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Percentage and Profit & Loss

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Percentage and Profit & Loss

PrepBank · পাতা ৪ / ১৭ · ৩০১–৪০০ / ১,৬৯৬

৩০১.
A trader sold a cycle at a loss of 10%. If the selling price had been increased by Tk. 200, there would have been a gain of 6%. The cost price of the cycle is-
  1. ক
    Tk. 1480
  2. খ
    Tk. 1250
  3. গ
    Tk. 1350
  4. ঘ
    Tk. 1200
সঠিক উত্তর: খ
Tk. 1250
উত্তর
সঠিক উত্তর: খ
Tk. 1250
খ
ব্যাখ্যা
Question: A trader sold a cycle at a loss of 10%. If the selling price had been increased by Tk. 200, there would have been a gain of 6%. The cost price of the cycle is-

Solution:
Let the Cost price of cycle be x

Case I,
Selling Price of cycle = 90x/100 = 9x/10 = 0.9x

Case II,
106% of x = (9x/10) + 200
⇒ (106x/100) - (9x/10) = 200
⇒ (106x - 90x)/100 = 200
⇒ 16x/100 = 200
⇒ x = (200 × 100)/16
⇒ x = 1250

∴ The cost price of the cycle is Tk. 1250.
৩০২.
A shopkeeper lost 7.5% by selling an article. If he had bought it at 10% less and sold it for Tk.31 more, he would have gained 20%. Find the cost price of the article.
  1. ক
    ক) 50 Tk.
  2. খ
    খ) 125 Tk.
  3. গ
    গ) 200 Tk.
  4. ঘ
    ঘ) 300 Tk.
সঠিক উত্তর: গ
গ) 200 Tk.
উত্তর
সঠিক উত্তর: গ
গ) 200 Tk.
গ
ব্যাখ্যা
৭.৫% ক্ষতিতে,
ক্রয়মূল্য ১০০ টাকা হলে বিক্রয়মূল্য = (১০০ - ৭.৫) টাকা 
                                                       = ৯২.৫ টাকা 

১০% কমে,
দ্রব্যটির ক্রয়মূল্য = (১০০ - ১০) টাকা = ৯০ টাকা 
২০% লাভে,
ক্রয়মূল্য ১০০ টাকা হলে বিক্রয়মূল্য = (৯০ + ৯০ এর ২০%) টাকা 
                                                      = (৯০ + ৯০ এর ২০/১০০) টাকা 
                                                      = ১০৮  টাকা 

বিক্রয়মূল্য বেশি = (১০৮ - ৯২.৫) টাকা  = ১৫.৫ টাকা 

১৫.৫ টাকা বিক্রয়মূল্য বেশি যখন ক্রয়মূল্য ১০০ টাকা 
১ টাকা বিক্রয়মূল্য বেশি যখন ক্রয়মূল্য ১০০/১৫.৫ টাকা 
৩১  টাকা বিক্রয়মূল্য বেশি যখন ক্রয়মূল্য (১০০ × ৩১)/১৫.৫ টাকা 
                                                             = ২০০ টাকা
৩০৩.
The cost of a bicycle was Tk. 6000. The cost was reduced by 15% after it was increased by 20%. How much profit or loss percentage does it remain?
  1. ক
    5% loss
  2. খ
    2% profit
  3. গ
    2.5% loss
  4. ঘ
    3% profit
সঠিক উত্তর: খ
2% profit
উত্তর
সঠিক উত্তর: খ
2% profit
খ
ব্যাখ্যা
Question: The cost of a bicycle was Tk. 6000. The cost was reduced by 15% after it was increased by 20%. How much profit or loss percentage does it remain?

Solution: 
first the price was increased by 20% and then reduced by 15%
after increase the price is = (6000 + 20% of 6000)
= 7200

after reducing the price the price is = (7200 - 15% of 7200)
= 6120

profit = 6120 - 6000
= 120 

percentage = (120/6000)100%
= 2%
৩০৪.
The price of a coat in a certain store in Tk. 500. If the price of the coat is to be reduced by Tk. 150, by what percent is the price to be reduced?
  1. ক
    ক) 10%
  2. খ
    খ) 15%
  3. গ
    গ) 20%
  4. ঘ
    ঘ) 30%
সঠিক উত্তর: ঘ
ঘ) 30%
উত্তর
সঠিক উত্তর: ঘ
ঘ) 30%
ঘ
ব্যাখ্যা
x% of 500 = 150
x/100 of 500 = 150
5x = 150
x = 30
৩০৫.
A salesman receives daily wage of Tk. 150 and earns a commission of 25% on all sales he makes. How much taka worth of sales does he need to make in order to bring his total daily income of Tk. 1000?
  1. ক
    ক) Tk. 3800
  2. খ
    খ) Tk. 3600
  3. গ
    গ) Tk. 3400
  4. ঘ
    ঘ) Tk. 3200
সঠিক উত্তর: গ
গ) Tk. 3400
উত্তর
সঠিক উত্তর: গ
গ) Tk. 3400
গ
ব্যাখ্যা
Question: A salesman receives daily wage of Tk. 150 and earns a commission of 25% on all sales he makes. How much taka worth of sales does he need to make in order to bring his total daily income of Tk. 1000?

Solution: 
দৈনিক মোট আয় করতে হবে = 1000 টাকা
দৈনিক মজুরি = 150 টাকা 

∴ অবশিষ্ট = (1000 - 150) টাকা 
= 850 টাকা 

25% সেলস কমিশন = 850 টাকা 
1% সেলস কমিশন = 850/25 টাকা 
∴ 100% সেলস কমিশন = (850 × 100)/25 টাকা
= 3400 টাকা
৩০৬.
The contents of a certain box consist of 14 apples and 23 oranges. How many oranges must be removed from the box so that 70% of the pieces of fruit in the box will be apples ?
  1. ক
    ক) 6
  2. খ
    খ) 12
  3. গ
    গ) 17
  4. ঘ
    ঘ) 36
সঠিক উত্তর: গ
গ) 17
উত্তর
সঠিক উত্তর: গ
গ) 17
গ
ব্যাখ্যা

Total number of fruits = (14 + 23) = 37
Let x oranges be removed.
Then,
70% of (37 - x) = 14
⇒ 7 (37 - x) = 140
⇒ 37 - x = 20
⇒ x = 17

৩০৭.
A man sold his watch at a loss of 5 %. Had he sold it for Tk 56.25 more he would have gained 10%. What was the cost of the watch?
  1. ক
    Taka 375
  2. খ
    Taka 306
  3. গ
    Taka 366
  4. ঘ
    Taka 300
সঠিক উত্তর: ক
Taka 375
উত্তর
সঠিক উত্তর: ক
Taka 375
ক
ব্যাখ্যা
Question: A man sold his watch at a loss of 5 %. Had he sold it for Tk 56.25 more he would have gained 10%. What was the cost of the watch?

Solution:
Let, the price of watch x taka
According to the question,
x(100% - 5%) + 56.25 = x(100% + 10 %)
→ 95%x + 56.25 = 110% x
→ 15%x = 56.25
→ x = (5625/15)
→ x = 375 taka
৩০৮.
A manufacturer marked an article at Tk.50 and sold it allowing 20% discount. If his profit was 25%, then the cost price of the article was-
  1. ক
    Tk.32
  2. খ
    Tk.35
  3. গ
    Tk.37
  4. ঘ
    Tk.40
  5. ঙ
    Tk.35.8
সঠিক উত্তর: ক
Tk.32
উত্তর
সঠিক উত্তর: ক
Tk.32
ক
ব্যাখ্যা

Selling price = 50 - (50 × 20%)
= 50 - 10
= 40
Cost Price = (100/100+25) × 40
= (100/125) × 40
= 32

৩০৯.
A man sells a watch for Tk. 550 and makes a profit of 10%. What was the cost price of the watch?
  1. ক
    600 Taka
  2. খ
    670 Taka
  3. গ
    700 Taka
  4. ঘ
    500 Taka
সঠিক উত্তর: ঘ
500 Taka
উত্তর
সঠিক উত্তর: ঘ
500 Taka
ঘ
ব্যাখ্যা

Question: A man sells a watch for Tk. 550 and makes a profit of 10%. What was the cost price of the watch?

Answer:
Selling Price = 110% of Cost Price
⇒ Cost Price = 550 ÷ 1.1 
= 500

Another Method,
With 10% gain,
The selling price is 110 Taka when the cost price is 100 Taka
∴ The selling price is 1 Taka when the cost price is = 100/110 Taka
∴ The selling price is 550 Taka when the cost price is (100 × 550)/110 Taka 
= 500 Taka

৩১০.
2% of 2 = ?
  1. ক
    ক) 0.0004
  2. খ
    খ) 0.4
  3. গ
    গ) 0.02
  4. ঘ
    ঘ) 0.04
সঠিক উত্তর: ঘ
ঘ) 0.04
উত্তর
সঠিক উত্তর: ঘ
ঘ) 0.04
ঘ
ব্যাখ্যা

2 এর 2% = 2 এর 2/100 = 4/100 = 0.04

৩১১.
An article when sold at a gain of 5% yields Tk. 15 more than when sold at a loss of 5%. Its cost price would be -
  1. ক
    Tk 130
  2. খ
    Tk 150
  3. গ
    Tk 120
  4. ঘ
    Tk 110
  5. ঙ
    Tk 115
সঠিক উত্তর: খ
Tk 150
উত্তর
সঠিক উত্তর: খ
Tk 150
খ
ব্যাখ্যা

At 5% profit, selling price = 100 + 5 = 105 tk
At 5% loss, selling price = 100 - 5 = 95 tk
Difference between selling price = 105 - 95 = 10 tk
When the difference 10, buying price is 100 tk
∴ When the difference is 15, buying price is (100 × 15)/10 tk
= 150 tk

৩১২.
30% of 10 is 10% of which?
  1. ক
    ক) 30
  2. খ
    খ) 60
  3. গ
    গ) 40
  4. ঘ
    ঘ) 600
সঠিক উত্তর: ক
ক) 30
উত্তর
সঠিক উত্তর: ক
ক) 30
ক
ব্যাখ্যা

30% of 10 = 10% of z
⇒(30/100)×10=(10/100)×z
⇒3=z/10
So,z=30

৩১৩.
A person incurs a loss of 5% by selling a watch for Tk. 1,140. At what price should the watch be sold to earn 5% profit ?
  1. ক
    ক) Tk. 1,580
  2. খ
    খ) Tk. 1,180
  3. গ
    গ) Tk. 1,260
  4. ঘ
    ঘ) Tk. 1,225
সঠিক উত্তর: গ
গ) Tk. 1,260
উত্তর
সঠিক উত্তর: গ
গ) Tk. 1,260
গ
ব্যাখ্যা
5% ক্ষতিতে 
বিক্রয়মূল্য 95 টাকা হলে ক্রয়মূল্য 100 টাকা 
বিক্রয়মূল্য 1 টাকা হলে ক্রয়মূল্য 100/95 টাকা 
বিক্রয়মূল্য 1140 টাকা হলে ক্রয়মূল্য (100 × 1140)/95 টাকা 
                                                       = 1200 টাকা 
                 
 5% লাভে 
ক্রয়মূল্য 100 টাকা হলে বিক্রয়মূল্য 105 টাকা 
ক্রয়মূল্য ১ টাকা হলে বিক্রয়মূল্য 105/100 টাকা 
ক্রয়মূল্য ১ টাকা হলে বিক্রয়মূল্য (105 × 1200)/100 টাকা 
                                                    = 1260 টাকা
৩১৪.
Out of 7500 candidates 75% were offered to study in arts and 45% in Business. How many were offered both?
  1. ক
    ক) 1000
  2. খ
    খ) 1750
  3. গ
    গ) 2000
  4. ঘ
    ঘ) 1500
  5. ঙ
    ঙ) 2500
সঠিক উত্তর: ঘ
ঘ) 1500
উত্তর
সঠিক উত্তর: ঘ
ঘ) 1500
ঘ
ব্যাখ্যা

