Percentage and Profit & Loss

PrepBank · পাতা ৩ / ১৭ · ২০১–৩০০ / ১,৬৯৬

২০১.

In a class of 120 students, 70 percent can speak only Bengali and the rest can speak English. If 25 percent of those in the class who can speak English can also speak Bengali, how many of the students in the class can speak Bengali?

ক
ক) 39
খ
খ) 48
গ
গ) 84
ঘ
ঘ) 93

ব্যাখ্যা

Question: In a class of 120 students, 70 percent can speak only Bengali and the rest can speak English. If 25 percent of those in the class who can speak English can also speak Bengali, how many of the students in the class can speak Bengali?

Solution:
শুধু বাংলায় কথা বলতে পারে ১২০ জনের ৭০%
= ১২০ × ৭০/১০০
= ৮৪ জন

ইংরেজিতে কথা বলতে পারে = (১২০ - ৮৪) = ৩৬ জন
৩৬ জনের মধ্যে বাংলায় ও কথা বলতে পারে = ৩৬ এর ২৫% = ৯ জন।

∴ বাংলায় মোত কথা বলতে পারে = ৮৪ + ৯ = ৯৩ জন

২০২.

A cloth merchant on selling 33 meters of cloth obtains a profit equal to the selling price of 11 meters of cloth the profit is = ?

ক
11%
খ
40%
গ
50%
ঘ
None of these

ব্যাখ্যা

Question: A cloth merchant on selling 33 meters of cloth obtains a profit equal to the selling price of 11 meters of cloth the profit is = ?

Solution:
Profit = selling price of 11 m of cloth = 1/3 selling price of 33 m of cloth

Let the selling price of 33 meters of cloth = 3x
∴ profit = 1/3 (3x) = x

So, cost price = selling price - profit = 3x - x = 2x

% Profit = (x/2x) × 100% = 50%

২০৩.

25 percent of 30 is 75 percent of what number?

ক
8
খ
10
গ
12
ঘ
16

ব্যাখ্যা

Question: 25 percent of 30 is 75 percent of what number?

Solution:
let, 25 percent of 30 is 75 percent of x

25% of 30 = 75% of x
⇒ (25/100) × 30 = (75/100) × x
⇒ 15/2 = 3x/4
⇒ 6x = 60
∴ x = 10

২০৪.

In order to obtain an income of Tk. 800 from 12% stock at Tk. 96, one must make an investment of-

ক
Tk. 5400
খ
Tk. 6500
গ
Tk. 7200
ঘ
Tk. 6400
ঙ
Tk. 6800

ব্যাখ্যা

Question: In order to obtain an income of Tk. 800 from 12% stock at Tk. 96, one must make an investment of-

Solution:
To obtain Tk. 12, investment = Tk. 96
To obtain Tk. 800, investment = Tk. (96/12) × 800
= Tk. 6400

২০৫.

After decreasing 24% in the price of an article costs Tk.912. Find the actual cost of an article?

ক
ক) 1400
খ
খ) 1300
গ
গ) 1200
ঘ
ঘ) 1100

ব্যাখ্যা

CP× (76/100) = 912
CP = 12 × 100
=> CP = 1200

২০৬.

By what percentage above the cost price, a fan should be sold if a shopkeeper wants to make a profit of Tk. 500 and the marked price of the article is Tk 6000 which is 50% above the cost price?

ক
ক) 25.0%
খ
খ) 15.5%
গ
গ) 20.0%
ঘ
ঘ) None of these

ব্যাখ্যা

ATQ,
Cost price = 100/150 × 6000 = 4000
Selling price = 4000+ 500 = 4500
So, Percentage needed to be above the cost price by = 500/4000 × 100 = 12.5%

২০৭.

The MRP of a Jacket is given as Tk. 2000 and the merchant decides to provide successive discounts of 30% and 20% on the product. Find the selling price.

ক
Tk. 1050
খ
Tk. 1100
গ
Tk. 1120
ঘ
Tk. 1200

ব্যাখ্যা

Question: The MRP of a Jacket is given as Tk. 2000 and the merchant decides to provide successive discounts of 30% and 20% on the product. Find the selling price.

Solution:
After 30% discount, = 2000 - 2000 × 30/100
= 2000 - 600
= 1400

After 20% discount, = 1400 - 1400 × 20/100
= 1400 - 280
= 1120 taka

২০৮.

(X% of Y) + (Y% of X) is equal to:

ক
ক) X% of Y
খ
খ) 20% of XY
গ
গ) 2% of XY
ঘ
ঘ) 2% of 100 XY

ব্যাখ্যা

According to question,
XY/100 + YX/100
= 2XY/100
= 2% o fXY

২০৯.

In a college election between two candidates, one candidate got 55% of the total valid votes. 15% of the votes were invalid. If the total votes were 15200, what is the number of valid votes the other candidate got?

ক
5814
খ
6022
গ
7282
ঘ
7778
ঙ
None

ব্যাখ্যা

Question: In a college election between two candidates, one candidate got 55% of the total valid votes. 15% of the votes were invalid. If the total votes were 15200, what is the number of valid votes the other candidate got?

Solution:

Number of valid votes

= (100 - 15)% of 15200

= 85% of 15200

= (85/100) × 15200

= 12920

Valid votes polled by other candidates

= (100 - 55)% of 12920

= 45% of 12920

= (45/100) × 12920

= 5814

∴ The number of valid votes the other candidate got was 5814

২১০.

When 15% is lost in grinding wheat, a country can export 30 lakh tons of wheat. On the other hand, if 10% is lost in grinding, it can export 40 lakh tons of wheat. The production of wheat in the country is:

ক
120
খ
150
গ
200
ঘ
220

ব্যাখ্যা

Question: When 15% is lost in grinding wheat, a country can export 30 lakh tons of wheat. On the other hand, if 10% is lost in grinding, it can export 40 lakh tons of wheat. The production of wheat in the country is:

Solution:
Let, The production of wheat in the country is x lakh tons.

(0.9 - 0.85)x = 40 - 30
⇒ 0.05x = 10
⇒ x = 10/0.05
= 200

২১১.

If two values are 20% and 60% of a third value, what percentage is the first value of the second value?

ক
22.2%
খ
31.1%
গ
27.7%
ঘ
33.3%

ব্যাখ্যা

Question: If two values are 20% and 60% of a third value, what percentage is the first value of the second value?

Solution:
Let
The third value x
∴ First value (20x)/100 = x/5
∴ Second value (60x)/100 = 3x/5

Now,
(First Value/Second value) × 100
= (x/5) × (5/3x) × 100
= 33.33%

২১২.

If 45% of (A - B) is equal to 3/10 of (A + B), then what percent of A is B?

ক
20%
খ
5%
গ
25%
ঘ
30%

ব্যাখ্যা

Question: If 45% of (A - B) is equal to 3/10 of (A + B), then what percent of A is B?

Solution:
Given that,
45% of (A - B) = (3/10) of (A + B)
⇒ (45/100) of (A - B) = (3/10) of (A + B)
⇒ (9/20) of (A - B) = (3/10) of (A + B)
⇒ (9/2) of (A - B) = 3 of (A + B)
⇒ 9(A - B) = 6(A + B)
⇒ 9A - 9B = 6A + 6B
⇒ 3A = 15B
⇒ B/A = 3/15 = 1/5
⇒ B = (1/5) × A
∴ B = (1/5) × 100% of A = 20% of A

So B is 20% of A

২১৩.

If the average, of a given number, 50% of that number and 25% of the same number is 350, then the number is-

ক
ক) 560
খ
খ) 480
গ
গ) 600
ঘ
ঘ) 660

ব্যাখ্যা

Question: If the average, of a given number, 50% of that number and 25% of the same number is 350, then the number is-

Solution:
Let the number be x
According to the question,
⇒ (x + 50% of x + 25% of x)/3 = 350
⇒ (x + x/2 + x/4)/3 = 350
⇒ 7x/12 = 350
⇒ x = (350 × 12)/7
⇒ x = 600

∴ The number is 600

২১৪.

What will be the difference between simple and compound interest at 10% on a sum of Tk. 1000 after 4 years?

ক
ক) Tk. 64
খ
খ) Tk. 74
গ
গ) Tk. 78
ঘ
ঘ) Tk. 81

ব্যাখ্যা

Simple interest = (10 × 4 × 1000)/100 = Tk. 400
Compound amount, c = p(1 + r)ⁿ
= 1000{1 + (10/100)}⁴
= 1000(11/10)⁴
= 1464.10

∴ Compound interest
= 1464.10 - 1000
= 464.10

∴ Difference between Simple and Compound interest = 464.10 - 400 = Tk. 64.10 ≈ Tk. 64
------------------------------------------------------------------
10% সুদে, 1,000 টাকার 4 বছরের সুদ = (10 × 4 × 1000)/100
= 400 টাকা।
আমরা জানি,
চক্রবৃদ্ধি মুনাফায় সবৃদ্ধিমূল, c = p(1 + r)ⁿ
= 1000{1 + (10/100)}⁴
= 1000(11/10)⁴
= 1464.10 টাকা

∴ চক্রবৃদ্ধি মুনাফা
= 1464.10 - 1000
= 464.10 টাকা

∴ সরল এবং চক্রবৃদ্ধি মুনাফার মধ্যে পার্থক্য = 464.10 - 400 = 64.10 টাকা

২১৫.

