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Bank Math

মোট প্রশ্ন১৬,১২৪এই পাতা১০০প্রতি পাতা১০০
প্রশ্ন দেখুনঅনুশীলন
ঘনত্ব
উত্তর
উত্তরিতবর্তমানপুনরায় দেখুনঅসম্পূর্ণ

Bank Math

PrepBank · পাতা ১৪১ / ১৬১ · ১৪,০০১–১৪,১০০ / ১৬,১২৪

১৪,০০১.
The average of a,b,c is 6 and a - b = 4, ab = 21, What is the value of c?
  1. ক
    6
  2. খ
    7
  3. গ
    8
  4. ঘ
    5
  5. ঙ
    4
ব্যাখ্যা
(a + b + c)/ 3 = 6
a + b + c = 18  ---------- (1)

a - b = 4
(a - b)2 = 16
(a + b)2 - 4ab = 16
(a + b)2 - 4.21 = 16
(a + b)2 = 100
a + b = 10
From (1) we get,
C = 18 - 10 = 8
১৪,০০২.
Between two book-ends in your study are displayed your five books. If you decide to arrange the five books in every possible combination and moved just one book every minute, how long would it take you?
  1. ক
    5 hours
  2. খ
    4 hours
  3. গ
    3 hours
  4. ঘ
    2 hours
ব্যাখ্যা
Question: Between two book-ends in your study are displayed your five books. If you decide to arrange the five books in every possible combination and moved just one book every minute, how long would it take you?

Solution:

Here,
Number of ways of arranging 5 books
= 5!
= 5 × 4 × 3 × 2 × 1
= 120

So, total time taken
= 120 minutes [ 60 minutes = 1 hour ]
= 2 hours

১৪,০০৩.
If the product of three consecutive integers is 720, then the sum of the two largest integers is-
  1. ক
    ক) 10
  2. খ
    খ) 15
  3. গ
    গ) 17
  4. ঘ
    ঘ) 19
ব্যাখ্যা

Question: If the product of three consecutive integers is 720, then the sum of the two largest integers is-

Solution: 
720 =  2 × 2 × 2 × 2 × 3 × 3 × 5
       = (2 × 2 × 2) ×  (3 × 3) × (2 × 5)
       = 8 × 9 × 10 

 The sum of the two largest integers is = 9 + 10 = 19

১৪,০০৪.
Rimon subtracts two numbers and finds the square of the resultant to be 9. When he squares the two numbers and adds them. The resultant is 225. Find the product of two numbers.
  1. ক
    96
  2. খ
    108
  3. গ
    125
  4. ঘ
    169
ব্যাখ্যা

Let numbers be A and B
∴ (A - B)2 = 9
∴ A2 - 2AB + B2 = 9
Further, A2 + B2 = 225
∴ 225 - 2AB = 9
∴ AB = 108 = product of the two numbers.

১৪,০০৫.
Find the value of sec4θ - tan4θ if sec2θ + tan2θ = 3?
  1. ক
    ক) 1/3
  2. খ
    খ) 1/√3
  3. গ
    গ) 3
  4. ঘ
    ঘ) √3
ব্যাখ্যা
Question: Find the value of sec4θ - tan4θ if sec2θ + tan2θ = 3?

Solution: 
sec4θ - tan4θ
= (sec2θ + tan2θ)(sec2θ - tan2θ)
= 3 × 1 [1 + tan2θ = sec2θ]
= 3
১৪,০০৬.
A pipe can fill a tank in x hours and another pipe can empty it in y (y > x) hours. If both pipes are open, in how many hours will the tank is filled?
  1. ক
    ক) (x - y) hours
  2. খ
    খ) (y - x) hours
  3. গ
    গ) xy/(x - y) hours
  4. ঘ
    ঘ) xy/(y - x) hours
ব্যাখ্যা

Net part filled in 1 hour
= (1/x − 1/y)
= (y−x)/xy
∴ The tank will be filled in
= xy/(y−x) hours

১৪,০০৭.
The sum of three numbers is 116. The second number and the third number are in the ratio of 9 : 16 while the first number and the third number are in the ratio of 1 : 4. Find the second number.
  1. ক
    30
  2. খ
    36
  3. গ
    39
  4. ঘ
    40
ব্যাখ্যা
Question : The sum of three numbers is 116. The second number and the third number are in the ratio of 9 : 16 while the first number and the third number are in the ratio of 1 : 4. Find the second number.