Both offered = (75 + 45)% - 100% = 20%
Numbers of student offered both = 7500 × 20% = 1500

৩১৫.
Badhan has 60 kg of 18% sugar solution. How much sugar should he add to make it 40% sugar solution?
  1. ক
    20 kg
  2. খ
    22 kg
  3. গ
    24 kg
  4. ঘ
    26 kg
সঠিক উত্তর: খ
22 kg
উত্তর
সঠিক উত্তর: খ
22 kg
খ
ব্যাখ্যা
Sugar in solution = 60 × 18/100 = 10.8 kg
Water in solution = 60 - 10.8 = 49.2 kg
In 40% sugar solution, if solution is 100 kg, then sugar is 40  kg and water is 60 kg.
According to the question,
(10.8 + y)/49.2 = 40/60
Therefore, y = 22
৩১৬.
If the ratio of cost price and selling price of an article be 10 : 11, the percentage of profit is-
  1. ক
    ক) 5%
  2. খ
    খ) 10%
  3. গ
    গ) 15%
  4. ঘ
    ঘ) 20%
সঠিক উত্তর: খ
খ) 10%
উত্তর
সঠিক উত্তর: খ
খ) 10%
খ
ব্যাখ্যা
Question: If the ratio of cost price and selling price of an article be 10 : 11, the percentage of profit is-

Solution:
⇒ CP = 10x
⇒ SP = 11x
⇒ Profit = 11x - 10x
              =  x
⇒ Profit% = {x/10x} × 100
               =10%
৩১৭.
A grocer buys some eggs at Tk. 3 each. He finds that 12 of them are broken, but he sells the others at Tk. 4 each and makes a profit of Tk. 96. How many eggs did he buy?
  1. ক
    120
  2. খ
    132
  3. গ
    144
  4. ঘ
    118
সঠিক উত্তর: গ
144
উত্তর
সঠিক উত্তর: গ
144
গ
ব্যাখ্যা
ধরি, মুদি ব্যবসায়ী x টি ডিম কিনেছিল।
প্রশ্নমতে, 4 (x - 12) - 3x = 96
বা, 4x - 48 - 3x = 96
বা,  x = 96 + 48
বা, x = 144
৩১৮.
একটি কলম 11 টাকায় বিক্রি করলে 10% লাভ হয়। কলমটির ক্রয়মূল্য কত?
  1. ক
    9 টাকা
  2. খ
    10 টাকা
  3. গ
    11 টাকা
  4. ঘ
    12 টাকা
সঠিক উত্তর: খ
10 টাকা
উত্তর
সঠিক উত্তর: খ
10 টাকা
খ
ব্যাখ্যা
প্রশ্ন: একটি কলম 11 টাকায় বিক্রি করলে 10% লাভ হয়। কলমটির ক্রয়মূল্য কত?

সমাধান:
10% লাভে,
ক্রয়মূল্য 100 টাকা হলে বিক্রয়মূল্য = 110 টাকা

এখন,
বিক্রয়মূল্য 110 টাকা হলে ক্রয়মূল্য = 100 টাকা
বিক্রয়মূল্য 1 টাকা হলে ক্রয়মূল্য = 100/110 টাকা
বিক্রয়মূল্য 11 টাকা হলে ক্রয়মূল্য = (100 × 11)/110 টাকা
= 10 টাকা
৩১৯.
A shopkeeper sells two items for Tk. 6,000 each, neither gaining nor losing in the overall transaction. If he sold one item at a gain of 20%, what is the cost price of the other item?
  1. ক
    Tk. 7000
  2. খ
    Tk. 5200
  3. গ
    Tk. 8500
  4. ঘ
    Tk. 6800
সঠিক উত্তর: ক
Tk. 7000
উত্তর
সঠিক উত্তর: ক
Tk. 7000
ক
ব্যাখ্যা
Question: A shopkeeper sells two items for Tk. 6,000 each, neither gaining nor losing in the overall transaction. If he sold one item at a gain of 20%, what is the cost price of the other item?

Solution:
প্রথম পণ্যের ক্রয়মূল্য-
ধরি, ক্রয়মূল্য = ১০০ টাকা
২০% লাভে বিক্রয়মূল্য = ১০০ + ২০ = ১২০ টাকা

বিক্রয়মূল্য ১২০ টাকা হলে ক্রয়মূল্য = ১০০ টাকা
বিক্রয়মূল্য ১ টাকা হলে ক্রয়মূল্য = ১০০/১২০ টাকা
বিক্রয়মূল্য ৬০০০ টাকা হলে ক্রয়মূল্য = (১০০ × ৬০০০)/১২০ = ৫০০০ টাকা

আবার,
মোট বিক্রয়মূল্য = ৬০০০ + ৬০০০ = ১২০০০
মোট ক্রয়মূল্য = মোট বিক্রয়মূল্য = ১২০০০ (কারণ কোনো লাভ বা ক্ষতি হয়নি)

∴ অন্য পণ্যের ক্রয়মূল্য = ১২০০০ - ৫০০০ = ৭০০০ টাকা
৩২০.
If 10x equals 0.1 percent of 10y, where x and y are integers, which of the following must be true?
  1. ক
    y = 1000x
  2. খ
    x = 1000y
  3. গ
    y = x + 2
  4. ঘ
    y = x + 3
সঠিক উত্তর: ঘ
y = x + 3
উত্তর
সঠিক উত্তর: ঘ
y = x + 3
ঘ
ব্যাখ্যা
Question: If 10x equals 0.1 percent of 10y, where x and y are integers, which of the following must be true?

Solution:
ATQ,
10x = 0.1% × 10y
⇒ 10x = (0.1/100) × 10y
⇒ 10x = 0.001 × 10y
⇒ 10x = 1 × 10y - 3
⇒ 10x = 10y - 3
⇒ x = y - 3
∴ y = x + 3
৩২১.
Joni buys a 40 tk shares in a company, which pays 10% dividend. Joni buys the share at such a price that his profit is 16% on his investment. At what price did Joni buy the share?
  1. ক
    ক) 20 tk
  2. খ
    খ) 22 tk
  3. গ
    গ) 24 tk
  4. ঘ
    ঘ) 25 tk
সঠিক উত্তর: ঘ
ঘ) 25 tk
উত্তর
সঠিক উত্তর: ঘ
ঘ) 25 tk
ঘ
ব্যাখ্যা
Question: Joni buys a 40 tk shares in a company, which pays 10% dividend. Joni buys the share at such a price that his profit is 16% on his investment. At what price did Joni buy the share?

Solution: 
Dividend (profit) given by the company on 1 share = 10% of  40 = 4 tk.

Suppose the man buys one share for x.

Therefore, Joni’s profit = 16% of  x = 16x/100
According to the problem, 16x/100 = 4
⟹ x = 25

Joni bought the share at  25 tk.
৩২২.
Jamal started a business investing Tk. 9000. After five months, Sakib joined with a capital of Tk. 8000. If at the end of the year, they earn a profit of Tk. 6970, then what will be the share of Sakib in the profit?
  1. ক
    Tk. 2280
  2. খ
    Tk. 2180
  3. গ
    Tk. 2350
  4. ঘ
    Tk. 2380
সঠিক উত্তর: ঘ
Tk. 2380
উত্তর
সঠিক উত্তর: ঘ
Tk. 2380
ঘ
ব্যাখ্যা
Question: Jamal started a business investing Tk. 9000. After five months, Sakib joined with a capital of Tk. 8000. If at the end of the year, they earn a profit of Tk. 6970, then what will be the share of Sakib in the profit?

Solution: 
Jamal invested for 12 months and Sakib invested for 7 months.

So Jamal : Sakib = (9000 × 12) : (8000 × 7)
= 108 : 56
= 27 : 14

∴ Sakib Ratio in profit will be
= 6970 × 14/41
= Tk. 2380
৩২৩.
Azim sells an object to Belal at a profit of 15%, Belal sells that object to karim for Tk. 1012 and makes a profit of 10%. At what cost did Azim purchase the object?
  1. ক
    Tk. 950
  2. খ
    Tk. 900
  3. গ
    Tk. 850
  4. ঘ
    Tk. 800
সঠিক উত্তর: ঘ
Tk. 800
উত্তর
সঠিক উত্তর: ঘ
Tk. 800
ঘ
ব্যাখ্যা
Question: Azim sells an object to Belal at a profit of 15%, Belal sells that object to karim for Tk. 1012 and makes a profit of 10%. At what cost did Azim purchase the object?

Solution:
Let the actual cost price at which Azim bought the object be x
When Azim sells the object to Belal
Profit % = 15%
∴ selling price of object = [(100 + 15)/100] × x = 1.15x

Now, this cost price of the object for Belal
When Belal sells the object to karim
Selling Price = Tk. 1012
Profit % = 10%
∴ Selling price = [(100 + 10)/100] × 1.15x
⇒ 1012 = [(100 + 10)/100] × 1.15x
⇒ x = (1012 × 1000)/(11 × 115)
∴ x = 800
Therefore, the price at which Azim bought the object is Tk. 800.
৩২৪.
There were 1000 students in a school in 2024. In 2025, 5% of the male students left, and 15% new female students joined the school. But the total number of students remained unchanged. How many female students were in the school in 2024?
  1. ক
    200
  2. খ
    225
  3. গ
    250
  4. ঘ
    275
  5. ঙ
    300
সঠিক উত্তর: গ
250
উত্তর
সঠিক উত্তর: গ
250
গ
ব্যাখ্যা

Question: There were 1000 students in a school in 2024. In 2025, 5% of the male students left, and 15% new female students joined the school. But the total number of students remained unchanged. How many female students were in the school in 2024?

Solution:
ধরি, 2024 সালে ছাত্রীর সংখ্যা ছিল x 
এবং ছাত্রের সংখ্যা ছিল (1000 - x)
প্রশ্ন অনুযায়ী, 2025 সালে ছাত্রীর সংখ্যা বৃদ্ধি পায় 15% এবং ছাত্রের সংখ্যা হ্রাস পায় 5%। কিন্তু মোট ছাত্রছাত্রীর সংখ্যা অপরিবর্তিত থাকে।

প্রশ্নমতে,
(x + x এর 15%) + {(1000 - x) - (1000 - x) এর 5%} = 1000
⇒ x + (15x/100) + (1000 - x) - {5(1000 - x)/100} = 1000
⇒ 15x/100 - 5(1000 - x)/100 = 0
⇒ 15x - 5(1000 - x) = 0
⇒ 15x - 5000 + 5x = 0
⇒ 20x = 5000
⇒ x = 5000/20
⇒ x = 250

সুতরাং, 2024 সালে স্কুলে ছাত্রীর সংখ্যা ছিল 250 জন।

৩২৫.
A seller marks his goods 30% above their cost price but allows 15% discount for cash payment. His percentage of profit when sold in cash is 
  1. ক
    ক) 15%
  2. খ
    খ) 9%
  3. গ
    গ) 10.5%
  4. ঘ
    ঘ) 8.5%
সঠিক উত্তর: গ
গ) 10.5%
উত্তর
সঠিক উত্তর: গ
গ) 10.5%
গ
ব্যাখ্যা
ধরি,
বিক্রেতার ক্রয়মূল্য x  টাকা 
তালিকা মূল্য = x + x  এর 30 % 
                     = x + 30x/100
                      = 130x/100
                      = 13x/10
15%  ছাড়ে,
বিক্রয়মূল্য = 13x/10 - 13x/10 এর 15% 
                  = 13x/10 - (13x × 15)/(10×100) 
                  = 13x/10  - 39x/200
                  = 260x - 39x/ 200 
                   = 221x/200 
 লাভ = 221x/200 - x 
        = 221sx - 200x/ 200 
         = 21x/200 

 শতকরা লাভ হয় = (21x/200)/x 100%
                            = (21x/200 ×1/x 100)%
                             = 10.5%
৩২৬.
Fresh grapes contain 80 percent water while dry grapes contain 10 percent water. If the weight of the dry grapes is 350 kg what is total weight when it was fresh?
  1. ক
    1225 kg
  2. খ
    1475 kg
  3. গ
    1545 kg
  4. ঘ
    1575 kg
সঠিক উত্তর: ঘ
1575 kg
উত্তর
সঠিক উত্তর: ঘ
1575 kg
ঘ
ব্যাখ্যা
Question: Fresh grapes contain 80 percent water while dry grapes contain 10 percent water. If the weight of the dry grapes is 350 kg what is total weight when it was fresh?