Solution X contains 40% salt and 60% water by weights. Solution Y contains 25% salt and 75 % water. If a mixture of X and Y contains 30% salt, What percent of the weight of this mixture is solution X ?

ক
ক) 10%
খ
খ) 33.3%
গ
গ) 40%
ঘ
ঘ) 42.5%

ব্যাখ্যা

প্রশ্ন: Solution X contains 40% salt and 60% water by weights. Solution Y contains 25% salt and 75 % water. If a mixture of X and Y contains 30% salt, What percent of the weight of this mixture is solution X ?

সমাধান:
X দ্রবণে লবণ আছে = 40%
Y দ্রবণে লবণে আছে = 25%

মিশ্রণে লবণ আছে = 30%

এখন
x এর 40% + y এর 25% = (x + y) এর 30%
40x/100 + 25y/100 = 30(x + y)/100
40x + 25y = 30(x + y)
40x + 25y = 30x + 30y
40x - 30x = 30y - 25y
10x = 5y
x/y = 5/10
x : y = 1 : 2

x এর পরিমাণ = (1/3) × 100%
= 33.33%

২১৬.

In an election between two candidates, winner got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 80,000, the number of valid votes that the loser candidate got, was-

ক
28,800
খ
29,700
গ
30,500
ঘ
30,900

ব্যাখ্যা

Question: In an election between two candidates, winner got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 80,000, the number of valid votes that the loser candidate got, was-

Solution:
Given,
20% of the votes were invalid
∴ the valid votes = (100 - 20) = 80%

∴ Number of valid votes = (80% of 80,000)
= (80/100 of 80,000)
= 64,000

∴ Winner candidates got = (55% of 64,000)
= (55/100 of 64,000)
= 35,200

So, the loser got = (64,000 - 35,200)
= 28,800

২১৭.

A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had how many apples?

ক
ক) 500
খ
খ) 700
গ
গ) 600
ঘ
ঘ) 650

ব্যাখ্যা

প্রশ্ন: A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had how many apples?

সমাধান:
বাকি রইল ৬০%

৬০টি বাকি আছে ১০০টি থেকে
∴৪২০টি বাকি আছে (১০০ × ৪২০)/৬০টি থেকে
= ৭০০টি

২১৮.

75% of 0.08 = ?

ক
ক) 0.04
খ
খ) 0.50
গ
গ) 0.06
ঘ
ঘ) 0.006
ঙ
ঙ) 6.0

ব্যাখ্যা

Question: 75% of 0.08 = ?

Solution:
75% of 0.08 = (75/100) × 0.08
= 0.06

২১৯.

In school, three rows are formed of the students. First row has 50% more students than the second row and the third row has 50% less students than the second row. If the total number of students in all the rows is 900, then find the number of students in the third row.

ক
100
খ
150
গ
300
ঘ
450

ব্যাখ্যা

Question: In school, three rows are formed of the students. First row has 50% more students than the second row and the third row has 50% less students than the second row. If the total number of students in all the rows is 900, then find the number of students in the third row.

Solution:
Let the number of students in the second row is 100.
Then number of students in first row is 150 and number of students in third row is 50.
Total students = 150 + 100 + 50 = 300
Given = 900
Then 900/300 = 3
Third row has 50 × 3 =150 students.

২২০.

There were 800 students in a school in 2025. In 2026, 10% of the male students left the school, while the number of female students increased by 40%. If the total number of students remained unchanged, how many female students were there in the school in 2025?

ক
160
খ
180
গ
200
ঘ
240
ঙ
224

ব্যাখ্যা

Question: There were 800 students in a school in 2025. In 2026, 10% of the male students left the school, while the number of female students increased by 40%. If the total number of students remained unchanged, how many female students were there in the school in 2025?

Solution:
ধরি, 2025 সালে ছাত্রীর সংখ্যা ছিল x জন।
এবং ছাত্রের সংখ্যা ছিল (800 - x) জন।

প্রশ্ন অনুযায়ী, 2026 সালে ছাত্রীর সংখ্যা 40% বৃদ্ধি পায় এবং ছাত্রের সংখ্যা 10% হ্রাস পায়, কিন্তু মোট ছাত্র-ছাত্রীর সংখ্যা 800-ই থাকে।
অর্থাৎ, ছাত্রীর বৃদ্ধির পরিমাণ = ছাত্রের হ্রাসের পরিমাণ।

প্রশ্নমতে,
x এর 40% = (800 - x) এর 10%
⇒ 40x/100 = 10(800 - x)/100
⇒ 40x = 8000 - 10x
⇒ 40x + 10x = 8000
⇒ 50x = 8000
⇒ x = 8000/50
⇒ x = 160

∴ 2025 সালে স্কুলে ছাত্রীর সংখ্যা ছিল 160 জন।

২২১.

A school has only 3 classes having 20, 30 and 50 students respectively. The percentages of students passed are 30%, 50% and 60% respectively. Find the percentage of passed students of the entire school.

ক
ক) 40%
খ
খ) 51%
গ
গ) 60%
ঘ
ঘ) None

ব্যাখ্যা

Question: A school has only 3 classes having 20, 30 and 50 students respectively. The percentages of students passed are 30%, 50% and 60% respectively. Find the percentage of passed students of the entire school.

Solution:

পাশ করা ছাত্রের সংখ্যা = 20 × 30% + 30 × 50% + 50 × 60% = 6 + 15 + 30 = 51
সুতরাং, পাশ করা ছাত্রের সংখ্যার হার = 51/100 × 100 = 51%

২২২.

Bus fares were recently increased from Taka 1.70 to Taka 2.00. What was the approximate percentage of increase?

ক
18%
খ
15%
গ
0.15%
ঘ
0.18%

ব্যাখ্যা

Question: Bus fares were recently increased from Taka 1.70 to Taka 2.00. What was the approximate percentage of increase?

Solution:
বাস ভাড়া বাড়ে = (2.00 - 1.70) টাকা
= 0.30 টাকা

বাস ভাড়া শতকরা বাড়ে = (0.30/1.70) × 100%
= 17.647 %
≈ 18%

২২৩.

In a certain population group, 57% of the people have characteristics X and 63% have characteristics Y. If every person in the group has at lest one of the of the two characteristics, then what percent of the people have both X and Y?

ক
ক) 20%
খ
খ) 18%
গ
গ) 12%
ঘ
ঘ) 6%

ব্যাখ্যা

প্রশ্ন : In a certain population group, 57% of the people have characteristics, X and 63% have characteristics Y. If every person in the group has at lest one of the of the two characteristics, then what percent of the people have both X and Y?

সমাধান:

N (X) = 57%

N (Y)= 63%

N (X ∪ Y) = 100%

অতএব,

N (X ∪ Y) = N (X) + N (Y) - N (X ∩ Y)

বা, N (X ∩ Y) = N (X) + N (Y) - N (X ∪ Y)

= 57% + 63% - 100%

= 120% - 100%

= 20%

২২৪.

In country A, the first 1,000 dollar of any inheritance are untaxed. After the first 1,000 dollar, inheritances are taxed at a rate of 65%. How large must an inheritance be, to the nearest dollar, in order to amount to 2,500 dollar after the inheritance tax?

ক
ক) 7,143
খ
খ) 5,286
গ
গ) 4,475
ঘ
ঘ) 3,475

ব্যাখ্যা

প্রথম 1000 ডলার এর জন্য ট্যাক্স দিতে হয় না।
বাকি টাকা = (2500 - 1000) = 1500 টাকা

এখানে, (100 - 65)% = 35%

প্রশ্নমতে, 35% = 1500
∴ 1% = 1500/35
∴ 100% = 1500×100/35
= 4285.71 ≅ 4286

∴ নির্ণেয় টাকার পরিমাণ = (4286 +1000) = 5286 টাকা

২২৫.

A machine is sold at a profit of 10%. Had it been sold for Tk. 40 less, there would have been a loss of 10%. What was the cost price?

ক
Tk. 250
খ
Tk. 200
গ
Tk. 175
ঘ
Tk. 225

ব্যাখ্যা

Question: A machine is sold at a profit of 10%. Had it been sold for Tk. 40 less, there would have been a loss of 10%. What was the cost price?

Solution:
Let, the cost price of the machine is x taka

Selling price = 1.1x taka

ATQ,
1.1x - 40 = 0.9x
⇒ 1.1x - 0.9x = 40
⇒ 0.2x = 40
⇒ x = 40/.2
= Tk. 200

২২৬.

A bag costs 20% more than a purse. A wallet costs 30% less than the bag. If the price of the purse is 200 Tk, then by what percentage is the wallet cheaper than the purse?

