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Bank Math Master

পরীক্ষাBank Math Masterতারিখতারিখ অনির্ধারিতসময়28 minutes
মোট প্রশ্ন২১
সিলেবাস
Exam - 7: Revision Exam [Exam 04, 05 & 06]
প্রশ্ন দেখুনঅনুশীলন
ঘনত্ব
উত্তর
উত্তরিতবর্তমানপুনরায় দেখুনঅসম্পূর্ণ

Bank Math Master

Bank Math Master · তারিখ অনির্ধারিত · ২১ প্রশ্ন

১.
If 4(P’s Capital) = 6(Q’s Capital) = 10(R’s Capital), then out of the total profit of Tk. 4650, Q will receive-
  1. ক
    ক) Tk. 2250
  2. খ
    খ) Tk. 1500
  3. গ
    গ) Tk. 1400
  4. ঘ
    ঘ) Tk. 900
ব্যাখ্যা
প্রশ্ন: If 4(P’s Capital) = 6(Q’s Capital) = 10(R’s Capital), then out of the total profit of Tk. 4650, Q will receive-

সমাধান: 
Let,
P’s capital = p
Q’s capital = q 
R’s capital = r
Then
4p = 6q = 10r
⇒ 2p = 3q = 5r
Here,
q = (2p)/3
r = (2p)/5

∴ P : Q : R = p : (2p)/3 : (2p)/5
= 15p : 10p : 6p
= 15 : 10 : 6

∴ Q will receive = 4650 × (10/31) = 150 × 10 = 1500
২.
There are pieces of mangoes in a bowl is 8/15. Calculate the ratio of mangoes to other pieces of fruit in the bowl.
  1. ক
    ক) 8 : 7
  2. খ
    খ) 8 : 15
  3. গ
    গ) 7 : 15
  4. ঘ
    ঘ) None of these.
ব্যাখ্যা
প্রশ্ন: There are pieces of mangoes in a bowl is 8/15. Calculate the ratio of mangoes to other pieces of fruit in the bowl.

সমাধান: 
Let the total number of pieces of fruit be 15.
The number of mangoes is 8.
The number of other pieces of fruit is therefore 7.

∴ The ratio of mangoes to other pieces of fruit is therefore 8 : 7
৩.
Oranges of type A that cost 60 Tk./Kg is mixed with the orange of type B that costs 80 Tk./Kg in a ratio of 3 : 5. What will be the price of the resultant mixture of oranges?
  1. ক
    ক) Tk. 72
  2. খ
    খ) Tk. 72.5 
  3. গ
    গ) Tk. 74.5 
  4. ঘ
    ঘ) Tk. 75
ব্যাখ্যা
প্রশ্ন: Oranges of type A that cost 60 Tk./Kg is mixed with the orange of type B that costs 80 Tk./Kg in a ratio of 3 : 5. What will be the price of the resultant mixture of oranges?

সমাধান: 
Let,
Type A oranges is 3x Kg
Type B oranges is 5x Kg 
The price  Of the resultant mixure is P

Now,
60 × 3x + 80 × 5x = (3x + 5x) × P
⇒ 180x + 400x = 8xP
⇒ 8xP = 580x
⇒ P = 580x/8x
∴ P = 72.5

∴ The price  Of the resultant mixure is Tk. 72.5 
৪.
A man travels at 3 mph in still water. If the current’s velocity is 1 mph, it takes 3 hours to row to a place and come back. How far is the place?
  1. ক
    ক) 2 miles
  2. খ
    খ) 3 miles
  3. গ
    গ) 4 miles
  4. ঘ
    ঘ) 5 miles
ব্যাখ্যা
প্রশ্ন: A man travels at 3 mph in still water. If the current’s velocity is 1 mph, it takes 3 hours to row to a place and come back. How far is the place?

সমাধান: 
Let,
the distance be d miles.

Time taken to cover the distance upstream + Time taken to cover the distance downstream = 3 hours 
Here,
Speed upstream = 3 - 1 = 2 mph

Speed downstream = 3 + 1 = 4 mph

So, our equation would be,
d/2 + d/4 = 3 
⇒ (2d + d)/4 = 3
⇒ 3d = 12
⇒ d = 12/3 
∴ d = 4 

The distance is 4 miles.
৫.
Tofail, Hasib, Hemal enter into a partnership. Tofail initially invests 25 lakh & adds another 10 lakhs after one year. Hasib initially invests 35 lakh & withdrawal 10 lakh after 2 years and Hemal invests 30 Lakh. In what ratio should the profit be divided at the end of 3 years?
  1. ক
    ক) 19 : 19 : 18
  2. খ
    খ) 17 : 18 : 19
  3. গ
    গ) 18 : 18 : 19
  4. ঘ
    ঘ) 17 : 17: 19
ব্যাখ্যা
প্রশ্ন: Tofail, Hasib, Hemal enter into a partnership. Tofail initially invests 25 lakh & adds another 10 lakhs after one year. Hasib initially invests 35 lakh & withdrawal 10 lakh after 2 years and Hemal invests 30 Lakh. In what ratio should the profit be divided at the end of 3 years?