Solution:
Quantity of water in 350 kg dry grapes = 350 × (10/100)
= 35 kg
Then, pulp of grapes = (350 - 35) kg = 315 kg.

We get 20 kg pulp in 100 kg fresh grapes
To get 315 kg pulp, we need fresh grapes = (100 × 315)/20 kg
= 1575 kg.
৩২৭.
What is the difference between 0.6 and 0.6%?
  1. ক
    0.594
  2. খ
    5.94
  3. গ
    54
  4. ঘ
    60
সঠিক উত্তর: ক
0.594
উত্তর
সঠিক উত্তর: ক
0.594
ক
ব্যাখ্যা
Question: What is the difference between 0.6 and 0.6%?

Solution: 
Difference = 0.6 - 0.6%
= 0.6 - 0.006
= 0.594
৩২৮.
A reduction of 20% in the price of potato enables a dealer to purchase 25 kg more potato for TK. 25000. What is the reduced price per kg of potato?
  1. ক
    220 TK.
  2. খ
    200 TK.
  3. গ
    270 TK.
  4. ঘ
    300 TK.
সঠিক উত্তর: খ
200 TK.
উত্তর
সঠিক উত্তর: খ
200 TK.
খ
ব্যাখ্যা

Question: A reduction of 20% in the price of potato enables a dealer to purchase 25 kg more potato for TK. 25000. What is the reduced price per kg of potato?

Solution:
Let, the original price of potato be TK.x kg
After reduction the price becomes = x − 20% of x = (4x/5) per kg
Now,
25000/(4x/5) − 25000/x = 25
or, 25000 × (5/4x) - (25000/x) = 25
or, (31250/x) - (25000/x) = 25
or, (31250 - 25000)/x = 25
or, 6250/x = 25
or, x = 6250/25
∴ x = 250 Tk.
Hence, new price = (4 × 250)/5 = 200 TK.  per kg 

৩২৯.
A sells an article to B at a profit of 10% B sells the article back to A at a loss of 10%. In this transaction -
  1. ক
    makes a profit of 25%
  2. খ
    A neither losses nor gains
  3. গ
    A makes a profit of 11%
  4. ঘ
    B loses 15%
সঠিক উত্তর: গ
A makes a profit of 11%
উত্তর
সঠিক উত্তর: গ
A makes a profit of 11%
গ
ব্যাখ্যা

Question: A sells an article to B at a profit of 10% B sells the article back to A at a loss of 10%. In this transaction -

Solution:
Let CP was 100 for A originally
A sells article to B at 10% profit,
CP for B = 100 + 10% of 100 = 110
Now, B sells it A again with loss 10%
Now, CP for A this time = 110 - 10% of 110 = 99
A makes Profit = 110 - 99 = 11

∴ %profit for A = (11 × 100)/100 = 11%

৩৩০.
Rahim borrowed Tk. 800 at 6% per annum and Karim borrowed Tk. 600 at 10% per annum. After how much time, will they both have equal debts?
  1. ক
    ক) 50/3 yr
  2. খ
    খ) 83/3 yr
  3. গ
    গ) 44/3 yr
  4. ঘ
    ঘ) 20/3 yr
সঠিক উত্তর: ক
ক) 50/3 yr
উত্তর
সঠিক উত্তর: ক
ক) 50/3 yr
ক
ব্যাখ্যা
Question: Rahim borrowed Tk. 800 at 6% per annum and Karim borrowed Tk. 600 at 10% per annum. After how much time, will they both have equal debts? 

Solution: 
ধরি,
ক বছর পর তাদের টাকা মুনাফা আসলে একই হবে।

ক বছরে রহিমের মুনাফা আসল = ৮০০ + {(৮০০ × ক × ৬)/১০০}
ক বছরে করিমের মুনাফা আসল = ৬০০ +{(৬০০ × ক × ১০)/১০০}

প্রশ্নমতে,
৮০০ + {(৮০০ × ক × ৬)/১০০} = ৬০০ +{(৬০০ × ক × ১০)/১০০}
৮০০ + ৪৮ক = ৬০০ + ৬০ক
৬০ক - ৪৮ক = ৮০০ - ৬০০
১২ক = ২০০
ক = ২০০/১২
= ৫০/৩ বছর
৩৩১.
A man paid tax on 12000 Taka at the rate of 20%. He paid the tax in 10 equal payments. what is the amount of each payment?
  1. ক
    Tk. 220
  2. খ
    Tk. 240
  3. গ
    Tk. 280
  4. ঘ
    Tk. 290
সঠিক উত্তর: খ
Tk. 240
উত্তর
সঠিক উত্তর: খ
Tk. 240
খ
ব্যাখ্যা

Question: A man paid tax on 12000 Taka at the rate of 20%. He paid the tax in 10 equal payments. what is the amount of each payment?

Solution:
100 টাকায় কর দেয় = 20 টাকা
∴ 1 টাকায় কর দেয় = 20/100 = 1/5 টাকা
∴ 12000 টাকায় কর দেয় (20× 12000)/100 = 2400 টাকা

∴ মোট কর = 2400 টাকা

10টি সমান কিস্তিতে পরিশোধ করে।

∴ প্রতি কিস্তিতে পরিশোধ = 2400/10 = 240 টাকা

৩৩২.
A train ticket price increased from Tk. 45 to Tk. 60. What is the approximate percentage increase? 
  1. ক
    20%
  2. খ
    33%
  3. গ
    12%
  4. ঘ
    37%
সঠিক উত্তর: খ
33%
উত্তর
সঠিক উত্তর: খ
33%
খ
ব্যাখ্যা

Question: A train ticket price increased from Tk. 45 to Tk. 60. What is the approximate percentage increase?

Solution:
Increase in ticket price = 60 - 45 = Tk. 15

Percentage increase = (15/45) × 100%
= (1/3) × 100%
= 33.33%
≈ 33%

∴ The approximate percentage increase is 33%.

৩৩৩.
The cost of 21 pencils and 9 clippers is Tk. 819. The cost price of 7 pencils and 3 clippers is = ?
  1. ক
    ক) Tk. 204
  2. খ
    খ) Tk. 223
  3. গ
    গ) Tk. 409
  4. ঘ
    ঘ) Tk. 273
  5. ঙ
    ঙ) Tk. 208
সঠিক উত্তর: ঘ
ঘ) Tk. 273
উত্তর
সঠিক উত্তর: ঘ
ঘ) Tk. 273
ঘ
ব্যাখ্যা

Cost of 21 pencils and 9 clippers = Tk. 819
Cost of 7 pencils and 3 clippers = 819/3 = Tk. 273

৩৩৪.
If the price of a commodity increased by 50% by what fraction must its consumption be reduced so as to keep the same expenditure on its consumptions?
  1. ক
    ক) 1/4
  2. খ
    খ) 1/3
  3. গ
    গ) 1/2
  4. ঘ
    ঘ) 1/6
  5. ঙ
    ঙ) 1/5
সঠিক উত্তর: খ
খ) 1/3
উত্তর
সঠিক উত্তর: খ
খ) 1/3
খ
ব্যাখ্যা

r = 50
So consumption should reduced = (r/100+r) × 100
= (50/150) × 100
= 33.33% that means 1/3

৩৩৫.
A lead ore mine contains 50% metal. Of this metal, 4/5% is gold and the remainder is lead. If 6000 kg of ore is extracted, what is the mass of the lead?
  1. ক
    1576 kg
  2. খ
    1976 kg
  3. গ
    276 kg
  4. ঘ
    2976 kg
সঠিক উত্তর: ঘ
2976 kg
উত্তর
সঠিক উত্তর: ঘ
2976 kg
ঘ
ব্যাখ্যা

Question: A lead ore mine contains 50% metal. Of this metal, 4/5% is gold and the remainder is lead. If 6000 kg of ore is extracted, what is the mass of the lead?

Solution:
Given mass of lead ore = 6000 kg 

The mass of metal is 50% of 6000 = 3000 kg 
∴ Mass of gold is 4/5% of 3000
= (4 × 3000)/(5 × 100)
= 24 kg 

∴ Mass of lead = Mass of metal - Mass of gold
= 3000 - 24 
= 2976 kg

৩৩৬.
একজন ব্যবসায়ী ৮০ টাকায় একটি পণ্য বিক্রয় করে ২৫% লাভ করে। ব্যয় ও বিক্রয় মূল্যের অনুপাত কত?
  1. ক
    ক) ৩ : ৮
  2. খ
    খ) ৪ : ৫
  3. গ
    গ) ৫ : ৬
  4. ঘ
    ঘ) ২ : ৩
সঠিক উত্তর: খ
খ) ৪ : ৫
উত্তর
সঠিক উত্তর: খ
খ) ৪ : ৫
খ
ব্যাখ্যা
প্রশ্ন: একজন ব্যবসায়ী ৮০ টাকায় একটি পণ্য বিক্রয় করে ২৫% লাভ করে। ব্যয় ও বিক্রয় মূল্যের অনুপাত কত?

সমাধান: 
এখানে ব্যয় বলতে ব্যবসায়ীর ক্রয় মূল্যকে বুঝানো হয়েছে। 

২৫% লাভে,
বিক্রয় মূল্য ১২৫ টাকা হলে ক্রয় মূল্য ১০০ টাকা 
বিক্রয় মূল্য ৮০ টাকা হলে ক্রয় মূল্য (১০০ × ৮০)/১২৫ টাকা 
= ৬৪ টাকা 

∴ ব্যয় : বিক্রয় মূল্য = ৬৪ : ৮০
= ৮ : ১০
= ৪ : ৫
৩৩৭.
A shopkeeper marks his goods 20% above cost price, but allows 30% discount for cash payment. His net loss is?
  1. ক
    13%
  2. খ
    15%
  3. গ
    16%
  4. ঘ
    18%
সঠিক উত্তর: গ
16%
উত্তর
সঠিক উত্তর: গ
16%
গ
ব্যাখ্যা
Let the cost price of goods = Tk. 100
Market price of goods = 120% of 100  
                                     = 120/100×100
                                     = Tk. 120
At 30% discount for cash payment, real price = (100 - 30)% = 70%
After discount selling price of goods
= 70% of 120
= Tk. 84
Loss = Tk. (100 − 84) = Tk. 16
Loss % = (16/100) × 100 = 16%
৩৩৮.
What percentage of numbers from 1 to 70 have squares that end in the digit 1?
  1. ক
    14
  2. খ
    12
  3. গ
    20
  4. ঘ
    21
সঠিক উত্তর: গ
20
উত্তর
সঠিক উত্তর: গ
20
গ
ব্যাখ্যা
Question: What percentage of numbers from 1 to 70 have squares that end in the digit 1?