ক
12%
খ
20%
গ
16%
ঘ
21.5%

ব্যাখ্যা

Question: A bag costs 20% more than a purse. A wallet costs 30% less than the bag. If the price of the purse is 200 Tk, then by what percentage is the wallet cheaper than the purse?

Solution:
Given,
the price of the purse = 200 tk

∴ Price of the bag = 200 + (200 × 20%)
= 240 tk

Price of the wallet = 240 − (240 × 30%)
= 240 − 72
= 168 Tk

Difference is = (200 - 168) = 32 tk

∴ Percentage = (32 × 100)/200 = 16%

২২৭.

A man sells two chairs at Tk. 120 each and by doing so he gains 25% on one chair and loses 25% on the other. His loss on the whole in Tk. is = ?

ক
ক) Tk. 16
খ
খ) Tk. 20
গ
গ) Tk. 18
ঘ
ঘ) Tk. 22

ব্যাখ্যা

Question: A man sells two chairs at Tk. 120 each and by doing so he gains 25% on one chair and loses 25% on the other. His loss on the whole in Tk. is = ?

Solution:
Cost price of first chair = (100/125) × 120
= Tk. 96

Cost price of second chair = (100/75) × 120
= Tk. 160

∴ Loss = (160 + 96) - 240
= 256 - 240
= Tk. 16

২২৮.

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. 24700
খ
Tk. 18500
গ
Tk. 30000
ঘ
Tk. 22500

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।

২২৯.

A reduction of 15% in the price of apples would enable a purchaser to get 2 kg more apples for Tk.240. The new price (per kg) of apple

ক
Tk.12
খ
Tk.15
গ
Tk.18
ঘ
Tk. 20

ব্যাখ্যা

Question: A reduction of 15% in the price of apples would enable a purchaser to get 2 kg more apples for Tk.240. The new price (per kg) of apples is-

Solution:
Let, the original rate = x per kg
New rate = 85% of x = 85x/100
= 17x/20
Original quantity for Tk. 240 = 240/x

∴ New quantity = 240 × (20/17x)
= 4800/17x

ATQ,
(4800/17x) - (240/x) = 2
⇒ (4800 - 4080)/17x = 2
⇒ (720/17x) = 2
⇒ x = 720/(2 × 17)

∴ Original rate per kg = Tk. 720/34
So, Reduced rate = Tk. 17x/20
= Tk. (17/20) × (720/34)
= Tk.18

২৩০.

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

ক
Tk. 32
খ
Tk. 16
গ
Tk. 64
ঘ
Tk. 36

ব্যাখ্যা

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

Solution:
Let,
The cost price of each article be Tk. 1
The cost price of 'p' articles = Tk. p
The selling price of 'p' articles = Tk. 40

∴ Profit = Tk. (40 - p)

According to the question,
(40 - p)/p = 25%
Or, 100(40 - p)/p = 25
Or, 4000 - 100p = 25p
Or, 125p = 4000
∴ p = 32

২৩১.

When a discount of 20% is given on a sweater, the profit is 28%. If the discount is 14%, then the profit is

ক
41.2%
খ
34.8%
গ
37.6%
ঘ
43.4%

ব্যাখ্যা

Question: When a discount of 20% is given on a sweater, the profit is 28%. If the discount is 14%, then the profit is

Solution:
Let the C.P. of sweater be Tk. 100 and its marked price be Tk. x.
ATQ,
x × (80/100) = 128
⇒ 4x/5 = 128
⇒ x = 128 Tk

When discount = 14%, then
S.P. of sweater = 160 × (100 - 14)%
= (160 × 86)/100
= 137.6 Tk

∵ C.P. = Rs. 100; Profit % = 37.6%

২৩২.

Vendor sells apples at a certain price in order to make a profit of 30%. If he charges Tk. 1.5 higher per apple he would get a profit of 60%. Find the original price at which he sold an apple?

ক
ক) Tk. 3.75
খ
খ) Tk. 3.25
গ
গ) Tk. 4.25
ঘ
ঘ) Tk. 4.50

ব্যাখ্যা

Question: Vendor sells apples at a certain price in order to make a profit of 30%. If he charges Tk. 1.5 higher per apple he would get a profit of 60%. Find the original price at which he sold an apple?

Solution:
Cost price of an apple = Tk. x
and original selling price = selling price at 30% profit = 130% of x = Tk. 1.3x
Again at 60% profit selling price = 160% of x = Tk. 1.6x

ATQ,
1.6x = x + 1.5
⇒ 1.6x - x = 1.5
⇒ .6x = 1.5
⇒ x = 1.5/.6
∴ x = 2.5

Hence, original selling price = 1.3x = Tk. (1.5 × 2.5) = Tk. 3.25

২৩৩.

What will be the compound interest at 10% on a sum of TK. 5000 after 5 years?

ক
ক) Tk. 3052
খ
খ) Tk. 3068
গ
গ) Tk. 3072
ঘ
ঘ) Tk. 3075

ব্যাখ্যা

Compound interest = Amount − Principal
Amount = 5000(1 + 10/100)⁵ = 8052.55
So, compound interest = Tk. (8052.55 - 5000) = Tk. 3052.55 ≈ Tk. 3052

২৩৪.

In an election the votes between the winner and loser candidate are in the ratio 3 : 2. If total number of eligible voters are 1000, out of which 15% did not cast their vote and among the remaining vote 10% declared invalid. What is the number of votes the winner candidate get?

ক
ক) 411
খ
খ) 427
গ
গ) 459
ঘ
ঘ) 475

ব্যাখ্যা

Question: In an election the votes between the winner and loser candidate are in the ratio 3 : 2. If total number of eligible voters are 1000, out of which 15% did not cast their vote and among the remaining vote 10% declared invalid. What is the number of votes the winner candidate get?

Solution:
Ratio of winner and loser 3 : 2
Total number of votes casted actually = 1000 × (85/100) × (90/100) = 765

ATQ,
3x + 2x = 765
⇒ 5x = 765
⇒ x = 765/5
∴ x = 153

∴ Votes of winner candidate = 3 × 153 = 459

২৩৫.

A man gains 30% by selling an article for a certain price. If he sells it at double the current selling price, then what will be the profit percentage?

ক
60%
খ
160%
গ
90%
ঘ
120%

ব্যাখ্যা

Question: A man gains 30% by selling an article for a certain price. If he sells it at double the current selling price, then what will be the profit percentage?

Solution:
Let,
the cost price be Tk. x.

∴ Selling price = Tk. 1.3x

Now,
new SP = Tk. 2.6x

∴ Profit % = [(2.6x - x )/x] × 100 % = 160%

২৩৬.

90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 40% of the total school population of x students, what is x?

ক
125
খ
150
গ
225
ঘ
250

ব্যাখ্যা

Question: 90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 40% of the total school population of x students, what is x?

Solution:
Let,
Total students x.
Number of boys = 40% of x.
= (40/100)× x
= (4x)/10
= 0.4x

ATQ,
x% of 0.4x = 90
⇒ (x/100) × 0.4x = 90
⇒ 0.4x² = 90 × 100
⇒ x² = 9000/0.4
⇒ x² = 22500
∴ x = 150

২৩৭.

If a number x is 10% less than another number y and y is 10% more than 125, then x is equal to:

ক
123.75
খ
140.55
গ
143
ঘ
150

ব্যাখ্যা

Question: If a number x is 10% less than another number y and y is 10% more than 125, then x is equal to:

Solution:
y = 125 + 125 এর 10%
y = 125 + 125 এর 10/100
y = 125 + 12.5
y = 137.5

x = y - y এর 10%
x = 137.5 - 137.5 এর 10%
x = 137.5 - 137.5 এর 10/100
x = 137.5 - 13.75
x = 123.75

২৩৮.

15% of 40% of a number is 120. What is 16% of that number?

ক
480
খ
420
গ
320
ঘ
300

ব্যাখ্যা

Question: 15% of 40% of a number is 120. What is 16% of that number?

Solution:
Let, a number be x

ATQm
x × 0.15 × 0.4 = 120
⇒ x = 120/( 0.15 × 0.4)
= 2000

16% of that number is = 2000 × 0.16
= 320

২৩৯.

If an article is sold for Tk. 356 at a loss of 11%, what should be its selling price in order to earn a profit of 11%?

ক
Tk. 222
খ
Tk. 444
গ
Tk. 442
ঘ
Tk. 224

ব্যাখ্যা

Question: If an article is sold for Tk. 356 at a loss of 11%, what should be its selling price in order to earn a profit of 11%?

Solution:
Selling Price of the article = Tk. 356
Loss % = 11%

∴ Cost Price = {100/(100 - 11)} × 356
= (356 × 100)/89 = 400

Now Cost Price = Tk. 400 and Profit% = 11%
∴ New Selling Price = {(100 + 11)/100} × 400 = (111 × 400)/100 = 444 Tk.

Therefore, the article should be sold at Tk. 444

২৪০.