সমাধান: 
Tofail : Hasib : Hemal = (25 × 1 + 35 × 2) : (35 × 2 + 25 × 1) : (30 × 3)
= (25 + 70) : (70 + 25) : 90
= 95 : 95 : 90
= 19 : 19: 18 
৬.
A trader mixes 26 kg of rice at Tk. 20 per kg with 30 kg of rice of other variety at Tk. 36 per kg and sells the mixture at Tk. 30 per kg. His profit percent is:
  1. ক
    ক) 5%
  2. খ
    খ) 15%
  3. গ
    গ) 12%
  4. ঘ
    ঘ) 8%
ব্যাখ্যা
প্রশ্ন: A trader mixes 26 kg of rice at Tk. 20 per kg with 30 kg of rice of other variety at Tk. 36 per kg and sells the mixture at Tk. 30 per kg. His profit percent is:

সমাধান: 
C.P. of 56 kg rice = (26 × 20 + 30 × 36)
= (520 + 1080)
=1600

S.P. of 56 kg rice = (56 × 30)
= 1680.

∴ Profit = 1680 - 1600
= 80 

 ∴ Profit percentage = (80/1600) × 100% = 5%
৭.
Krishna invests Tk. 500 in the A Bank of Bangladesh at a simple interest rate of 8%. How much will be in his account after 5 years?
  1. ক
    ক) Tk. 550
  2. খ
    খ) Tk. 540
  3. গ
    গ) Tk. 700
  4. ঘ
    ঘ) Tk. 800
ব্যাখ্যা

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

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

∴ I = Pnr 
= 500 × 5 × (8/100) 
= 200

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

৮.
Haris and Sunny share some sweets in the ratio of 7 : 5. Haris has 12 more sweets than Sunny. How many sweets were there altogether?
  1. ক
    ক) 42
  2. খ
    খ) 72
  3. গ
    গ) 30
  4. ঘ
    ঘ) 144
ব্যাখ্যা

প্রশ্ন: Haris and Sunny share some sweets in the ratio of 7 : 5. Haris has 12 more sweets than Sunny. How many sweets were there altogether?

সমাধান: 
Let,
Haris has 7x sweets 
Sunny has 5x sweets 
∴ Total sweets 7x + 5x = 12x

ATQ,
7x - 5x = 12
⇒ 2x = 12
∴ x = 6

∴ There were 12 × 6 = 72 sweets altogether.

৯.
The ratio of milk and water in a solution is 20 : 7 and after adding 5 liters of water in it the ratio of milk and water becomes 5 : 3, then find the final amount of water in the final solution.
  1. ক
    ক) 7 liters
  2. খ
    খ) 10 liters
  3. গ
    গ) 11 liters
  4. ঘ
    ঘ) 12 liters
ব্যাখ্যা
প্রশ্ন: The ratio of milk and water in a solution is 20 : 7 and after adding 5 liters of water in it the ratio of milk and water becomes 5 : 3, then find the final amount of water in the final solution.

সমাধান: 
Let the initial amount of milk be 20x liters and amaount of water 7x liters

Ratio of milk and water after adding 5 liters = 20x/(7x + 5) = 5/3
⇒ 60x = 35x + 25
⇒ 25x = 25
⇒ x = 1.

∴ Final amount of water in solution = 7x + 5 = 7 + 5 = 12 liters.
১০.
A train is going at 1/3 of its usual speed and it takes an extra 30 minutes to reach its destination. Find its usual time to cover the same distance.
  1. ক
    ক) 15 min
  2. খ
    খ) 20 min
  3. গ
    গ) 25 min
  4. ঘ
    ঘ) 30 min
ব্যাখ্যা

প্রশ্ন: A train is going at 1/3 of its usual speed and it takes an extra 30 minutes to reach its destination. Find its usual time to cover the same distance.

সমাধান: 
Let,
The usual speed is x 
The distance is d 
The usual time is t min 

So, 
In usual speed, d = xt 

In 1/3 of usual speed, d = (x/3) × (t + 30) 

Now, We can say that,
xt = x(t + 30)/3 
⇒ t = (t + 30)/3
⇒ 3t = t + 30 
⇒ 2t = 30
∴ t = 15 

∴ The usual time to cover the same distance is 15 min.