Solution:
The numbers from 1 to 70 that have their squares ending in digit 1 are
1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69
Total 14 in numbers 
∴ Required percentage = (14/70) × 100 = 20%
৩৩৯.
In an election involving two candidates, 60 votes were declared invalid. The winning secures 53% and wins by 90 votes. The total number of votes polled is -
  1. ক
    ক) 1440
  2. খ
    খ) 1500
  3. গ
    গ) 1560
  4. ঘ
    ঘ) 1620
সঠিক উত্তর: গ
গ) 1560
উত্তর
সঠিক উত্তর: গ
গ) 1560
গ
ব্যাখ্যা
Question: In an election involving two candidates, 60 votes were declared invalid. The winning secures 53% and wins by 90 votes. The total number of votes polled is -

Solution:
Let the number of valid votes be x.

ATQ,
53% of x - 47% of x = 90
⇒ 6% of x = 90
⇒ 6x/100 = 90
⇒ 6x = 9000
⇒ x = 1500

So, the total number of votes polled = 1500 + 60 = 1560
৩৪০.
A shopkeeper marks his items 40% above the cost price and then gives a 20% discount on the marked price. What is his gain percentage?
  1. ক
     11%
  2. খ
     10%
  3. গ
     22%
  4. ঘ
     12%
সঠিক উত্তর: ঘ
 12%
উত্তর
সঠিক উত্তর: ঘ
 12%
ঘ
ব্যাখ্যা

Question: A shopkeeper marks his items 40% above the cost price and then gives a 20% discount on the marked price. What is his gain percentage?

Solution:
Let,
the cost price (CP) be Tk. 100

Marked Price = 40% more than cost price
= 100 + 40
= 140 Tk.

Discount = 20% of 140
= (20/100) ​× 140
= 28 Tk.

Selling Price (SP)= 140 - 28 = 112 Tk.

∴ Profit = SP - CP = 112 - 100 = 12 Tk.

∴ Gain percent = 12%

৩৪১.
A book marked at Tk. 80 is sold for Tk. 64. The rate of discount is-
  1. ক
    ক) 12%
  2. খ
    খ) 15%
  3. গ
    গ) 20%
  4. ঘ
    ঘ) 25%
সঠিক উত্তর: গ
গ) 20%
উত্তর
সঠিক উত্তর: গ
গ) 20%
গ
ব্যাখ্যা
Discount = 80 - 64
               = 16
Discount Rate = (16/80) × 100
                       = 20%
৩৪২.
The percentage profit earned by selling an article for Tk. 1920 is equal to the percentage loss by selling the same article for Tk. 1280. At what price should the article be sold to make 25% profit?
  1. ক
    Tk 2100
  2. খ
    Tk 1900
  3. গ
    Tk 2000
  4. ঘ
    None of the above
সঠিক উত্তর: গ
Tk 2000
উত্তর
সঠিক উত্তর: গ
Tk 2000
গ
ব্যাখ্যা
Question: The percentage profit earned by selling an article for Tk. 1920 is equal to the percentage loss by selling the same article for Tk. 1280. At what price should the article be sold to make 25% profit?

Solution:
Let the cost price of the article be C.
From the given problem, the percentage profit made by selling the article for Tk. 1920 is equal to the percentage loss incurred by selling the article for Tk. 1280. This can be expressed as:
{(1920 - C)/C​} × 100 = {(C - 1280)/C} ​×100
⇒ 1920 - C = C - 1280
⇒ 1920 + 1280 = 2C
⇒ 3200 = 2C
∴ C = 1600

Now, to make a 25% profit, the selling price should be:
Selling Price = C + (25/100) × C = 1600 + (25/100) ×1600 = 1600 + 400 = 2000
৩৪৩.
The sale price of an article including the Sales Tax is Tk. 616. The rate of Sales Tax is 10%. If the shopkeeper has made a profit of 12%, then the cost price of the article is-
  1. ক
    ক) Tk. 600
  2. খ
    খ) Tk. 550
  3. গ
    গ) Tk. 500
  4. ঘ
    ঘ) Tk. 400
সঠিক উত্তর: গ
গ) Tk. 500
উত্তর
সঠিক উত্তর: গ
গ) Tk. 500
গ
ব্যাখ্যা
Question: The sale price of an article including the Sales Tax is Tk. 616. The rate of Sales Tax is 10%. If the shopkeeper has made a profit of 12%, then the cost price of the article is-

Solution:
Let,
Cost price be x.
Selling price = x + 12% of x
= x + (12x/100)
= 28x/25

ATQ,
(28x/25) + 10% of (28x/25) = 616
⇒ (28x/25) + (280x/2500) = 616
⇒ (28x/25) + (14x/125) = 616
⇒ (140x + 14x)/125 = 616
⇒ 154x = 77000
∴ x = 500

∴ Cost price tk. 500.
৩৪৪.
If the price of a commodity is decreased by 20% and its consumption is increased by 20%, what will be the increase or decrease in expenditure on the commodity?
  1. ক
    4% increase
  2. খ
    4% decrease
  3. গ
    8% increase
  4. ঘ
    8% decrease
সঠিক উত্তর: খ
4% decrease
উত্তর
সঠিক উত্তর: খ
4% decrease
খ
ব্যাখ্যা
Question: If the price of a commodity is decreased by 20% and its consumption is increased by 20%, what will be the increase or decrease in expenditure on the commodity?

Solution:
Let,
The initial expenditure on the commodity be Tk. 100.
Now, the price decreases by 20%,
∴ Current Price = (100 - 20% of 100) = Tk. 80.

Same time due to decrements in price 20% consumption has been increased.
So, Current expenses on commodity = (80 + 20% of 80) = Tk. 96.

Here,
The initial expenditure was Tk. 100 which became Tk. 96 at the end, it means there is 4% decrements in the expenditure of the commodity.
৩৪৫.
A trader dealing in pressure cookers reduced the price by 20% as a result of which his sale went up by 80%. What is the net effect of his sales income?
  1. ক
    ক) 44% decrease
  2. খ
    খ) 44% increase
  3. গ
    গ) 64% increase
  4. ঘ
    ঘ) 66% increase
সঠিক উত্তর: খ
খ) 44% increase
উত্তর
সঠিক উত্তর: খ
খ) 44% increase
খ
ব্যাখ্যা
Question: A trader dealing in pressure cookers reduced the price by 20% as a result of which his sale went up by 80%. What is the net effect of his sales income?

Solution: 
ধরি, দাম কমানোর আগে x টি প্রেশার কুকার বিক্রি হতো ও প্রত্যেকটির দাম = y টাকা 
মোট বিক্রয়মূল্য = xy টাকা 

দাম কমানোর পরে, প্রেশার কুকার বিক্রি হয় = x + x এর 80%
= x + (80x/100)
= x + (4x/5)
= 9x/5

প্রত্যেকটির দাম = y - y এর 20%
= y - (20y/100)
= y - (y/5)
= 4y/5

মোট বিক্রয়মূল্য = (9x/5) × (4y/5)
= 36xy/25

লাভ = (36xy/25) - xy
= (36 - 25)xy/25
= 11xy/25

∴ শতকরা লাভ = (11xy/25xy) × 100%
= 44%
৩৪৬.
40% of 200 is what percent of 160?
  1. ক
    ক) 20
  2. খ
    খ) 80
  3. গ
    গ) 60
  4. ঘ
    ঘ) 50
সঠিক উত্তর: ঘ
ঘ) 50
উত্তর
সঠিক উত্তর: ঘ
ঘ) 50
ঘ
ব্যাখ্যা
160 × x/100 = 200 × 40%
=> 8x/5 = 80
=> 8x = 400
=> x = 50
৩৪৭.
Jakaria's present salary is Tk. 3500. It will increase by 10% next year. What will be Jakaria's salary after the increment?
  1. ক
    Tk. 3800
  2. খ
    Tk. 3850
  3. গ
    Tk. 3890
  4. ঘ
    Tk. 4150
  5. ঙ
    None of the above
সঠিক উত্তর: খ
Tk. 3850
উত্তর
সঠিক উত্তর: খ
Tk. 3850
খ
ব্যাখ্যা
Question: Jakaria's present salary is Tk. 3500. It will increase by 10% next year. What will be Jakaria's salary after the increment?

Solution:
Here, Jakaria's present salary = Tk. 3500

Salary is increased by 10%

Hence, the increased salary of Jakaria
= (3500 × 110)/100
= 3850

∴ Jakaria's salary after the increment will be Tk. 3850
৩৪৮.
A machine making cost is Tk 2000, sold with two successive discounts of 20% and 10%. An additional discount of 5% is offered for cash payment. What is the total loss in the selling price of the machine at cash payment?
  1. ক
    632 Tk
  2. খ
    540 Tk
  3. গ
    426 Tk
  4. ঘ
    None of the above
সঠিক উত্তর: ক
632 Tk
উত্তর
সঠিক উত্তর: ক
632 Tk
ক
ব্যাখ্যা
Question: A machine making cost is Tk 2000, sold with two successive discounts of 20% and 10%. An additional discount of 5% is offered for cash payment. What is the total loss in the selling price of the machine at cash payment?
 
Solution:
Making price = 2000 Tk
Selling Price after first Discount of 20% = 2000 - 20% of 2000
= 2000 - {(20/100) × 2000}
= 1600 Tk

The selling price after the second Discount of 10% = 1600 - 10% of 1600
= 1600 - {(10/100) × 1600
= 1440 Tk

∴ The final selling price at cash = 1440 - 5% of 1440
= 1440 - {(5/100) × 1440}
= 1368 Tk

Total loss = 2000 - 1368 = 632 Tk
৩৪৯.
1.14 expressed as a per cent of 1.9 is:
  1. ক
    45%
  2. খ
    60%
  3. গ
    72%
  4. ঘ
    65%
সঠিক উত্তর: খ
60%
উত্তর
সঠিক উত্তর: খ
60%
খ
ব্যাখ্যা
Required Percentage = 1.14 × 100/1.9 = 60%
৩৫০.
Sumon sells a mobile phone to Tania at a profit of 20%. Tania then sells that phone to Rafi for Tk. 1800, making a profit of 25%. At what price did Sumon purchase the mobile phone?
  1. ক
    Tk. 1200
  2. খ
    Tk. 1000
  3. গ
    Tk. 1600
  4. ঘ
    Tk. 1400
সঠিক উত্তর: ক
Tk. 1200
উত্তর
সঠিক উত্তর: ক
Tk. 1200
ক
ব্যাখ্যা

প্রশ্ন: Sumon sells a mobile phone to Tania at a profit of 20%. Tania then sells that phone to Rafi for Tk. 1800, making a profit of 25%. At what price did Sumon purchase the mobile phone?