A shopkeeper first increased the price of an article by 25% and then by 20%. What is the total percent increase?

ক
40%
খ
45%
গ
50%
ঘ
55%

ব্যাখ্যা

Let,
the original price be Tk. 100
New final price = 120% of (Tk. 125% of 100)
= Tk. {(120/100) × (125/100) × 100)}
= Tk. 150
∴ Increase = (150 - 100)%
= 50%.

২৪১.

A shopkeeper sells goods at 25% profit. If he had sold for Tk. 200 more, the profit would have been 30%. What is the cost of that goods?

ক
Tk. 2,800
খ
Tk. 3,200
গ
Tk. 3,600
ঘ
Tk. 4,000

ব্যাখ্যা

Question: A shopkeeper sells goods at 25% profit. If he had sold for Tk. 200 more, the profit would have been 30%. What is the cost of that goods?

Solution:
Let the cost price = C Tk.

Selling price at 25% profit:
SP₁ = C + 25% of C = C × 1.25

Selling price at 30% profit:
SP₂= C + 30% of C = C × 1.30

Difference:
SP₂ - SP₁= 200
⇒ 1.30C - 1.25C = 200
⇒ 0.05C = 200
⇒ C = 200/0.05
⇒ C = 4,000 Tk.

∴ Cost Price = 4,000 Tk.

২৪২.

A man spends 35% of his income on food, 25% on children's education and 80% of the remaining on house rent. What percent of his income he is left with?

ক
ক) 6%
খ
খ) 8%
গ
গ) 10%
ঘ
ঘ) 12%
ঙ
ঙ) 15%

ব্যাখ্যা

Let, total income = 100
Total expense food and education = 35 + 25
= 60
Remaining = (100 - 60) = 40
Expense on house rent = 40 × (80/100) = 32
Remaining after all expense = 40 - 32 = 8

২৪৩.

By selling a property for Tk. 45000 a person incurs a loss of 10%. Find the selling price to gain the profit of 15%?

ক
58000
খ
57500
গ
60000
ঘ
55000

ব্যাখ্যা

Question: By selling a property for Tk. 45000 a person incurs a loss of 10%. Find the selling price to gain the profit of 15%?

Solution:
S.P = 45000
Loss% = 10%

C.P = (100)/ (100- L %)) × S.P

C.P = (100/ (100-10))× 45000
C.P= (100/90) × 45000
C.P = 50000

Now, to gain the profit of 15%:

S.P = ((100+P %) /100) × C.P

S.P = ((100+15)/100) × 50000
S.P = (115/100)× 50000
S.P = 57500

২৪৪.

A dozen Bombay peppers are purchased for Tk. 37.50 and sold for Tk. 39.75. What is the profit percentage?

ক
8%
খ
4%
গ
6%
ঘ
5%

ব্যাখ্যা

Question: A dozen Bombay peppers are purchased for Tk. 37.50 and sold for Tk. 39.75. What is the profit percentage?

Solution:
∴ লাভ = ৩৯.৭৫ - ৩৭.৫০ = ২.২৫ টাকা

∴ ৩৭.৫০ টাকায় লাভ হয় = ২.২৫ টাকা
∴ ১ টাকায় লাভ হয় = ২.২৫/৩৭.৫০ টাকা
∴ ১০০ টাকায় লাভ হয় = (২.২৫ × ১০০)/৩৭.৫০ টাকা
= (২২৫ × ১০০)/৩৭৫০ টাকা
= ৬ টাকা বা ৬%

২৪৫.

A batsman scored 120 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?

ক
ক) 42%
খ
খ) 45%
গ
গ) 50%
ঘ
ঘ) 55%

ব্যাখ্যা

Question: A batsman scored 120 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?

Solution:
4 এবং 6 এর মাধ্যমে সে রান নিল = (3 x 4 ) + (6 × 8) = 12 + 48 = 60 রান
অতএব, সে দৌড়ে রান নিল = 120 - 60 = 60 রান

∴ শতকরা দৌঁড়ে রানের পরিমাণ = {(60/120) × 100}%
= 50%

২৪৬.

A person subscribing to Netflix for a year pays BDT. 1560. If the monthly subscription is BDT. 150, how much discount does a yearly subscriber get?

ক
10%
খ
12.50%
গ
13.33%
ঘ
15%

ব্যাখ্যা

Question: A person subscribing to Netflix for a year pays BDT. 1560. If the monthly subscription is BDT. 150, how much discount does a yearly subscriber get?

Solution:
Yearly subscription rate = BDT. 1560
Charge for 12 month as rate of BDT. 150 per month = 12 × 150
= BDT. 1800

∴ Discount = 1800 - 1560 = BDT. 240

Hence, discount % = (240 × 100)/1800
= 13.33%

২৪৭.

A dealer originally bought 100 identical batteries at a total cost of Tk. q. If each battery was sold at 50 percent above the original cost per battery, then, in terms of q, for how many Tk. was each battery sold?

ক
(3q)/200
খ
(3q)/2
গ
150q
ঘ
q/100
ঙ
150/q

ব্যাখ্যা

Question: A dealer originally bought 100 identical batteries at a total cost of Tk. q. If each battery was sold at 50 percent above the original cost per battery, then, in terms of q, for how many Tk. was each battery sold?

Solution:
The cost of 100 batteries is Tk. q
∴ The cost of 1 battery is Tk. q/100

Since the selling price is 50% greater than the cost price than the selling price is (q/100) × 1.5
= (q/100) × (3/2)
= (3q)/200

২৪৮.

If the price of a commodity increases by 50%, by what fraction should the quantity consumed be decreased to maintain the same total expenditure?

ক
1/2
খ
1/3
গ
1/4
ঘ
1/5
ঙ
None

ব্যাখ্যা

Question: If the price of a commodity increases by 50%, by what fraction should the quantity consumed be decreased to maintain the same total expenditure?

Solution:
Let the initial price of the commodity be 100.

After a 50% increase in price,
The increased price will be 150.
Now, we have to reduce the consumption to keep expenditure at 100.

Increase in price = 150 - 100 = 50

∴ We have to reduce the consumption
= (50/150) × 100
= 33.33% or 1/3

২৪৯.

If a boy sells a book for Tk. 450 he gets a loss of 10%, then finds the cost price. To gain 10%, what should be the selling price?

ক
ক) 400, 500
খ
খ) 550, 600
গ
গ) 500, 550
ঘ
ঘ) 475, 525

ব্যাখ্যা

1) Find the cost price

Let C.P. of book = x and S.P. = Tk. 450
S.P. of book = C.P. – (10% of C.P.)
S.P. = x – (0.10x)
450 = 0.9 x
x i.e cost price = Tk. 500

2) Find Selling Price to gain 10%.

Now, we are asked to find a selling price to gain 10% profit.
Selling price = (100 + Gain%)/100 × C.P.
Selling price = (100 + 10)/100 × 500
Selling price = (110/100) × 500
= Tk. 550

২৫০.

Robi buys a second-hand car for Tk. 2,00,000. He then repaints it for Tk. 2000. He attaches new threading to all 4 tyres. Cost of threading per tyre is Tk. 200. At what price he should resell the car so that he gains 10%?

ক
223080
খ
223090
গ
232080
ঘ
223880

ব্যাখ্যা

Cost of second hand car = Tk. 2,00,000
Repainting cost = Tk. 2000
Cost of threading per tyre = Tk. 200
Cost of threading for all tyres = Tk. 200 x 4 = Tk. 800
Total costs involved = Actual cost + Repainting costs + Threading costs
= 2,00,000 + 2000 + 800
= 202800
Profit Percentage = 10% = (SP - CP)/CP x 100%
Or, 10% = (SP - 202800)/202800 x 100%
Or, 10 = (SP - 202800)/2028
Or, 20280 = SP - 202800
Or, SP = 20280 + 202800
= 223080.
∴ Selling Price = 223080

২৫১.

A reduction of 25% in the price of sugar enables a housewife to purchase 5 kg more for 600 Taka. What is the original price per kg of sugar?

ক
Tk. 48
খ
Tk. 28
গ
Tk. 32
ঘ
Tk. 40

ব্যাখ্যা

Question: A reduction of 25% in the price of sugar enables a housewife to purchase 5 kg more for 600 Taka. What is the original price per kg of sugar?

Solution:
Let original price per kg = p Taka
Reduced price = p - p of 25% = 0.75p
Original quantity for 600 Taka
Q₁ = 600/p kg

And
New quantity for 600 Taka
Q₂ = 600/0.75p = 800/p kg

Now, quantity difference,
Q₂ - Q₁ = 5
(800/p) - (600/p) = 5
200/p = 5
p = 200/5
p = 40

∴ Original price per kg = Tk. 40

২৫২.