Solution : 
Given,
Second : Third = 9 : 16
Third : first = 4 : 1
= 16 : 4

So the ratio of Second  :Third : first = 9 : 16 : 4

∴ The second number = (116 × 9/29)
= 36
১৪,০০৮.
√6 x √27 is equal to:
  1. ক
    9√2
  2. খ
    3√3
  3. গ
    2√2
  4. ঘ
    9√3
  5. ঙ
    5√3
ব্যাখ্যা

√6 x √27
= √(6 x 27)
= √(2 x 3 x 3 x 3 x 3)
= (3 x 3)√2
= 9√2

১৪,০০৯.
Find the speed of the boat in still water, if a boat covers a certain distance upstream in 2 hours, while it comes back in 3/2 hours. If the speed of the stream be 3 kmph.
  1. ক
    12 Kmph
  2. খ
    18 Kmph
  3. গ
    21 Kmph
  4. ঘ
    24 Kmph
ব্যাখ্যা
Question: Find the speed of the boat in still water, if a boat covers a certain distance upstream in 2 hours, while it comes back in 3/2 hours. If the speed of the stream be 3 kmph.

Solution:
Let the speed of the boat in still water be x kmph.
Then,
Speed downstream = (x + 3) kmph,
Speed upstream = (x - 3)kmph.

(x - 3) × 2 = (x + 3) × (3/2)
⇒ 4x - 12 = 3x + 9
∴ x = 21 kmph.
১৪,০১০.
If the radius of a circle is reduced by 40%, its circumference is reduced by-
  1. ক
    30%
  2. খ
    35%
  3. গ
    40%
  4. ঘ
    60%
ব্যাখ্যা
Question: If the radius of a circle is reduced by 40%, its circumference is reduced by-

Solution: 
If radius of a circle is r, circumference 2πr where 2π is constant 
So, if radius is changed, the circumference will change by the same amount.

The radius of a circle is reduced by 40%,then its circumference is reduced by 40%
১৪,০১১.
A merchant has 1000 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 18% profit.
  1. ক
    400kg
  2. খ
    560kg
  3. গ
    600kg
  4. ঘ
    640kg
ব্যাখ্যা
Question: A merchant has 1000 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 18% profit.

Solution:
Let the cost price of 1kg of sugar be Tk.100.

The selling price of 1kg sugar sold at 8% profit
⇒ 100 × 108/100 = Tk.108

The selling price of 1kg sugar sold at 18% profit
⇒ 100 × 118/100 = Tk.118

The average selling price of 1kg of sugar
⇒ 100 × 114/100 = Tk.114

Using the rule of the allegation,

The ratio of sugar sold at 8% and 18% profit
⇒ (118 - 114) : (114 - 108)
⇒ 4 : 6 = 2 : 3

∴ Quantity sold at 18% profit = 3/5 × 1000 = 600 kg
১৪,০১২.
If sin 17° = (x/y) , then sec 17° is equal to
  1. ক
    {√(y2 - x2)}/y
  2. খ
    {√(y2 - x2)}/x
  3. গ
    y/{√(y2 - x2)}
  4. ঘ
    x/{√(y2 - x2)}
ব্যাখ্যা
Question: If sin 17° = (x/y) , then sec 17° is equal to

Solution:
sin 17° = (x/y)
⇒ sin 73° = sin (90° – 17°)
= cos 17°

∴ cos 17° = √(1 - sin217°)
= √{1 - (x2/y2)}
= √{(y2 - x2)/y2}
= {√(y2 - x2)}/y

∴ sec 17° = y/{√(y2 - x2)}
১৪,০১৩.
A shopkeeper expects a gain of 25% on his cost price. If in a week, his sale was Tk. 1600, what was his profit?
  1. ক
    Tk. 250
  2. খ
    Tk. 280
  3. গ
    Tk. 320
  4. ঘ
    Tk. 350
ব্যাখ্যা
Question: A shopkeeper expects a gain of 25% on his cost price. If in a week, his sale was Tk. 1600, what was his profit?