সমাধান:
২৫% লাভে,
তানিয়ার বিক্রয়মূল্য ১২৫ টাকা হলে ক্রয়মূল্য ১০০ টাকা
∴ তানিয়ার বিক্রয়মূল্য ১ টাকা হলে ক্রয়মূল্য ১০০/১২৫ টাকা
∴ তানিয়ার বিক্রয়মূল্য ১৮০০ টাকা হলে ক্রয়মূল্য (১০০ × ১৮০০)/১২৫ টাকা
= ১৪৪০ টাকা

এখানে,
তানিয়ার ক্রয়মূল্য = সুমনের বিক্রয়মূল্য

২০% লাভে,
সুমনের বিক্রয়মূল্য ১২০ টাকা হলে ক্রয়মূল্য = ১০০ টাকা
∴ সুমনের বিক্রয়মূল্য ১ টাকা হলে ক্রয়মূল্য = ১০০/১২০ টাকা
∴ সুমনের বিক্রয়মূল্য ১৪৪০ টাকা হলে ক্রয়মূল্য = (১০০ × ১৪৪০)/১২০ = ১২০০ টাকা

 ∴ সুমনের-এর ক্রয়মূল্য = ১২০০ টাকা

৩৫১.
P scored 30% marks and failed by 15 marks. Q scored 45% marks and obtained 30 marks more than the pass marks. What is the pass percentage?
  1. ক
    28%
  2. খ
    35%
  3. গ
    25%
  4. ঘ
    22%
সঠিক উত্তর: খ
35%
উত্তর
সঠিক উত্তর: খ
35%
খ
ব্যাখ্যা

Question: P scored 30% marks and failed by 15 marks. Q scored 45% marks and obtained 30 marks more than the pass marks. What is the pass percentage?

Solution:
Let the total marks be x.

Given,
P scored 30% marks and failed by 15 marks:
0.30x + 15 = Pass marks
Q scored 45% marks and obtained 30 marks more than pass marks:
0.45x - 30 = Pass marks

Now,
0.30x + 15 = 0.45x - 30
⇒ 0.45x - 0.30x = 15 + 30
⇒ 0.15x = 45
⇒ x = 45/0.15
∴ x = 300

Pass marks = 0.30 × 300 + 15
= 90 + 15 = 105

∴ Pass percentage = (105/300) × 100% = 35%

৩৫২.
Last year Parimal saved 10 percent of his annual earnings. This year he earned 5 percent more than last year and he saved 12 percent of his annual earnings. The amount saved this year was what percent of the amount saved last year?
  1. ক
    122%
  2. খ
    124%
  3. গ
    126%
  4. ঘ
    128%
  5. ঙ
    130%
সঠিক উত্তর: গ
126%
উত্তর
সঠিক উত্তর: গ
126%
গ
ব্যাখ্যা
Question: Last year Parimal saved 10 percent of his annual earnings. This year he earned 5 percent more than last year and he saved 12 percent of his annual earnings. The amount saved this year was what percent of the amount saved last year?

Solution:
Let,
Last Year
Earnings = 100
Amount saved = 10% of 100 = 0.1 × 100 = 10

This Year
Earnings = 100 + 5% 0f 100 = 100 + (0.05 ×100) = 100 + 5 = 105
Amount saved = 12% of 105 = 0.12 × 105 = 12.6

The amount saved this year as a percent of the amount saved last year is ⇒ (this year)/(last year) × 100 = (12.6/10)× 100% =126%.
৩৫৩.
How many litres of a 30% alcohol solution should be added to 40 litres of a 60% alcohol solution to prepare a 50% solution?
  1. ক
    ক) 30
  2. খ
    খ) 28
  3. গ
    গ) 20
  4. ঘ
    ঘ) 24
সঠিক উত্তর: গ
গ) 20
উত্তর
সঠিক উত্তর: গ
গ) 20
গ
ব্যাখ্যা
Question: How many litres of a 30% alcohol solution should be added to 40 litres of a 60% alcohol solution to prepare a 50% solution?

Solution:
Let,
x litres of 30% alcohol solution be added.

ATQ,
30% of x + 60% of 40 = 50% of (x + 40)
⇒ (30x/100) + (60 × 40)/100 = 50 × (x + 40)/100
⇒ (30x + 2400)/100 = (50x + 2000)/100
⇒ 30x + 2400 = 50x + 2000
⇒ 50x - 30x = 2400 - 2000
⇒ 20x = 400
∴ x = 20
৩৫৪.
Half percent, written as a decimal, is -
  1. ক
    ক) 0.5
  2. খ
    খ) 0.05
  3. গ
    গ) 0.005
  4. ঘ
    ঘ) 0.0005
সঠিক উত্তর: গ
গ) 0.005
উত্তর
সঠিক উত্তর: গ
গ) 0.005
গ
ব্যাখ্যা
Question: Half percent, written as a decimal, is - 

Solution:
As we know,
1% = 1/100

Hence,
1/2% = 1/2 × 1/100 = 1/200 = 0.005
৩৫৫.
List price of a book is Tk. 100. A dealer sells three such books for Tk. 274.50 after allowing discount at a certain rate, find the rate of discount = ?
  1. ক
    ক) 8.33%
  2. খ
    খ) 8.16%
  3. গ
    গ) 8.50%
  4. ঘ
    ঘ) 8.34%
সঠিক উত্তর: গ
গ) 8.50%
উত্তর
সঠিক উত্তর: গ
গ) 8.50%
গ
ব্যাখ্যা

Given,
= MRP of book = Tk. 100
= Selling price of 3 books = Tk. 274.50
= Selling price of 1 book = Tk. 91.50
Discount on each book
= 100 - 91.50 = Tk. 8.50
Therefore discount %
=8.50/100×100%
=8.50%

৩৫৬.
Three individuals contributed Tk. 9000 each toward the purchase of television. If they bought the television on sale for Tk. 22000 plus 8% sales tax, how much money should be refunded to each individual?
  1. ক
    Tk 1080
  2. খ
    Tk 880
  3. গ
    Tk 700
  4. ঘ
    Tk 1200
সঠিক উত্তর: ক
Tk 1080
উত্তর
সঠিক উত্তর: ক
Tk 1080
ক
ব্যাখ্যা
Question: Three individuals contributed Tk. 9000 each toward the purchase of television. If they bought the television on sale for Tk. 22000 plus 8% sales tax, how much money should be refunded to each individual?

Solution:
Three individuals contributed Tk 9000 each,
So the total contribution of=  9000 × 3 = 27000

∴ The sales tax is 8% of Tk 22000 is = 22000 × (8/100) = 1760

∴  The total cost of the television, including tax, is
= 22000 +1760
= 23760

∴  Excess Money = 27000 − 23760 = 3240
∴  Refund per individual = 3240​/3 = 1080

So Each individual should be refunded Tk 1080.
৩৫৭.
250 candidates appeared for an examination, of which 50 failed. The pass percentage is-
  1. ক
    20% 
  2. খ
    40% 
  3. গ
    60% 
  4. ঘ
    80% 
সঠিক উত্তর: ঘ
80% 
উত্তর
সঠিক উত্তর: ঘ
80% 
ঘ
ব্যাখ্যা
Question: 250 candidates appeared for an examination, of which 50 failed. The pass percentage is- 

Solution: 
Pass = 250 - 50 = 200

pass percentage = (200/250) × 100% 
 = 80% 
৩৫৮.
By selling 33 meters of cloth, one gains the selling price of 11 meters. Find the gain percent.
  1. ক
    50%
  2. খ
    45%
  3. গ
    40%
  4. ঘ
    60%
সঠিক উত্তর: ক
50%
উত্তর
সঠিক উত্তর: ক
50%
ক
ব্যাখ্যা
Question: By selling 33 meters of cloth, one gains the selling price of 11 meters. Find the gain percent.

Solution:
Gain = (SP of 33 m) - (CP of 33 m) = SP of 11m
⇒ SP of 22m = CP of 33m

Let
CP of each meter be Tk 1.
Then,
CP of 22 m = Tk. 22.
CP of 33 m = Tk. 33

Hence, SP of 22m = Tk. 33
∴ Gain = 33 - 22 = Tk. 11

∴ %Gain = (11/22) × 100
= 50%
৩৫৯.
Due to a 25% increase in the price of salt, a person got 10kg less quantity for Tk. 500 than he was getting before the increase. What was the initial price per kg of salt in Taka?
  1. ক
    Tk. 15
  2. খ
    Tk. 10
  3. গ
    Tk. 5
  4. ঘ
    Tk. 20
সঠিক উত্তর: খ
Tk. 10
উত্তর
সঠিক উত্তর: খ
Tk. 10
খ
ব্যাখ্যা
Question: Due to a 25% increase in the price of salt, a person got 10kg less quantity for Tk. 500 than he was getting before the increase. What was the initial price per kg of salt in Taka?

Solution:
25% বৃদ্ধিতে পূ‍‍র্বমূল্য 100 টাকা হলে ব‍‍র্তমান মূল্য 125 টাকা
∴ পূ‍‍র্বমূল্য 500 টাকা হলে ব‍‍র্তমান মূল্য (125 × 500)/100 টাকা
= 625 টাকা

10kg লবণের ব‍‍র্তমান মূল্য = (625 - 500) = 125 টাকা
∴ 1kg লবণের ব‍‍র্তমান মূল্য = 125/10 টাকা
= 12.5 টাকা

ব‍‍র্তমানে 500 টাকায় পাওয়া যায় = 500/12.5 = 40 kg
পূ‍‍র্বে 500 টাকায় পাওয়া যেতো = 40 + 10 = 50 kg
∴ প্রতি কেজি লবণের পূ‍‍র্বমূল্য = 500/50 = 10 টাকা
৩৬০.
By what percentage must 40 be increased to become 70?
  1. ক
    75%
  2. খ
    5%
  3. গ
    55%
  4. ঘ
    65%
সঠিক উত্তর: ক
75%
উত্তর
সঠিক উত্তর: ক
75%
ক
ব্যাখ্যা

Question: By what percentage must 40 be increased to become 70?

Solution: 
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.

৩৬১.
A company makes a profit of 6% on its first Tk. 1,000 of sales each day and Tk. 55 per thousand on all sales in excess of Tk. 1,000 for that day. How much profit will the company make in a day when sales are Tk. 6,000?
  1. ক
    250
  2. খ
    300
  3. গ
    320
  4. ঘ
    335
  5. ঙ
    None of these
সঠিক উত্তর: ঘ
335
উত্তর
সঠিক উত্তর: ঘ
335
ঘ
ব্যাখ্যা
Question: A company makes a profit of 6% on its first Tk. 1,000 of sales each day and Tk. 55 per thousand on all sales in excess of Tk. 1,000 for that day. How much profit will the company make in a day when sales are Tk. 6,000?

Solution:
Company makes profit for 1st Tk. 1000 of sales = 6% of 1000 = Tk. 60

Profit for Next Tk. (6000 - 1000) = Tk. 5000 of sales = 55 × 5 = Tk. 275

∴ Total profit = 60 + 275 = Tk. 335
৩৬২.
A merchant marks his goods 40% above the cost price and sell them at a discount of 15%. Find his gain % = ?
  1. ক
    ক) 25%
  2. খ
    খ) 22%
  3. গ
    গ) 19%
  4. ঘ
    ঘ) 20%
সঠিক উত্তর: গ
গ) 19%
উত্তর
সঠিক উত্তর: গ
গ) 19%
গ
ব্যাখ্যা

Let the cost price = 100 units
Marked price = 140 units
Selling price = 140 × 85/100 = 119
Profit % = 19/100×100 = 19%

৩৬৩.
By selling 90 balls for Tk. 160 a person loses 20%. How many ball pens should be sold for Tk. 96 so as to have a profit of 20%?
  1. ক
    ক) 28
  2. খ
    খ) 30
  3. গ
    গ) 32
  4. ঘ
    ঘ) 36
সঠিক উত্তর: ঘ
ঘ) 36
উত্তর
সঠিক উত্তর: ঘ
ঘ) 36
ঘ
ব্যাখ্যা
Question: By selling 90 balls for Tk. 160 a person loses 20%. How many ball pens should be sold for Tk. 96 so as to have a profit of 20%?