60% of a smaller number is 6 less than 50% of a larger number. The larger number is 60 greater than the smaller one. The sum of these two number is-

ক
520
খ
640
গ
500
ঘ
540

ব্যাখ্যা

Question: 60% of a smaller number is 6 less than 50% of a larger number. The larger number is 60 greater than the smaller one. The sum of these two number is-

Solution:
Let the smaller number be x and larger number be y
According to the question,
60% of x + 6 = 50% of y
⇒ (3x/5) + 6 = y/2
⇒ 6x + 60 = 5y
⇒ 6x - 5y = - 60 ................ (1)
and
y - x = 60 ----------- (2)

By using (1) and (2), we get
x = 240
y = 300

∴ The sum of these two number =(300 + 240) = 540

২৫৩.

A sales person earns a commission of 5% on all sales between Tk. 2000 and Tk. 6000 and 8% on all sales over Tk. 6000. What is his total commission in a week in which his sales total Tk. 10,000?

ক
500
খ
540
গ
620
ঘ
720
ঙ
800

ব্যাখ্যা

Commission for sale upto 6000 = 6000 × 5% = 300
Commission for sales over 6000 = 4000 × 8% = 320
Total commission = 620.

২৫৪.

A shopkeeper has sufficient money to buy 50 books. On reduction in the price of each book by Tk. 4, he could buy 10 books more. How much money does he have?

ক
Tk. 800
খ
Tk. 1000
গ
Tk. 1200
ঘ
Tk. 1500

ব্যাখ্যা

Question: A shopkeeper has sufficient money to buy 50 books. On reduction in the price of each book by Tk. 4, he could buy 10 books more. How much money does he have?

Solution:
১টি বইয়ে দাম কমে ৪ টাকা
∴ ৫০টি বইয়ে দাম কমে (৫০ × ৪) টাকা
= ২০০ টাকা

সে মোট বই কিনে (৫০ + ১০) টি
= ৬০টি

১০টি বইয়ের দাম ২০০ টাকা
∴ ৬০টি বইয়ের দাম (২০০ × ৬০)/১০ টাকা
= ১২০০ টাকা

∴ তার কাছে ১২০০ টাকা আছে।

২৫৫.

In an election 4% of votes cast are invalid. A candidate gets 55% of casted votes and wins the election by 4800 votes. Find the total number of votes casted.

ক
50000
খ
45000
গ
42000
ঘ
60000

ব্যাখ্যা

Question: In an election 4% of votes cast are invalid. A candidate gets 55% of casted votes and wins the election by 4800 votes. Find the total number of votes casted.

Solution:
বিজয়ী প্রার্থী ভোট পায়= 55%
বৈধ ভোট = (100 - 4)% = 96%

বিজয়ী প্রার্থী বৈধ ভোটের শতকরা পায় = (55 × 96)/100
= 52.8%

পরাজিত প্রার্থী ভোট পায় = (96 - 52.8)%
= 43.2%

বিজয়ী প্রার্থী ও পরাজিত প্রার্থীর ভোটের পার্থক্য = (52.8 - 43.2)%
= 9.6%

প্রশ্নমতে
9.6% = 4800
1% = 4800/9.6
100% = (4800 × 100)/9.6
= 50000

২৫৬.

Every 3 minutes, 4 litres of water are poured into a 2,000 litre tank. After 2 hours, what percent of the tank will be full?

ক
0.4%
খ
4%
গ
8%
ঘ
12%

ব্যাখ্যা

Question: Every 3 minutes, 4 litres of water are poured into a 2,000 litre tank. After 2 hours, what percent of the tank will be full?

Solution:
In 3 minutes, 4 liters is poured
In, 120 minutes = (120 × 4)/3 = 160 liters

So, percentage filled = (160 × 100)/2000
= 8%

২৫৭.

What percentage of numbers from 1 to 30 has 1 or 9 in the unit's digit?

ক
22%
খ
20%
গ
15%
ঘ
12%

ব্যাখ্যা

Question: What percentage of numbers from 1 to 30 has 1 or 9 in the unit's digit?

Solution:
Such numbers from 1 to 30 are 1, 9, 11, 19, 21, 29
Number of such numbers =6
Required percentage is (6/30) × 100% = 20%

২৫৮.

Tahir gets paid travelling expenses according to the distance he drives in his car plus a weekly sum of Tk. 21. He claims for 420 miles travelled and receives an expenses payment of Tk. 105. What is the payment rate per mile?

ক
ক) 20 cents
খ
খ) 32 cents
গ
গ) 48 cents
ঘ
ঘ) 51 cents

ব্যাখ্যা

যেহেতু তাহিরকে ২১ টাকা প্রতি সপ্তাহে বাধ্যতামূলক দিতে হয়,
সেহেতু তাহিরের পারিশ্রমিক নেয় ১০৫-২১ = ৮৪ টাকা৷
অর্থাৎ, সে ৪২০ কি.মি. এর জন্য পায় ৮৪ টাকা।
সুতরাং, প্রতি কি.মি. এর জন্য পাবে ৪২০/৮৪ = ০.২ = ২০ সেন্ট।

২৫৯.

A sum of money amounts to Tk. 920 in 3 years and to Tk. 1000 in five years. Find the rate percent per amount -

ক
ক) 2%
খ
খ) 11%
গ
গ) 4%
ঘ
ঘ) 5%

ব্যাখ্যা

After 5 years the sum = Tk. 1000
After 3 years the sum = Tk. 920
The interest of 2 years = Tk. (1000 - 920) = Tk. 80
The interest of 3 years, I = Tk. 80 x (3/2) = Tk. 120
The principle, P = Tk. (920 - 120) = Tk. 800
So, the rate = I/Pn = 120/(800 x 3) × 100% = 5%

২৬০.

If 60% of A's income is equal to 75% of B's income, then B's income is equal to x% of A's income. The value of x is :

ক
110
খ
80
গ
60
ঘ
90

ব্যাখ্যা

Question: If 60% of A's income is equal to 75% of B's income, then B's income is equal to x% of A's income. The value of x is :

Solution:
ATQ,
60 × (A/100) = 75 × (B/100)
⇒ 60A = 75B
⇒ 4A = 5B
⇒ B = 4A/5

Again,
B = A × (x/100)
⇒ 4A/5 = A × (x/100)
⇒ 4/5 = x/100
⇒ 5x = 400
⇒ x = 400/5
∴ x = 80

২৬১.

করিমের বার্ষিক আয় রহিমের চেয়ে ১০% বেশি, অন্যদিকে রহিমের বার্ষিক আয় খালেকের আয়ের চেয়ে ২০% বেশি । খালেকের মাসিক আয় ২০০০ টাকা হলে ৩ জনের মোট মাসিক আয় কত?

ক
ক) ৬৮৭২ টাকা
খ
খ) ৭০৪৬ টাকা
গ
গ) ৭৭৭২ টাকা
ঘ
ঘ) ৭০৪০ টাকা

ব্যাখ্যা

প্রশ্ন: করিমের বার্ষিক আয় রহিমের চেয়ে ১০% বেশি, অন্যদিকে রহিমের বার্ষিক আয় খালেকের আয়ের চেয়ে ২০% বেশি । খালেকের মাসিক আয় ২০০০ টাকা হলে ৩ জনের মোট মাসিক আয় কত?

সমাধান:
খালেকের মাসিক আয় ২০০০ টাকা

রহিমের মাসিক আয় = ২০০০ + (২০০০ × (২০/১০০) টাকা
= ২০০০ + ৪০০ টাকা
= ২৪০০ টাকা

করিমের মাসিক আয় = ২৪০০ + (২৪০০ × (১০/১০০) টাকা
= ২৪০০ + ২৪০ টাকা
= ২৬৪০ টাকা

৩ জনের মোট মাসিক আয় (২০০০ + ২৪০০ + ২৬৪০) টাকা
= ৭০৪০ টাকা

২৬২.

Two discount of 8% and 12% are equal to a single discount of:

ক
20%
খ
19.04%
গ
18.96%
ঘ
18%

ব্যাখ্যা

Question: Two discount of 8% and 12% are equal to a single discount of:

Solution:
Let,
The initial price = Tk. 100
After first 8% discount,
100 - 8% of 100 = 100 - 8 = 92

After second 12% discount,
92 - 12% of 92 = 92 - 11.04 = 80.96

∴ Single discount = 100 - 80.96 = 19.04%

২৬৩.

One-fifth of half of a number is 20. Then 20% of that number is:

ক
ক) 20
খ
খ) 25
গ
গ) 30
ঘ
ঘ) 40

ব্যাখ্যা

Question: One-fifth of half of a number is 20. Then 20% of that number is:

Solution:
Let the number is = x

ATQ,
1/5 of 1/2 of x = 20
⇒ 1/5 × 1/2 × x = 20
⇒ x/10 = 20
∴ x = 200

∴ 20% of 200 = (20/100) × 200
= 40

২৬৪.

500 shares, of par value TK. 20 each, are purchased from Rasel by Himel at a price of Tk. 25 each. Find the amount required to purchase the shares.

ক
ক) 10000 tk.
খ
খ) 12000 tk.
গ
গ) 12500 tk.
ঘ
ঘ) 20000 tk.

