয়মূল্য =(100 - a) টাকা

a% লাভে
ক্রয়মূল্য 100 টাকা হলে বিক্রয়মূল্য =(100 + a) টাকা

এখন
10 × 100/(100 - a) = 12 × 100/(100 + a)
10/(100 - a) =12/(100 + a)
1000 + 10a = 1200 - 12a
10a + 12a = 1200 - 1000
22a = 200
a = 200/22
a = 100/11

৯৯৬.

If b is equal to 20% of a, then what is b% of 20 equal to?

ক
4% of a
খ
5% of a
গ
20% of a
ঘ
10% of a

ব্যাখ্যা

Question: If b is equal to 20% of a, then what is b% of 20 equal to?

Solution:
20% of a = b
⇒ 20a/100 = b

∴ b% of 20
= (b/100) × 20
= (20a/100) × (1/100) × 20
= 4a × (1/100)
= 4% of a

৯৯৭.

Population of a town increase 2.5% annually but is decreased by 0.5% every year due to migration. What will be the percentage increase in 2 years?

ক
6%
খ
5.2%
গ
4.04%
ঘ
3.5%

ব্যাখ্যা

Question: Population of a town increase 2.5% annually but is decreased by 0.5% every year due to migration. What will be the percentage increase in 2 years?

Solution:
Net percentage increase in Population = (2.5 - 0.5) = 2% each year.
Assuming initial population = 100

Population of Town after 1st year = (100 + 2% of 100)
= 100 + 2 = 102

Population of Town after 2nd year = (102 + 2% of 102)
= 102 + 2.04 = 104.04

Increase = 104.04 - 100 = 4.04
∴ Percentage increase = (4.04/100) × 100% = 4.04%

৯৯৮.

A product is sold for Tk. 3600 with a 25% profit margin. How much profit or loss would there be if it was sold for Tk. 2700 instead?

ক
profit 7.75%
খ
loss 5.25%
গ
loss 6.25%
ঘ
None of the above

ব্যাখ্যা

Question: A product is sold for Tk. 3600 with a 25% profit margin. How much profit or loss would there be if it was sold for Tk. 2700 instead?

Solution:
The cost price = (3600 × 100)/125 = 2880
New selling price = Tk. 2700

∴ Loss = 2880 - 2700 = 180

∴ Loss percentage = (100 × 180)/2880 = 6.25%.

৯৯৯.

A trader buys egg for TK. M dozen and sells them for Tk M/6 per piece. What is his profit?

ক
20%
খ
50%
গ
60%
ঘ
100%
ঙ
None of these

ব্যাখ্যা

Selling price of egg Tk (M/6) × 12 per dozen
= 2M
profit = 2M - M = M
profit percentage = (M/M) × 100
= 100%.

১,০০০.

Fresh fruit contains 68% water and dry fruit contains 20% water. How much dry fruit can be obtained from 100kg of fresh fruits?

ক
ক) 20 kg
খ
খ) 30 kg
গ
গ) 35 kg
ঘ
ঘ) 40 kg

ব্যাখ্যা

100kg of fresh fruit is 68kg of water and 32kg of non water.
If you dry it you still have 32kg of non water but now it's 80% non water and 20% water.

80% of dry food = 32
100% of dry food = 32 × 100/80 = 40 kg