Solution: 
S.P of 90 ball pens  = Tk. 160 
C.P of 90 ball pens  = Tk. {160×(100/80)} =Tk. 200 

Desired  S.P of 90 ball pens  = Tk. (120/100) × 200  =  Tk. 240

For Tk. 240 ball pen sold = 90 
For Tk. 96 ball pen sold = (90/240) × 96 
= 36 
৩৬৪.
In a class of 65 students and 4 teachers, each student got sweets that are 20% of the total number of students and each teacher got sweets that are 40% of the total number of students. How many sweets are there?
  1. ক
    104
  2. খ
    845
  3. গ
    949
  4. ঘ
    897
সঠিক উত্তর: গ
949
উত্তর
সঠিক উত্তর: গ
949
গ
ব্যাখ্যা
Question: In a class of 65 students and 4 teachers, each student got sweets that are 20% of the total number of students and each teacher got sweets that are 40% of the total number of students. How many sweets are there?

Solution:
There are 65 students and 4 teachers
Each student got sweets that are 20% of the total number of students.
So each student got sweets = 65 × 20%
= 13 sweets.

∴ Total sweets for students is = 65 × 13 = 845

Each teacher got sweets that are 40% of the total number of students.
So each teacher got sweets = 65 × 40% = 26 sweets.

There are 4 teachers, so total sweets for teachers = 4 × 26 = 104

∴ Total sweets = sweets for students + sweets for teachers
= 845 + 104
= 949

Therefore, the total number of sweets is 949.
৩৬৫.
Doubling the selling price results in tripling the profit. Calculate the profit percentage.
  1. ক
    100%
  2. খ
    50%
  3. গ
    70%
  4. ঘ
    110%
সঠিক উত্তর: ক
100%
উত্তর
সঠিক উত্তর: ক
100%
ক
ব্যাখ্যা
Question: Doubling the selling price results in tripling the profit. Calculate the profit percentage.

Solution:
Let the first selling price Tk. 100
then, the 2nd selling price Tk. 200
Suppose, the first profit is Tk x

ATQ,
100 - x = 200 - 3x
⇒ 2x = 100
⇒ x = 50

So, the profit is Tk 50
Then, the cost price is = 100 - 50 = 50

∴ Profit = (50/50) × 100 = 100%
৩৬৬.
Alam sold two vehicles for Tk. 46,000 each. If he gained 10% on the first and lost 10% on another, then what is his percentage profit or loss in this transaction?
  1. ক
    ক) 2% loss
  2. খ
    খ) 1% profit
  3. গ
    গ) 1% loss
  4. ঘ
    ঘ) None of these
সঠিক উত্তর: গ
গ) 1% loss
উত্তর
সঠিক উত্তর: গ
গ) 1% loss
গ
ব্যাখ্যা

Question: Alam sold two vehicles for Tk. 46,000 each. If he gained 10% on the first and lost 10% on another, then what is his percentage profit or loss in this transaction?

Solution:
In the first case he gains 10%
∴ C. P. of the first car = (100 × 46000)/110 = 41,818.18

In the second case he loses 10%
∴ C. P. of the second car = (100 × 46000)/90 = 51,111.11

∴ Total cost of both cars = 41818.18 + 51111.11 = Tk 92,929.29
∴ Total S. P. of both cars = 2 × 46000 = Tk.92,000

Total loss = 92,929.29 - 92,000 = Tk. 929.29

%loss = (929.29/92,929.29) ×100 ​= 0.99% ≈ 1%

৩৬৭.
A scored 30% marks and failed by 15 marks. B scored 40% marks and obtained 35 marks more than those required to pass. The pass percentage is -
  1. ক
    ক) 33%
  2. খ
    খ) 38%
  3. গ
    গ) 43%
  4. ঘ
    ঘ) 46%
সঠিক উত্তর: ক
ক) 33%
উত্তর
সঠিক উত্তর: ক
ক) 33%
ক
ব্যাখ্যা

Let,
total marks = x.
Then,
(30% of x) + 15 = (40% of x) - 35
⇒ (30x/100) + 15 = (40x/100) - 35
⇒ (x/10) = 50
⇒ x = 500.
So, passing marks = (30% of 500) + 15
= (30/100) × 500 + 15
= 165
∴ Pass percentage = {(165/500) × 100}% = 33%.

৩৬৮.
A dishonest shopkeeper professes to sell ghee at the cost price. But he uses a false weight of 950g for a Kilogram. His gain percentage is-
  1. ক
    4
  2. খ
    5.26
  3. গ
    3
  4. ঘ
    4.5
সঠিক উত্তর: খ
5.26
উত্তর
সঠিক উত্তর: খ
5.26
খ
ব্যাখ্যা
Question: A dishonest shopkeeper professes to sell ghee at the cost price. But he uses a false weight of 950g for a Kilogram. His gain percentage is-

Solution: 
Let, the cost price of 1 kg is 950 taka

selling price of 1 kg is = (950/950) × 1000 taka 
= 1000 taka 


His gain percentage is = {(1000 - 950)/950} × 100% 
= 100/19 % 
= 5.26%
৩৬৯.
Param purchased a bicycle for Tk. 5954. He had paid a VAT of 14.5%. Find the list price of the bicycle.
  1. ক
    Tk. 5400
  2. খ
    Tk. 5800
  3. গ
    Tk. 5200
  4. ঘ
    Tk. 6817.33
সঠিক উত্তর: গ
Tk. 5200
উত্তর
সঠিক উত্তর: গ
Tk. 5200
গ
ব্যাখ্যা
Question: Param purchased a bicycle for Tk. 5954. He had paid a VAT of 14.5%. Find the list price of the bicycle.
 
Solution:
Let the list price be Tk. a.
VAT = 14.5%
 
So,
a × (114.5/100) = 5954
⇒ a = (5954 × 100)/114.5
⇒ a = 5200
 
∴ The list price of the bicycle was Tk. 5200.
৩৭০.
A book in sold for Tk. 65. This price gives the seller a profit 30% on his cost. What will be the new selling price, if he cuts his profit to 10% of the cost?
  1. ক
    ক) Tk. 45
  2. খ
    খ) Tk. 50
  3. গ
    গ) Tk. 55
  4. ঘ
    ঘ) Tk. 60
সঠিক উত্তর: গ
গ) Tk. 55
উত্তর
সঠিক উত্তর: গ
গ) Tk. 55
গ
ব্যাখ্যা
Question: A book in sold for Tk. 65. This price gives the seller a profit 30% on his cost. What will be the new selling price, if he cuts his profit to 10% of the cost?

Solution:
৩০% লাভে বিক্রয়মূল্য = (১০০ + ৩০) টাকা = ১৩০ টাকা

বিক্রয়মূল্য ১৩০ টাকা হলে ক্রয়মূল্য ১০০ টাকা
বিক্রয়মূল্য ১ টাকা হলে ক্রয়মূল্য ১০০/১৩০ টাকা
বিক্রয়মূল্য ৬৫ টাকা হলে ক্রয়মূল্য (১০০ × ৬৫)/১৩০ টাকা
= ৫০ টাকা

১০% লাভে বিক্রয়মূল্য = (৫০ + ৫০ এর ১০%) টাকা
= (৫০ + ৫) টাকা
= ৫৫ টাকা
৩৭১.
The price of a certain television set is discounted by 10 percent, and the reduced price is then discounted by 10 percent. This series of successive discounts is equivalent to a single discount of-
  1. ক
    20%
  2. খ
    19%
  3. গ
    18%
  4. ঘ
    11%
  5. ঙ
    10%
সঠিক উত্তর: খ
19%
উত্তর
সঠিক উত্তর: খ
19%
খ
ব্যাখ্যা
Question: The price of a certain television set is discounted by 10 percent, and the reduced price is then discounted by 10 percent. This series of successive discounts is equivalent to a single discount of-

Solution:
Let the Original price be 100
Since the initial discount is 10%, the discounted price will be 90% of 100, giving a value of 90.
Since there is a further discount of 10%, the final discounted price will be (90% of 90) or 81.

Since there is a discount of (100 - 81) = 19%,
∴  answer is (B).
৩৭২.
Company C produces toy trucks at a cost of Tk. 5.00 each for the first 100 trucks and Tk. 3.50 for each additional truck. If 500 toy trucks were produced by company C and sold for Tk. 10.00 each, what was company C's gross profit?
  1. ক
    ক) Tk. 2,250
  2. খ
    খ) Tk. 2500
  3. গ
    গ) Tk. 3100
  4. ঘ
    ঘ) Tk. 3250
সঠিক উত্তর: গ
গ) Tk. 3100
উত্তর
সঠিক উত্তর: গ
গ) Tk. 3100
গ
ব্যাখ্যা
Cost price of first 100 trucks = 5 × 100 = Tk. 500
Cost price of the rest = 400 × 3.5 = Tk. 1400
Total cost = 500 + 1400 = Tk. 1900

Selling price of all trucks = 500 × 10 = Tk. 5,000
So, profit = Tk. (5000 - 1900) =  Tk. 3100
৩৭৩.
A book was sold for Tk. 160, which was 80% of its cost price. What was the original cost of the book?
  1. ক
    Tk. 200
  2. খ
    Tk. 220
  3. গ
    Tk. 160
  4. ঘ
    Tk. 180
সঠিক উত্তর: ক
Tk. 200
উত্তর
সঠিক উত্তর: ক
Tk. 200
ক
ব্যাখ্যা
Question: A book was sold for Tk. 160, which was 80% of its cost price. What was the original cost of the book?

Solution:
Let,
The cost price of book = x

ATQ,
80% of x = 160
⇒ (80/100) × x = 160
⇒ x = (160 × 100)/80
∴ x = 200

∴  The cost price of the book is Tk. 200
৩৭৪.
After two successive equal percentage rises in the salary the sum of 30000 Tk. turned into 43200 Tk. Find the percentage rise in the salary.
  1. ক
    20%
  2. খ
    30%
  3. গ
    25%
  4. ঘ
    24%
সঠিক উত্তর: ক
20%
উত্তর
সঠিক উত্তর: ক
20%
ক
ব্যাখ্যা
Question: After two successive equal percentage rises in the salary the sum of 30000 Tk. turned into 43200 Tk. Find the percentage rise in the salary.

Solution:
Let, the salary increment is X%
after the first increment,
salary = 30000 + (X% of 30000)
= 30000 + 300X

after the second increment,
salary = 30000 + 300X + {X% of (30000 + 300X)}
= 3X2 + 600X + 30000

ATQ,
3X2 + 600X + 30000 = 43200
or, 3X2 + 600X - 13200 = 0
or, X2 + 200X - 4400 = 0
or, X2 + 220X - 20X - 4400 = 0
or, (X + 220)(X - 20) = 0

∴ X - 20 = 0
X = 20%
৩৭৫.
A fruit seller sold a basket of mangoes for Tk. 1000. He sold it at 125% of the cost price. What was the cost price of the mangoes?
  1. ক
    1250
  2. খ
    1160
  3. গ
    1125
  4. ঘ
    975
  5. ঙ
    800
সঠিক উত্তর: ঙ
800
উত্তর
সঠিক উত্তর: ঙ
800
ঙ
ব্যাখ্যা
Question: A fruit seller sold a basket of mangoes for Tk. 1000. He sold it at 125% of the cost price. What was the cost price of the mangoes?

Solution:
Let,
The cost price of mangoes = x

ATQ,
125% of x = 1000
⇒ (125/100) × x = 1000
⇒ x = (1000 × 100)/125
∴ x = 800
৩৭৬.
The profit earned by selling a chair for Tk. 750 is 1.5 times the loss occurred when the same chair was sold for Tk. 300. What is the cost price of the chair? 
  1. ক
    ক) Tk. 360
  2. খ
    খ) Tk. 420 
  3. গ
    গ) Tk. 425 
  4. ঘ
    ঘ) Tk. 480 
সঠিক উত্তর: ঘ
ঘ) Tk. 480 
উত্তর
সঠিক উত্তর: ঘ
ঘ) Tk. 480 
ঘ
ব্যাখ্যা
Question: The profit earned by selling a chair for Tk. 750 is 1.5 times the loss occurred when the same chair was sold for Tk. 300. What is the cost price of the chair? 