ব্যাখ্যা

Question: 500 shares, of par value TK. 20 each, are purchased from Rasel by Himel at a price of Tk. 25 each. Find the amount required to purchase the shares.

Solution:
Face value of each share = Tk. 20
The market value of each share = Tk. 25
Number of shares = 500
Amount required to purchase the shares = 500 × 25
= 12500 tk.

২৬৫.

A sold a watch to B at a gain of 20% and B sold it to C at loss of 10%. If C bought the watch for TK. 432 at what price did A purchase it?

ক
Tk. 300
খ
Tk. 200
গ
Tk. 400
ঘ
Tk. 250

ব্যাখ্যা

Question: A sold a watch to B at a gain of 20% and B sold it to C at loss of 10%. If C bought the watch for TK. 432 at what price did A purchase it?

Solution:
A purchase at x taka
Selling price of A = purchasing price of B = x + 20% of x = 1.2x

Buying price of C = 1.2x - 10% of 1.2x = 1.2x - 0.12x = 1.08x

1.08x = 432
⇒ x = 432/1.08 = Tk. 400

২৬৬.

Which of the numbers below is not equivalent to 4%?

ক
ক) 1/25
খ
খ) 4/100
গ
গ) 0.40
ঘ
ঘ) 0.04

ব্যাখ্যা

প্রশ্ন: Which of the numbers below is not equivalent to 4%?

সমাধান:
ক) (১/২৫) × ১০০% = ৪%

খ) (৪/১০০) × ১০০% = ৪%

গ) ০.৪০ = (৪০/১০০) × ১০০% = ৪০%

ঘ) ০.০৪ = (৪/১০০) × ১০০% = ৪%

এখানে, ৪% এর সমান নয় ০.৪০

২৬৭.

A person sold a product at a gain of 15%. Had he bought it for 25% less and sold it for Tk. 1200 less, he would have made a profit of 32%. The cost price of the product was?

ক
Tk. 6600
খ
Tk. 6800
গ
Tk. 7280
ঘ
Tk. 7500

ব্যাখ্যা

Question: A person sold a product at a gain of 15%. Had he bought it for 25% less and sold it for Tk. 1200 less, he would have made a profit of 32%. The cost price of the product was?

Solution:
Let the original cost price = Tk. x

Now, Selling price = x + 15% of x
= 115x/100
= 23x/20

And Cost price = x - 25% of x
= x - (25x/100)
= 75x/100
= 3x/4

∴ Selling price = (3x/4) + 32% of (3x/4)
= (3x/4) + (32/100) × (3x/4)
= 99x/100

ATQ,
(23x/20) - (99x/100) = 1200
⇒ (115x - 99x)/100 = 1200
⇒ 16x = 1200 × 100
⇒ x = (1200 × 100)/16
∴ x = 7,500

২৬৮.

By selling a book for Tk 525, a seller incurs a loss equal to 2/5 of his cost price. If he sells it for Tk 950, what is his gain or loss percentage?

ক
8.57% gain
খ
10% loss
গ
12.67% gain
ঘ
13.45% loss
ঙ
No gain no loss

ব্যাখ্যা

Question: By selling a book for Tk 525, a seller incurs a loss equal to 2/5 of his cost price. If he sells it for Tk 950, what is his gain or loss percentage?

Solution:
Let cost price = x Tk
If the book’s selling price is 525 Tk, then loss = (x - 525) Tk

∴ x - 525 = x × (2/5)
⇒ 5(x - 525) = 2x
⇒ 5x - 2625 = 2x
⇒ 3x = 2625
⇒ x = 875

If the book’s selling price is 950 Tk, then gain = (950 - 875) = 75 Tk

∴ Gain percentage = (75 × 100)/875 = 8.57%

২৬৯.

In an election 10% of the voters on the voters' list did not cast their votes and 60 voters cast their ballot papers blank. There were only two candidates. The winner was supported by 47% of all the voters in the list and he got 308 votes more than his rival. The number of voters on the list was?

ক
5530
খ
5800
গ
6200
ঘ
6445

ব্যাখ্যা

Question: In an election 10% of the voters on the voters' list did not cast their votes and 60 voters cast their ballot papers blank. There were only two candidates. The winner was supported by 47% of all the voters in the list and he got 308 votes more than his rival. The number of voters on the list was?

Solution:
Let, total voters in the list = x
Votes got by the winner = 47x/100

Votes got by the loser,
x - (x/10) - 60 - (47x/100)
= (9x/10) - (47x/100) - 60
= (90x - 47x)/100 - 60
= (43x/100) - 60

ATQ,
(47x/100) - (43x/100) + 60 = 308
⇒ 4x/100 = 308 - 60
⇒ 4x/100 = 248
⇒ 4x = 248 × 100
⇒ x = (248 × 100)/4
∴ x = 6200

২৭০.

By how much percent is four-fifths of 70 lesser than five-sevenths of 112?

ক
12%
খ
24%
গ
36%
ঘ
40%
ঙ
None

ব্যাখ্যা

Question: By how much percent is four-fifths of 70 lesser than five-sevenths of 112?

Solution:

Here,
four-fifth of 70

= 4/5 × 70

= 56

Again,

five-seventh of 112

= 5/7 × 112

= 80

% lesser

= [(80 - 56)/80] × 100%

= (24/80) × 100%

= 30%

২৭১.

A merchant has 500 kg of sugar, part of which he sells at 8% and the remaining at 18% profit. He gains 14% on the whole. Find the quantity of sugar that he sold at 8% profit.

ক
300 kg
খ
250 kg
গ
200 kg
ঘ
150 kg

ব্যাখ্যা

Question: A merchant has 500 kg of sugar, part of which he sells at 8% and the remaining at 18% profit. He gains 14% on the whole. Find the quantity of sugar that he sold at 8% profit.

Solution:
Let,
The cost price of sugar be tk. x per kg
∴ Total cost price = Tk. 500x
∴ Total sell price = 500x + {500x × (14/100)}
= 500x + 70x
= 570x

The sugar sold at 8% gain by y kg
The sugar sold at 18% gain by (500 - y) kg

Now
{(108xy)/100} + [{118x(500 - y)}/100] = 570x
⇒ (108xy)/100 + (59000x - 118xy)/100 = 570x
⇒ 108xy + 59000x - 118xy =57000x
⇒ 10xy = 2000x
⇒ y = 2000/10
y = 200

∴ The sugar sold at 8% gain by 200 kg

২৭২.

A student attempts x number of questions. He answers 15 correctly out of the first 20 questions and of the remaining questions, he answers 1/3 correctly. If all questions have the same credit and the student gets 50% marks, then find the value of x.

ক
ক) 30
খ
খ) 35
গ
গ) 45
ঘ
ঘ) 50

ব্যাখ্যা

1) Student attempts x questions.
2) Out of 20 questions he answered 15 correctly and of (x – 20) questions he answered 1/3 correctly.
3) The student gets 50% marks.
Therefore,
15 + 1/3(x – 20)= 50% of x
⇒ 15 + 1/3(x – 20) = (50/100) × x
⇒ 15 + 1/3(x – 20) = x/2
⇒ 90 + 2(x - 20) = 3x
⇒ x = 50
Hence, the number of questions attempted by the students = 50.

২৭৩.

A merchant buys 30 kg of rice at Tk. 40/kg, and another 20 kg of rice at Tk. 30/kg. He mixes them and sells half of the mixture at Tk. 36/kg. At what price should he sell the remaining mixture to get an overall profit of 30%?

ক
Tk. 1460
খ
Tk. 1440
গ
Tk. 1420
ঘ
Tk. 1400

ব্যাখ্যা

Question: A merchant buys 30 kg of rice at Tk. 40/kg, and another 20 kg of rice at Tk. 30/kg. He mixes them and sells half of the mixture at Tk. 36/kg. At what price should he sell the remaining mixture to get an overall profit of 30%?

Solution:
Total cost for the entire quantity of rice = (30 × 40) + (20 × 30) = 1200 + 600 = 1800
If his profit is 30%, then the sales realization = (130/100) × 1800 = 2340.
Total rice = 30 + 20 = 50 kg
He sells 25 kg at Tk. 36/kg = 900.

Therefore to make the said amount of profit, he should sell the remaining 25 kg of rice at 2340 - 900 = 1440

২৭৪.

A retailer bought a glass at wholesale and marked it up 80% to its initial retail price of Tk. 45. By how many more taka does he need to increase the price to achieve a 100% markup?

ক
Tk. 3
খ
Tk. 5
গ
Tk. 10
ঘ
None of these

ব্যাখ্যা

Question: A retailer bought a glass at wholesale and marked it up 80% to its initial retail price of Tk. 45. By how many more taka does he need to increase the price to achieve a 100% markup?

Solution:
let, wholesale price x

1.8x = 45
⇒ x = 45/1.8
∴ x = 25 taka

to achieve a 100% markup retail price = 25 + 25 = 50 taka

he needs to increase = 50 - 45 taka
= Tk. 5

২৭৫.