১১.
Mijan,Jewel, and Tasif rent a pasture. Mijan puts 10 oxen for 7 months, Jewel puts 12 oxen for 5 months and Tasif puts 15 oxen for 3 months for grazing. If the rent of the pasture is Tk. 1750, how much must Tasif pay as his share of rent?
  1. ক
    ক) Tk. 700
  2. খ
    খ) Tk. 600
  3. গ
    গ) Tk. 450
  4. ঘ
    ঘ) Tk. 900
ব্যাখ্যা
প্রশ্ন: Mijan,Jewel, and Tasif rent a pasture. Mijan puts 10 oxen for 7 months, Jewel puts 12 oxen for 5 months and Tasif puts 15 oxen for 3 months for grazing. If the rent of the pasture is Tk. 1750, how much must Tasif pay as his share of rent?

সমাধান: 
Mijan : Jewel : Tasif = (10 × 7) : (12 × 5) : (15 × 3)
= 70 : 60 : 45
= 14 : 12 : 9

∴ Tasif's share of rent = 1750 × (9/35) =  450.
১২.
In a transaction, the profit percentage is 80% of the cost. If the cost further increases by 20% but the selling price remains the same, how much is the decrease in profit percentage?
  1. ক
    ক) 60%
  2. খ
    খ) 50%
  3. গ
    গ) 40%
  4. ঘ
    ঘ) 30%
ব্যাখ্যা
প্রশ্ন: In a transaction, the profit percentage is 80% of the cost. If the cost further increases by 20% but the selling price remains the same, how much is the decrease in profit percentage?

সমাধান: 
Let us assume CP = Tk. 100.
Then Profit = Tk. 80 and selling price = Tk. 180

The cost increases by 20% 
∴  New CP = Tk. 120,
SP = Tk. 180.

∴ Profit = 180 - 120 = Tk. 60
Profit % = (60/120) × 100% = 50%.

Therefore, Profit decreases by (80 - 50)% =  30%.
১৩.
A loan company charges Tk. 30 interest for a one month loan of Tk. 500. Find the annual interest rate they are charging.
  1. ক
    ক) 7.2%
  2. খ
    খ) 30%
  3. গ
    গ) 72%
  4. ঘ
    ঘ) 36%
ব্যাখ্যা
প্রশ্ন: A loan company charges Tk. 30 interest for a one month loan of Tk. 500. Find the annual interest rate they are charging.

সমাধান: 
Interest for 1 month = Tk. 30
∴ Interest for 12 months = Tk. (12 × 30)
= Tk. 360

r = I/(Pn)
= (360/500) × 100%
= 72%
১৪.
Mean proportional of 4 and 36 is x and third proportional of 18 and x is y. Find the value of y.
  1. ক
    ক) 9
  2. খ
    খ) 12
  3. গ
    গ) 8
  4. ঘ
    ঘ) 6
ব্যাখ্যা
প্রশ্ন: Mean proportional of 4 and 36 is x and third proportional of 18 and x is y. Find the value of y.

সমাধান: 
Given,
Mean proportional of 4 and 36 = x
∴ x2 = 4 × 36
⇒ x = 12

Third proportional of 18 and 12 = y
∴ 122 = 18 × y
⇒ 144 = 18 × y
⇒ y = 8
১৫.
A car takes 4 hours to cover a distance, if it travels at a speed of 40 mph. What should be its speed to cover the same distance in 1.5 hours?
  1. ক
    ক) 96.66 mph
  2. খ
    খ) 100 mph
  3. গ
    গ) 106.66 mph
  4. ঘ
    ঘ) 160 mph
ব্যাখ্যা
প্রশ্ন: A car takes 4 hours to cover a distance, if it travels at a speed of 40 mph. What should be its speed to cover the same distance in 1.5 hours?

সমাধান: 
Distance covered in 4 hours = 4 × 40 miles
= 160 miles

Speed required to cover the same distance in 1.5 hours = 160/1.5 mph
= 106.66 mph
১৬.
Rifat, Joy, Banik subscribe to Tk. 50,000 for a business. Rifat subscribes Tk. 4000 more than Joy and Joy subscribes Tk. 5000 more than Banik. Out of a total profit of Tk. 35000, Rifat receives-
  1. ক
    ক) Tk. 8400
  2. খ
    খ) Tk. 11900
  3. গ
    গ) Tk. 15200
  4. ঘ
    ঘ) Tk. 14700
ব্যাখ্যা
প্রশ্ন: Rifat, Joy, Banik subscribe to Tk. 50000 for a business. Rifat subscribes Tk. 4000 more than Joy and Joy subscribes Tk. 5000 more than Banik. Out of a total profit of Tk. 35000, Rifat receives-