Solution:
Let the cost price of the chair be x
ATQ,
750 - x = 1.5 (x - 300)
⇒ 7500 - 10x = 15x - 4500 
⇒ 15x + 10x = 7500 + 4500
⇒ 25x = 12000
⇒ x = 12000/25
∴ x = 480
 
∴ The price of the chair is Tk. 480
৩৭৭.
A number reduced by 25% becomes 300. What percent should it be increased so that it becomes 460? 
  1. ক
    ক) 15%
  2. খ
    খ) 20%
  3. গ
    গ) 25%
  4. ঘ
    ঘ) 30%
সঠিক উত্তর: ক
ক) 15%
উত্তর
সঠিক উত্তর: ক
ক) 15%
ক
ব্যাখ্যা
Question: A number reduced by 25% becomes 300. What percent should it be increased so that it becomes 460? 

Solution: 
Le the number be x
Then, 
x - 25% of x = 300
⇒ x - (25x/100) = 300
⇒ 3x/4 = 300
⇒ 3x = 1200
∴ x = 400

∴ Increase = (460 - 400) = 60

The percent should be increased = {(60 × 100)/400}%
= 15%
৩৭৮.
If a sum of money trebles itself in 40 years, what is the rate of interest?
  1. ক
    7%
  2. খ
    4%
  3. গ
    9%
  4. ঘ
    3%
  5. ঙ
    5%
সঠিক উত্তর: ঙ
5%
উত্তর
সঠিক উত্তর: ঙ
5%
ঙ
ব্যাখ্যা

Let the sum of money be x.
x becomes 3x in 40 years.
Simple interest = 3x - x
= 2x
R = (100 × 2x)/(x × 40)
= 5%

৩৭৯.
A salesman receives daily wage of Tk. 450 and earns a commission of 10% on all sales he makes. How much taka worth of sales does he need to make in order to bring his total daily income of Tk. 1200?
  1. ক
    Tk. 9000
  2. খ
    Tk. 8500
  3. গ
    Tk. 7500
  4. ঘ
    Tk. 6500
সঠিক উত্তর: গ
Tk. 7500
উত্তর
সঠিক উত্তর: গ
Tk. 7500
গ
ব্যাখ্যা
Question: A salesman receives daily wage of Tk. 450 and earns a commission of 10% on all sales he makes. How much taka worth of sales does he need to make in order to bring his total daily income of Tk. 1200?

Solution:
He has to earn only with commission (1200 - 450) Taka = 750 Taka

He earns 10 taka when sells 100 taka
∴ He earns 1 taka when sells 100/10 taka = 10 taka
∴ He earns 750 taka when sells 10 × 750 taka = 7500 taka
৩৮০.
The difference between two numbers is 1550. If 8 % of one number is 10 % of the other number, then find the two numbers.
  1. ক
    ক) 4973, 6523
  2. খ
    খ) 5450, 7000
  3. গ
    গ) 6200, 7750
  4. ঘ
    ঘ) 6500, 4950
সঠিক উত্তর: গ
গ) 6200, 7750
উত্তর
সঠিক উত্তর: গ
গ) 6200, 7750
গ
ব্যাখ্যা
Question: The difference between two numbers is 1550. If 8 % of one number is 10 % of the other number, then find the two numbers.

Solution:
Let two numbers be x and y.
It is given that, 8 % of x = 10 % of y
Therefore,
(8x)/100 = (10y)/100
⇒ 8x = 10y
⇒ x = (10y)/8
∴ x = (5y)/4 

Difference between two numbers (x - y) = 1550
Substituting the value of x, we get,
(5y)/4 - y = 1550
⇒ y/4 = 1550
⇒ y =1550 × 4
∴ y =  6200

And,
x = (5 × 6200)/4 = 7750
৩৮১.
If the price of the commodity is increased by 50% by what fraction must its consumption be reduced so as to keep the same expenditure on its consumption?
  1. ক
    1/4
  2. খ
    1/3
  3. গ
    1/2
  4. ঘ
    2/3
  5. ঙ
    None of these
সঠিক উত্তর: খ
1/3
উত্তর
সঠিক উত্তর: খ
1/3
খ
ব্যাখ্যা
Question: If the price of the commodity is increased by 50% by what fraction must its consumption be reduced so as to keep the same expenditure on its consumption?

Solution:
Let, x kg of the commodity costs 100 taka 

Increased by 50%,
∴  x kg costs = 100 + 100 × .5 = 150 taka

In 100 taka, new quantity of commodity = (100 × x)/150 = 2x/3 kg 

Fraction must its consumption be reduced = {x - (2x/3)}/x
= (x/3)/x
= 1/3
৩৮২.
A person having bought goods for Tk 400 sells half of it at a gain of 5%, at what gain % must he sell the remainder so as to gain 20% on the whole?
  1. ক
    ক) 32%
  2. খ
    খ) 33%
  3. গ
    গ) 34%
  4. ঘ
    ঘ) 35%
সঠিক উত্তর: ঘ
ঘ) 35%
উত্তর
সঠিক উত্তর: ঘ
ঘ) 35%
ঘ
ব্যাখ্যা

To gain 20% on whole he must sell all good for,
400 + 20% of 400 = 480
As he get 5% gain on half of the goods i.e.
200 + 5% of 200 = 210
So required balance = 480 - 210 = 270
He must gain Tk. 70 on rest Tk. 200
% gain on remainder goods =(70×100)/200 = 35%

৩৮৩.
The population of a town increases every year by 4%. If its present population is 50,000, then after 2 years it will be-
  1. ক
    54280
  2. খ
    50500
  3. গ
    60250
  4. ঘ
    54080
সঠিক উত্তর: ঘ
54080
উত্তর
সঠিক উত্তর: ঘ
54080
ঘ
ব্যাখ্যা
Question: The population of a town increases every year by 4%. If its present population is 50,000, then after 2 years it will be-
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 + (4/100)]2
= 50000 × [1 + 0.04]2
= 50000 × (1.04)2
= 54080

∴ Population after 2 years = 54080
৩৮৪.
Nobody went there, ______?
  1. ক
    did he
  2. খ
    did they
  3. গ
    didn't he
  4. ঘ
    did you
সঠিক উত্তর: খ
did they
উত্তর
সঠিক উত্তর: খ
did they
খ
ব্যাখ্যা

• Complete Sentence: Nobody went there, did they?

• Tag question করার নিয়ম:
- Tag question ব্যবহার করা হয় উক্তিটি সত্য না মিথ্যা তা নিশ্চিত করার জন্য।
- Statement positive হলে tag question টি negative হবে।
- Statement negative হলে tag question টি positive হবে।
- Subject tense অনুসারে auxiliary verb দ্বারা tag question হয়।
- Anybody, anyone, no one, nobody, none, neither যদি কোনো sentence এর subject রূপে ব্যবহৃত হয় তাহলে tag এর subject হবে they (you, he , she নয়)।

Source: A Passage to the English Language, S.M. Zakir Hussain.

৩৮৫.
If the list price of a mobile phone is Tk. 10000, and a Tk. 1500 discount is offered on the mobile phone, then what is the discount percentage?
  1. ক
    10%
  2. খ
    12.5%
  3. গ
    15%
  4. ঘ
    18.5%
সঠিক উত্তর: গ
15%
উত্তর
সঠিক উত্তর: গ
15%
গ
ব্যাখ্যা
Question: If the list price of a mobile phone is Tk. 10000, and a Tk. 1500 discount is offered on the mobile phone, then what is the discount percentage?

Solution:
Marked Price = Tk. 10000
Discount = Tk. 1500

Discount % = (Discount/marked Price) × 100%
Discount (%) = (1500/10000) × 100%
= 15%

∴ So the discount percentage is 15%.
৩৮৬.
Which of the following is closest to 1/3 + 0.4 + 65%? 
  1. ক
    1
  2. খ
    1.4
  3. গ
    2.5
  4. ঘ
    2.8
সঠিক উত্তর: খ
1.4
উত্তর
সঠিক উত্তর: খ
1.4
খ
ব্যাখ্যা
Question: Which of the following is closest to 1/3 + 0.4 + 65%? 

Solution: 
1/3 + 0.4 + 65%
= (1/3) + (4/10) + (65/100)
=  (1/3) + (2/5) + (13/20)
= 1.4
৩৮৭.
A shopkeeper makes an item at Tk 1,200 and gives a 10% discount. If he still makes a 20% profit, what was the cost price?
  1. ক
    Tk. 900
  2. খ
    Tk. 840
  3. গ
    Tk. 790
  4. ঘ
    Tk. 950
  5. ঙ
    None of these
সঠিক উত্তর: ক
Tk. 900
উত্তর
সঠিক উত্তর: ক
Tk. 900
ক
ব্যাখ্যা
Question: A shopkeeper makes an item at Tk 1,200 and gives a 10% discount. If he still makes a 20% profit, what was the cost price?

Solution:
Selling price after 10% discount
= 1200 - 10% of 1200
= 1200 - {(10/100) × 1200}
= 1200 - 120
= 1080

Let the cost price = x 
Profit = 20% 

Now,
⇒ x + 20% of x = 1080
⇒ x + (20/100)x = 1080
⇒ x + (x/5) = 1080
⇒ 6x = 5400
⇒ x = 5400/6
∴ x = 900

So, the cost price of that item is Tk. 900
৩৮৮.
Priom's income is 40% less than Ratul's income, Qader's income is 20% less than Priom's income, and Shahin's income is 40% less than Priom's income. If Ratul gave 60% of his income to Shahin and 40% of his income to Qader, Qader's new income would be what fraction of Shahin's new income?
  1. ক
    11/12
  2. খ
    13/17
  3. গ
    12/19
  4. ঘ
    None of these
সঠিক উত্তর: ক
11/12
উত্তর
সঠিক উত্তর: ক
11/12
ক
ব্যাখ্যা
Question: Priom's income is 40% less than Ratul's income, Qader's income is 20% less than Priom's income, and Shahin's income is 40% less than Priom's income. If Ratul gave 60% of his income to Shahin and 40% of his income to Qader, Qader's new income would be what fraction of Shahin's new income?

Solution: 
let, priom's income = 0.6 × ratul's income 
ratul's income = priom's income/0.6 

Qader's income = 0.8 × prioms income
Shahins income = 0.6 × prioms income

Qader's new income = (0.8 × prioms income) + (0.4/0.6) × prioms income
= (22/15) × prioms income

Shahins new income = (0.6 × proms income) + (.6/.6) × prioms income
= (8/5) × prioms income

fraction = {(22/15) × prioms income} / (8/5) × prioms income
= 11/12
৩৮৯.
In an election, 2 candidates participate in which the winner gets 60% of the total votes, and he wins the election by 2000 votes. Find the total number of votes in the election.
  1. ক
    3200
  2. খ
    6400
  3. গ
    10000
  4. ঘ
    13250
সঠিক উত্তর: গ
10000
উত্তর
সঠিক উত্তর: গ
10000
গ
ব্যাখ্যা
Question: In an election, 2 candidates participate in which the winner gets 60% of the total votes, and he wins the election by 2000 votes. Find the total number of votes in the election.