0.95 expressed as a percent of 1.9 is-

ক
6%
খ
10%
গ
50%
ঘ
90%
ঙ
None

ব্যাখ্যা

Question: 0.95 expressed as a percent of 1.9 is-

Solution:
Required Percentage = (0.95 ×100)/1.9
= (0.95 × 100 × 10)/(19 × 100)
= 50%

২৭৬.

A man wanted to sell his bat at 5% discount. His brother who was a cricketer wanted to buy that bat so the man sells it at 8% discount. In this deal, the man makes Tk. 60/- less in profit. How much was the marked price of the bat?

ক
ক) Tk. 1800
খ
খ) Tk. 2000
গ
গ) Tk. 6000
ঘ
ঘ) Tk. 9000

ব্যাখ্যা

Difference in discount = 8% - 5% = 3%
Due to this 3% man makes Tk. 60 less in profit
That means 3% of Marked Price = 60
(3/100) × M.P. = 60
∴ M.P. = Tk. 2000

২৭৭.

57 is 75 percent of which number given below?

ক
ক) 65
খ
খ) 87
গ
গ) 76
ঘ
ঘ) 98

ব্যাখ্যা

ধরি ,
x এর 75% = 57
x এর 75/100 = 57
3x/4 = 57
x = (57 × 4)/3 = 76

২৭৮.

An employee's annual salary was increased Tk.30,000. If her new annual salary now equals Tk. 105,000 what was the percent increase?

ক
ক) 20%
খ
খ) 40%
গ
গ) 30%
ঘ
ঘ) None of the above

ব্যাখ্যা

প্রশ্ন : An employee's annual salary was increased Tk.30,000. If her new annual salary now equals Tk. 105,000 what was the percent increase?

সমাধান :

New annual salary = 105,000
Salary increase = 30,000.
Original salary = 105,000 - 30,000 = 75,000

% Increase = (30,000/ 75,000 )×100 = 40%

২৭৯.

The ratio 5 : 4 expressed as a percent equals-

ক
12.5%
খ
100%
গ
80%
ঘ
125%

ব্যাখ্যা

Question: The ratio 5 : 4 expressed as a percent equals-

Solution:
Given,
The ratio = 5 : 4
= (5/4) × 100%
= 125%

২৮০.

An employee pays 3 workers X, Y and Z a total of Tk. 610 in a week. X is paid 125% of the amount Y is paid and 80% of the amount Z is paid. Hou much does X make a week?

ক
ক) Tk. 150
খ
খ) Tk. 175
গ
গ) Tk. 180
ঘ
ঘ) Tk. 200

ব্যাখ্যা

Question: An employee pays 3 workers X, Y and Z a total of Tk. 610 in a week. X is paid 125% of the amount Y is paid and 80% of the amount Z is paid. Hou much does X make a week?

Solution:
X = 125% Y
⇒ X = 125Y/100 = 5Y/4
∴ Y = 4X/5

X = 80% of Z
⇒ X = 80Z/100
⇒ X = 4Z/5
∴ Z = 5X/4

X + Y + Z = 610
⇒ X + 4X/5 + 5X/4 = 610
⇒ (20X + 16X + 25X)/20 = 610
⇒ 61X = 610 × 20
⇒ X = (610 × 20)/61
= 200 taka

২৮১.

Fifty percent of a number is 30 less than three-fourth of the same number. Find the number.

ক
210
খ
180
গ
150
ঘ
120

ব্যাখ্যা

Question: Fifty percent of a number is 30 less than three-fourth of the same number. Find the number.

Solution:
Let,
the number = x.

ATQ,
50% of x = (3/4) of x - 30
⇒ 50x/100 = (3x/4) - 30
⇒ x/2 = (3x/4) - 30
⇒ (3x/4) - (x/2) = 30
⇒ (3x - 2x)/4 = 30
⇒ x/4 = 30
∴ x = 120

So, the number is 120.

২৮২.

A man bought cookies at 3 for Tk. 1. How many for Tk. 1 should he sell to make a profit a 50%.

ক
1
খ
2
গ
1.5
ঘ
None of these

ব্যাখ্যা

Question: A man bought cookies at 3 for Tk. 1. How many for Tk. 1 should he sell to make a profit a 50%.

Solution:
CP of 3 cookies = Tk. 1
SP of 3 cookies = 150% of Tk. 1 = 3/2

For Tk. 3/2, the man sells 3 cookies.
Hence for Tk. 1, number of cookies sold = (3 × 2)/3 = 2

২৮৩.

Bus fares were recently increased from Taka 12 to Taka 16. What was the approximate percentage of increase?

ক
4%
খ
15%
গ
21%
ঘ
33%

ব্যাখ্যা

Question: Bus fares were recently increased from Taka 12 to Taka 16. What was the approximate percentage of increase?

Solution:
বাস ভাড়া বাড়ে = (16 - 12) টাকা
= 4 টাকা

বাস ভাড়া শতকরা বাড়ে = (4/12) × 100%
= 33.33%
≈ 33%

২৮৪.

Two numbers are respectively 20% and 25% lower than a third number. By how much percentage is the second number lower than the first?

ক
ক) (25/2)%
খ
খ) (25/4)%
গ
গ) 25%
ঘ
ঘ) (25/6)%

ব্যাখ্যা

Let
The third number be x

First number = 80% of x
= 80x/100
= 4x/5

Second number = 75% of x
= 75x/100
= 3x/4

Difference = (4x/5) - (3x/4)
= (16x - 15x)/20
= x/20

Required Percentage (x/20) × (5/4x) × 100% = (25/4)%

২৮৫.

A candidate scores 40% marks and fails by 20 marks. Another candidate scores 50% marks and gets 30 marks more than the minimum pass marks. What is the pass percentage?

ক
33%
খ
36%
গ
40%
ঘ
44%

ব্যাখ্যা

Question: A candidate scores 40% marks and fails by 20 marks. Another candidate scores 50% marks and gets 30 marks more than the minimum pass marks. What is the pass percentage?

সমাধান:
ধরি, মোট নম্বর = x

প্রশ্নমতে,
40% of x + 20 = 50% of x - 30
⇒ 0.40x + 20 = 0.50x - 30
⇒ 0.50x - 0.40x = 20 + 30
⇒ 0.10x = 50
⇒ x = 50/0.10
∴ x = 500

∴ পাশ নম্বর = 40% of x + 20
= 0.4 × 500 + 20
= 200 + 20 = 220

∴ পাশের শতকরা হার = (220/500) × 100
= 44%

২৮৬.

If loss is 1/3 of S.P. then the loss percentage is-

ক
ক) 20%
খ
খ) 25%
গ
গ) 23%
ঘ
ঘ) 30%

ব্যাখ্যা

Let
S.P = x
loss = x/3
C.P = x + (x/3)
=(3x + x)/3
= 4x/3
Loss percentage = [{(x/3)/(4x/3)} × 100]%
= {(x/3) ×(3/4x) × 100}%
= 25%

২৮৭.

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

ক
21,500
খ
22,000
গ
22,500
ঘ
23,500

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 8% salary increase. What was this worker's salary before the new contract?

Solution:
ধরি,
পূর্বে কর্মীর বেতন ছিলো = x টাকা

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

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

প্রশ্নমতে
(106x/100) + 450 = 108x/100
⇒ 450 = (108x/100) - (106x/100)
⇒ 450 = 2x/100
⇒ 450 = x/50
⇒ x = 50 × 450
∴ x = 22,500

২৮৮.

A trader sells goods to a customer at a profit of k% over the cost price, besides it he cheats his customer by giving 880 g only instead of 1 kg. Thus his overall profit percentage is 25%. Find the value of k?

ক
8.33%
খ
8.25%
গ
10%
ঘ
12.5%

ব্যাখ্যা

Question: A trader sells goods to a customer at a profit of k% over the cost price, besides it he cheats his customer by giving 880 g only instead of 1 kg. Thus his overall profit percentage is 25%. Find the value of k?

Solution:
1 kg = 1000 g
Let,
The cost price of per gram Tk. 1
∴ The cost price of 1000g Tk. 1000
∴ The cost price of 880 Tk. 880

Selling price of 880 gram = 1000 + k% of 1000 = 1000 + {(1000k)/100}
= 1000 + 10k

∴ Profit = 1000 + 10k - 880
= 120 + 10k

Overall % Profit = {(120 + 10k)/880} × 100

∴ {(120 + 10k)/880} × 100 = 25
⇒ (120 + 10k)/880 = 25/100
⇒ 120 + 10k = (25 × 880)/100
⇒ 120 + 10k = 220
⇒ 10k = 100
∴ k = 10

২৮৯.

A shopkeeper sold an item at 20% profit and another item at 10% loss. If the cost price of both the items is same, find the overall profit percent.

ক
ক) 7.55%
খ
খ) 6.00%
গ
গ) 5.00%
ঘ
ঘ) 6.50%

ব্যাখ্যা

Let, cost of each item = 100
At 20% profit, selling price = 120
At 10% loss, selling price = 90
Total selling price = 210
Total cost = 100+100 = 200
Profit = 210 - 200 = 10
Profit % = (10×100)/200 = 5%

২৯০.