সমাধান: 
Let,
Banik subscribes = x
Then,
Joy subscribe = x + 5000
Rifat subscribe = x + 5000 + 4000 = x + 9000
∴ x + x + 5000 + x + 9000 = 50000
⇒ 3x = 36000
⇒ x = 12000

Rifat : Joy : Banik = 21000 : 17000 : 12000
= 21 : 17 : 12

∴ Rifat’s share of profit = 35000 × (21/50) = 14700
১৭.
A man bought some toys at the rate of 10 for Tk. 40 and sold them at 8 for Tk. 35. Find his gain or loss percent.
  1. ক
    ক) 10%
  2. খ
    খ) 9.5%
  3. গ
    গ) (75/8)%
  4. ঘ
    ঘ) (71/5)%
ব্যাখ্যা
প্রশ্ন: A man bought some toys at the rate of 10 for Tk. 40 and sold them at 8 for Tk. 35. Find his gain or loss percent.

সমাধান: 
Cost price of 10 toys  = Tk. 40 
∴ CP of 1 toy = Tk. 4

Selling price of 8 toys = Tk. 35
∴ SP of 1 toy = Tk. 35/8

Therefore, Gain = 35/8 – 4 = 3/8.

Gain percent = {(3/8)/4} × 100% =(75/8)%
১৮.
Tk.1500 is invested at 5% per year simple interest. In how many years the investment will be Tk.1800?
  1. ক
    ক) 5 years
  2. খ
    খ) 4 years
  3. গ
    গ) 6 years
  4. ঘ
    ঘ) 3 years
ব্যাখ্যা

প্রশ্ন: Tk. 1500 is invested at 5% per year simple interest. In how many years the investment will be Tk. 1800?

সমাধান: 
Here,
P = Tk. 1500 
I = 1800 - 1500 = Tk. 300
r = 5% = 5/100 
n = ?

We know that,
∴ I = Pnr
⇒ n = I/(Pr)
= (300 × 100)/(1500 × 5)
= 4

∴ The investment will be Tk. 1800 in 4 years.

১৯.
There are 30 students in a class. The number of students who like Math and the ones who like Science is expressed in the ratio 2 : 3. Find the number of students who like Math.
  1. ক
    ক) 20
  2. খ
    খ) 18
  3. গ
    গ) 15
  4. ঘ
    ঘ) 12
ব্যাখ্যা
প্রশ্ন: There are 30 students in a class. The number of students who like Math and the ones who like Science is expressed in the ratio 2 : 3. Find the number of students who like Math.

সমাধান: 
Total number of students = 30.
Let
the number of students who like Math = 2x
the number of students who like Science = 3x

We can say that,
2x + 3x = 30
⇒ 5x = 30
⇒ x = 6

∴ the numbers of students who like Math = 2x = 2 × 6 = 12
২০.
A vacuum cleaner is bought for Tk. 399 and loses 22% of its value per year compound interest. What is the value of the vacuum cleaner after 2 years?
  1. ক
    ক) Tk.  250
  2. খ
    খ) Tk.  245.75 
  3. গ
    গ) Tk.  242.75 
  4. ঘ
    ঘ) Tk.  248.50
ব্যাখ্যা
প্রশ্ন: A vacuum cleaner is bought for Tk. 399 and loses 22% of its value per year compound interest. What is the value of the vacuum cleaner after 2 years?

সমাধান: 
Here,
P = Tk. 399
r = - 22%  [we use (-), because it is decrease rate]
n = 2 years 

We know that,
C = P(1 + r/100​)n 
= 399(1 - 22/100​)2
= 399(1 - 0.22)2
= 399(0.78)2
= 399 × 0.6084
= 242.75 

∴ The value of the vacuum cleaner after 2 years will be Tk.  242.75 
২১.
A dishonest merchant sells his grocery using weights 15% less than the true weights and shows that he makes profit of 20%. Find his actual gain percentage.
  1. ক
    ক) 41%
  2. খ
    খ) 41.17%
  3. গ
    গ) 40%
  4. ঘ
    ঘ) None of these
ব্যাখ্যা
প্রশ্ন: A dishonest merchant sells his grocery using weights 15% less than the true weights and shows that he makes profit of 20%. Find his actual gain percentage.

সমাধান: 
Let us consider 1 kg of grocery bag.
Its actual weight is 85% of 1000 gm = 850 gm.

Let the cost price of each gram be Tk. 1
Then the CP of each bag = Tk. 850

SP of 1 kg of bag = 120% of the true CP
Therefore, SP = (120/100) × 1000 = Tk. 1200

Gain = 1200 - 850 = Tk. 350

Hence Gain % = (350/850) × 100% = 41.17%