Solution:
Let total votes = 100
So, as per question, the winner gets 60 votes and the loser gets 40 votes.
Now, the difference between votes = 20, but ATQ, it is 2000.
So, we have to multiply 20 by 100 to make it equal to 2000.
So, 100 (the assumed total votes) are also required to be multiplied with 100.
Therefore, the total votes= 100 × 100= 10000.
৩৯০.
Sakil purchased 120 exercise books at the rate of Tk. 3 each and sold 1/3 of them at the of Tk. 4 each, 1/2 of them at the rate of Tk.5 each and the rest at the cost price. His profit percentage is-
  1. ক
    ক) (100/9)%
  2. খ
    খ) (200/9)%
  3. গ
    গ) (400/9)%
  4. ঘ
    ঘ) (500/9)%
সঠিক উত্তর: গ
গ) (400/9)%
উত্তর
সঠিক উত্তর: গ
গ) (400/9)%
গ
ব্যাখ্যা
Total Cost price = Tk. (120 × 3) = Tk. 360
Total Sell Price = Tk. (40 × 4) + (60 × 5) + (20 × 3) = Tk. 520 
Profit = Tk.(520 - 360) = Tk. 160
Profit% = {(160/360) × 100}% = (400/9)%
৩৯১.
A canvas costs Tk. 500 and the marked price is printed as Tk. 800. What is the profit % for the seller if he sells and offers a discount of 10% on the marked price?
  1. ক
    ক) 52%
  2. খ
    খ) 44%
  3. গ
    গ) 28%
  4. ঘ
    ঘ) 38%
সঠিক উত্তর: খ
খ) 44%
উত্তর
সঠিক উত্তর: খ
খ) 44%
খ
ব্যাখ্যা
Question: A canvas costs Tk. 500 and the marked price is printed as Tk. 800. What is the profit % for the seller if he sells and offers a discount of 10% on the marked price?
Solution: 
After allowing a discount of 10% we get,
⇒ 90% of 800
⇒ (90 / 100) × 800
⇒ 720

∴ S.P = Tk. 720

Profit = S.P - C.P
⇒ 720 - 500
⇒ 220

Profit% = (Profit / C.P) × 100
⇒ (220 / 500) × 100
⇒ 44%

The profit% for the seller is 44%.
৩৯২.
Rahul bought a bicycle and sold it at a loss of 15%. If he had bought it for 25% less and sold it for tk 80 more, he would have made a profit of 30%. What was the cost of the bicycle?
  1. ক
    640 tk
  2. খ
    780 tk
  3. গ
    820 tk
  4. ঘ
    810 tk
সঠিক উত্তর: ক
640 tk
উত্তর
সঠিক উত্তর: ক
640 tk
ক
ব্যাখ্যা
Question: Rahul bought a bicycle and sold it at a loss of 15%. If he had bought it for 25% less and sold it for tk 80 more, he would have made a profit of 30%. What was the cost of the bicycle?

Solution:
Let the cost price of the bicycle be x tk.
The selling price of the bicycle when sold at a 15% loss is 0.85x tk.
If the bicycle had been bought for 25% less, the cost price would be 0.75x tk.
If the selling price had been 80 tk more, the selling price would be 0.85x + 80 tk.
According to the problem, in this case, Rahul would have made a profit of 30%, so the selling price would be 1.3 × 0.75x = 0.975x tk.

ATQ,
0.85x + 80 = 0.975x
⇒ 0.975x - 0.85x = 80
⇒ 0.125x = 80
⇒ x = 80/0.125
⇒ x = 8000/125
∴ x = 640 tk
৩৯৩.
Due to a 10% reduction in the price of tea, a dealer can purchase 25 kg more tea for TK. 22500. Find the reduced price per kg.
  1. ক
    Tk. 75
  2. খ
    Tk. 80
  3. গ
    Tk. 95
  4. ঘ
    Tk. 90
সঠিক উত্তর: ঘ
Tk. 90
উত্তর
সঠিক উত্তর: ঘ
Tk. 90
ঘ
ব্যাখ্যা

Question: Due to a 10% reduction in the price of tea, a dealer can purchase 25 kg more tea for TK. 22500. Find the reduced price per kg.

Solution: 
Let the original price per kg be x.
After a 10% reduction, New price per kg = x - 10% of x = 0.9x
Total money = TK. 22500

According to the question, the dealer can buy 25 kg more tea after the reduction.
So,
⇒ 22500/0.9x = (22500/x) + 25
⇒ 25000/x = (22500/x) + 25
⇒ (25000/x) - (22500/x) = 25
⇒ (25000 - 22500)/x = 25
⇒ 2500/x = 25
⇒ x = 2500/25
∴ x = 100 

So, original price per kg = Tk. 100

∴ Reduced price per kg = 0.9 × 100 = Tk. 90

So the reduced price per kg of tea is Tk. 90.

৩৯৪.
Two stories A and B mark the price of an item identically. A allows 3 successive discounts of 10% each. B allows 10% discount on the list price and a subsequent discount of 19%. Under the circumstances, which of the following is true?
  1. ক
    The price of the article is same at A and B
  2. খ
    The price of the article is cheaper at A
  3. গ
    The price cannot be determined
  4. ঘ
    The price of the article is cheaper at B
সঠিক উত্তর: ক
The price of the article is same at A and B
উত্তর
সঠিক উত্তর: ক
The price of the article is same at A and B
ক
ব্যাখ্যা
Question: Two stories A and B mark the price of an item identically. A allows 3 successive discounts of 10% each. B allows 10% discount on the list price and a subsequent discount of 19%. Under the circumstances, which of the following is true?

Solution:
Let the M.P. of the item at each of the stories A and B be tk100.
The final price at A = 90% of 90% of 90% of tk 100 
= {(90/100) × (90/100) × (90/100) × 100} tk
= 72.9 tk

The final price at B = 81% of 90% of Rs. 100
= {(81/100) × (90/100) × 100} tk
= 72.9 tk

Hence, the price of the article is the same at A and B.
৩৯৫.
An employee's annual salary was increased to Tk. 20,000. If her new annual salary now equals Tk. 86,000 what was the percent increase?
  1. ক
    ক) 20%
  2. খ
    খ) 22%
  3. গ
    গ) 25%
  4. ঘ
    ঘ) 30%
সঠিক উত্তর: ঘ
ঘ) 30%
উত্তর
সঠিক উত্তর: ঘ
ঘ) 30%
ঘ
ব্যাখ্যা

New annual salary = 86,000
Salary increase = 20,000.
Original salary = 86,000 - 20,000.
= 66,000

% Increase = ($20,000/ $66,000 )×100
= 30%

৩৯৬.
A group of 20 friends formed an investment club, with each member contributing an equal amount to the general fund. The club then invested the entire fund, which amounted to 1 taka, in stock X. The value of the stock subsequently increased 40 percent, at that point the stock was sold and the proceeds divided evenly among the members. In terms of t, how much money did each member of the club receive from the sale?
  1. ক
    800t
  2. খ
    (t/2)
  3. গ
    (7t/5)
  4. ঘ
    (7t/100)
সঠিক উত্তর: ঘ
(7t/100)
উত্তর
সঠিক উত্তর: ঘ
(7t/100)
ঘ
ব্যাখ্যা

Question: A group of 20 friends formed an investment club, with each member contributing an equal amount to the general fund. The club then invested the entire fund, which amounted to t taka, in stock X. The value of the stock subsequently increased 40 percent, at that point the stock was sold and the proceeds divided evenly among the members. In terms of t, how much money did each member of the club receive from the sale?

Solution:
After 40% increase, amount = t + 40% of t 
= t + 0.4t 
= 1.4t

each member of the club received = 1.4t/20 
= 14t/(20 × 10)
= 7t/100

৩৯৭.
You have saved 104 Taka by purchasing a blanket with 13% discount on it. what is the quoted price of the blanket in Taka?
  1. ক
    ক) 820
  2. খ
    খ) 800
  3. গ
    গ) 840
  4. ঘ
    ঘ) 900
সঠিক উত্তর: খ
খ) 800
উত্তর
সঠিক উত্তর: খ
খ) 800
খ
ব্যাখ্যা
13% ছাড়ে 
13 টাকা ছাড় পাওয়া যায় যখন তালিকামূল্য 100 টাকা 
1 টাকা ছাড় পাওয়া যায় যখন তালিকামূল্য 100/13 টাকা 
104 টাকা ছাড় পাওয়া যায় যখন তালিকামূল্য (100 × 104)/13 টাকা 
                                                                      = 800 টাকা
৩৯৮.
The marked price of a shirt and trousers are in the ratio 1 : 2. The shopkeeper gives 40% discount on the shirt. If the total discount in the set of the shirt and trousers is 30%, the discount offered on the trousers is:
  1. ক
    15%
  2. খ
    20%
  3. গ
    25%
  4. ঘ
    30%
সঠিক উত্তর: গ
25%
উত্তর
সঠিক উত্তর: গ
25%
গ
ব্যাখ্যা
Question: The marked price of a shirt and trousers are in the ratio 1 : 2. The shopkeeper gives 40% discount on the shirt. If the total discount in the set of the shirt and trousers is 30%, the discount offered on the trousers is:

Solution:
Let,
the price of shirt and trouser be Tk. 100 and Tk. 200 respectively.
Then, price of set of shirt and trouser = Tk. 300.

After giving 30% discount on the set,
Selling Price = 300 - 30% of 300
= 210.

∴ Total Discount on Set = Original price × Discount percentage
= 300 × (30/100)
= 300 × 0.30
= Tk. 90

And Discount on shirt is 20% alone,
SP of shirt alone = 100 - 40% of 100 = 60.
Tk. 40 is the discount on shirt then Tk. 50 must be the discount on the trouser.
So, discount on trouser = (50 × 100)/200 = 25%
৩৯৯.
A cricket team has won 40 games out of 60 played. It has 30 more games to play. How many of these must the team win to make a record 70% win for them?
  1. ক
    27
  2. খ
    23
  3. গ
    21
  4. ঘ
    29
সঠিক উত্তর: খ
23
উত্তর
সঠিক উত্তর: খ
23
খ
ব্যাখ্যা
Team won 40 games out of 60 and the remaining games were 30.
Total games = 60 + 30
= 90
70% of 90 = 63
Team has to win 63 games in total.
Team has already won 40.
∴ Games to win = 63 - 40
= 23
৪০০.
If the price of sugar decreases by 20%, by what percentage must sugar consumption increase to keep the total expenditure the same?
  1. ক
    20%
  2. খ
    25%
  3. গ
    30%
  4. ঘ
    10%
সঠিক উত্তর: খ
25%
উত্তর
সঠিক উত্তর: খ
25%
খ
ব্যাখ্যা
Question: If the price of sugar decreases by 20%, by what percentage must sugar consumption increase to keep the total expenditure the same? 

Solution:
মনে করি,
চিনির পূর্বমূল্য = 100  টাকা

চিনির মূল্য 20% হ্রাস পেলে,
নতুন মূল্য হয়= 100 - 100 এর 20% = 100 - 20 = 80 টাকা 

চিনির মূল্য হ্রাস পায় = 100 - 80 = 20 টাকা 

তাহলে, খরচ একই রাখতে হলে 20 টাকার সমপরিমান চিনি বেশি ব্যাবহার করতে হবে। 

এখন, 
চিনির ব্যাবহার 80 টাকায় বৃদ্ধি করতে হবে = 20 টাকা 
∴ 1 টাকায় বৃদ্ধি করতে হবে = 20/80 টাকা
∴ 100 টাকায় বৃদ্ধি করতে হবে = (20× 100) / 80 = 25 টাকা

সুতরাং চিনির ব্যাবহার শতকরা 25% বৃদ্ধি করতে হবে।