A man buys an article for 25% more than its value and sells it for 20% less than its value. His gain or loss percentage is –

ক
25% gain
খ
33.33% loss
গ
28% gain
ঘ
36% loss

ব্যাখ্যা

Question: A man buys an article for 25% more than its value and sells it for 20% less than its value. His gain or loss percentage is –

Solution:
Let the original value of the article = 100 units
∴ Cost Price (CP) = 100 + 25% of 100
= 100 + 25 = 125 units

∴ Selling Price (SP) = 100 - 20% of 100
= 100 - 20 = 80 units

Since SP 80 is less than CP 125, there is a Loss.

∴ Loss = CP - SP = 125 - 80 = 45 units
∴ Loss percentage = (Loss/CP) × 100%
= (45/125) × 100%
= 36% loss

২৯১.

A shopkeeper procured 1600 boxes of a certain chocolate brand at a cost of tk 10 per box. If he sold (3/4)th of the boxes for one and half times their procurement cost and sold the remaining boxes at a loss of 25 percent of their procurement cost, what was the shopkeeper’s gross profit on the total sale?

ক
4500 tk
খ
5000 tk
গ
5500 tk
ঘ
6000 tk
ঙ
6500 tk

ব্যাখ্যা

Question: A shopkeeper procured 1600 boxes of a certain chocolate brand at a cost of tk 10 per box. If he sold (3/4)th of the boxes for one and half times their procurement cost and sold the remaining boxes at a loss of 25 percent of their procurement cost, what was the shopkeeper’s gross profit on the total sale?

Solution:
Total cost = 1600 x 10 =$16,000

⇒ (3/4) × 1600 = 1200
⇒ Selling price = 1.5 × 10 = tk 15
⇒ tk 15 × 1200 = tk 18000

The remaining 400 boxes were sold at 25% loss = tk 7.5/box
⇒ 400 × 7.5 = tk 3000

∴ Gross profit = 18000 + 3000 - 16000
= 21000 - 16000
= 5000

২৯২.

A person spends 30% of his income on food, 20% on transportation, and 50% of the remaining amount on house rent. What percentage of his income is left?

ক
20%
খ
25%
গ
30%
ঘ
28%

ব্যাখ্যা

Question: A person spends 30% of his income on food, 20% on transportation, and 50% of the remaining amount on house rent. What percentage of his income is left?

Solution:
Let, total income = 100
Total expense food and transportation = 30 + 20 = 50
∴ Remaining = (100 - 50) = 50

∴ Expense on house rent = 50 × (50/100) = 25
∴ Remaining after all expense = 50 - 25 = 25

The person is left with 25% of his income.

২৯৩.

Every 2 minutes, 5 litres of water are poured into a 1,500 litre tank. After 3 hours, what percent of the tank will be full?

ক
10%
খ
20%
গ
30%
ঘ
40%

ব্যাখ্যা

Question: Every 2 minutes, 5 litres of water are poured into a 1,500 litre tank. After 3 hours, what percent of the tank will be full?

Solution:
In 2 minutes, 5 liters is poured
In 180 minutes = (180 × 5)/2 = 450 liters

So, percentage filled = (450 × 100)/1500
= 30%

২৯৪.

After successive discount of 12% and 5% an article was sold for Tk.209. What was the original price of the article?

ক
ক) Tk. 220
খ
খ) Tk. 250
গ
গ) Tk. 260
ঘ
ঘ) Tk. 280

ব্যাখ্যা

Let the original price x
Now
95% of 88% of x = 209
(95/100) × (88/100) × x = 209
x = (209 × 100 × 100)/(95 × 88)
x = 250

২৯৫.

The cost prices of a book and a notebook are in the ratio 3 : 7, while their selling prices are in the ratio 1 : 4. If the loss incurred on selling each item is the same, find the ratio of the cost price to the selling price of the notebook.

ক
1 : 16
খ
21 : 16
গ
11 : 16
ঘ
8 : 16

ব্যাখ্যা

Question: The cost prices of a book and a notebook are in the ratio 3 : 7, while their selling prices are in the ratio 1 : 4. If the loss incurred on selling each item is the same, find the ratio of the cost price to the selling price of the notebook.

Answer:
Let,
cost price of
a book = 3x
a notebook = 7x

Selling price of
a book = y
a notebook = 4y

According to the question,
3x - y = 7x - 4y
⇒ 4y - y = 7x - 3x
⇒ 3y = 4x
∴ y = 4x/3

∴ The ratio of the cost price of a notebook : the selling price of a notebook = 7x : [4 × (4x/3)]
= 21 : 16

২৯৬.

X sells an item to Y at a profit of 28% on his cost and sells the same item to Z at a loss of 25% on his cost. If Y thus sold the item to Z a Tk. 2 less than the item to X, then what is the cost of the item to X?

ক
Tk. 40
খ
Tk. 45
গ
Tk. 48
ঘ
Tk. 50

ব্যাখ্যা

Question: X sells an item to Y at a profit of 28% on his cost and sells the same item to Z at a loss of 25% on his cost. If Y thus sold the item to Z a Tk. 2 less than the item to X, then what is the cost of the item to X?

Solution:
Assume the initial price of 100
X sold to Y at 28% profit, then the price is at 128
Y sold to Z at 25% loss, then the price is 128 × 75% = 96

The difference from X to Z is = (100 - 96) = 4

If Tk.4 less then cost item 100
Tk. 2 then cost item (100 × 2)/4
= Tk. 50

২৯৭.

By selling an article for Tk. 2,850, a shopkeeper gains 14%. If the profit is reduced to 6%, then the selling price will be-

ক
Tk. 2500
খ
Tk. 2650
গ
Tk. 2730
ঘ
Tk. 2750

ব্যাখ্যা

Question: By selling an article for Tk. 2,850, a shopkeeper gains 14%. If the profit is reduced to 6%, then the selling price will be-

Solution:
Let, Cost Price was = a
a + 14% of a = 2850
⇒ {a + (14a/100)} = 2850
⇒ (100a + 14a)/100 = 2850
⇒ 114a/100 = 2850
∴ a = 2500

So, Cost Price = Tk. 2500.
Now, Selling Price When profit remains at 6%,
= 2500 + 6% of 2500
= Tk. 2650

২৯৮.

A machine is sold at a profit of 10%. Had it been sold for Tk. 40 less, there would have been a loss of 10%. What was the cost price?

ক
Tk.175
খ
Tk. 200
গ
Tk. 225
ঘ
Tk. 250

ব্যাখ্যা

Question: A machine is sold at a profit of 10%. Had it been sold for Tk. 40 less, there would have been a loss of 10%. What was the cost price?

Solution:
Let, cost price of the machine is x taka

Selling price = 1.1x taka

ATQ,
1.1x - 40 = 0.9x
⇒ 1.1x - 0.9x = 40
⇒ 0.2x = 40
⇒ x = 40/.2
= Tk. 200

২৯৯.

The price of pulses is reduced by 20%. Due to this reduction, a customer buys 5 kg more pulses for Tk. 500. Find the original price per kg of pulses.

ক
50 Tk/kg.
খ
25 Tk/kg.
গ
45 Tk/kg.
ঘ
35 Tk/kg.

ব্যাখ্যা

Question: The price of pulses is reduced by 20%. Due to this reduction, a customer buys 5 kg more pulses for Tk. 500. Find the original price per kg of pulses.

Solution:
Let
Original price of pulses = x Tk/kg.
Original quantity = 500/x kg

New price = 0.80x Tk/kg
New quantity = 500/0.80x = 500/(4x/5) = (500 × 5)/4x = 625/x kg

ATQ,
625/x - 500/x = 5
⇒ (625 - 500)/x = 5
⇒ 125/x = 5
⇒ x = 125/5
∴ x = 25

Original price of pulses = 25 Tk/kg.

৩০০.

The combined salaries of M and N amount to Tk. 4000. M spends 75% of his salary, and N spends 85% of his salary. If both M and N save the same amount of money, what is the salary of M?

ক
Tk. 2500
খ
Tk. 5200
গ
Tk. 3500
ঘ
Tk. 500
ঙ
None

ব্যাখ্যা

Question: The combined salaries of M and N amount to Tk. 4000. M spends 75% of his salary, and N spends 85% of his salary. If both M and N save the same amount of money, what is the salary of M?

Solution:
Let M’s salary = x
and N’s salary = (4000 - x)

According to the question,
Savings of M = Savings of N
⇒ (100 - 75)% of M = (100 - 85)% of N
⇒ (25/100)x = (15/100)(4000 - x)
⇒ 25x = 15(4000 - x) [multiply both sides by 100]
⇒ 25x = 60000 - 15x
⇒ 25x + 15x = 60000
⇒ 40x = 60000
⇒ x = 60000/40
⇒ x = 1500

∴ M’s salary is Tk. 1500