Solution:
Let
the cost price be x

∴ The selling price = {x + (25% of x)}

ATQ,
x + (25% of x) = 1600
⇒ x + (25x/100) = 1600
⇒ x + (x/4) = 1600
⇒ (4x + x)/4 = 1600
⇒ 5x = 1600 × 4
⇒ x = (1600 × 4)/5
∴ x = 1280

∴ Profit = (1600 - 1280) = Tk. 320
১৪,০১৪.
Simple Interest on certain sum of money of 10 year is 3130 but if after 5 year principal become 5 times then find the total SI after 10 years.
  1. ক
    Tk. 3130
  2. খ
    Tk. 6260
  3. গ
    Tk. 9390
  4. ঘ
    Tk. 15650
ব্যাখ্যা
Question: Simple Interest on certain sum of money of 10 year is 3130 but if after 5 year principal become 5 times then find the total SI after 10 years.

Solution:
SI of 10 years = 3130 
Simple Interest same in every year. 
So, SI in first 5 year = (3130/10) × 5 = 1565 

If principal become 5 times in 5 year than interest will also become 5 times. 
So, Interest of next 5 years= 1565 × 5 = 7825 
Total Simple Interest = 7825 + 1565 = 9390
১৪,০১৫.
A circle can have how many parallel tangents at a single time?
  1. ক
    2
  2. খ
    3
  3. গ
    4
  4. ঘ
    1
ব্যাখ্যা

Question: A circle can have how many parallel tangents at a single time?

Solution:
- একটি বৃত্তের স্পর্শক (Tangent) হলো এমন একটি সরলরেখা যা বৃত্তকে কেবল একটি বিন্দুতে স্পর্শ করে।
- একটি বৃত্তে একটি নির্দিষ্ট দিকে সর্বোচ্চ এক জোড়া বা ২টি সমান্তরাল স্পর্শক থাকা সম্ভব। এই সমান্তরাল স্পর্শক দুটি সর্বদা বৃত্তের ব্যাসের (Diameter) বিপরীত প্রান্তবিন্দুতে অবস্থিত থাকে।
- যদি ব্যাসের দুই প্রান্ত ছাড়া অন্য কোনো বিন্দুতে তৃতীয় একটি সমান্তরাল রেখা আঁকা হয়, তবে সেটি হয় বৃত্তকে দুই বিন্দুতে ছেদ করবে (Secant) অথবা বৃত্তকে স্পর্শই করবে না।

∴ একটি বৃত্তে একসাথে ঠিক ২টি সমান্তরাল স্পর্শক থাকতে পারে (যেকোনো নির্দিষ্ট দিকের জন্য)।

১৪,০১৬.
  1. ক
    ক) 1/2
  2. খ
    খ) 1
  3. গ
    গ) 2
  4. ঘ
    ঘ) 2/3
ব্যাখ্যা
Question: 


Solution: 
১৪,০১৭.
The age of a mother today is thrice that of her daughter. After 12 years, the age of the mother will be twice that of her daughter. The present age of the daughter is = ?
  1. ক
    24 Years
  2. খ
    20 Years
  3. গ
    16 Years
  4. ঘ
    12 Years
ব্যাখ্যা
Question: The age of a mother today is thrice that of her daughter. After 12 years, the age of the mother will be twice that of her daughter. The present age of the daughter is = ?

Solution:
Let, the daughter's age be x years
Then, mother's age = 3x years

According to the question,
3x + 12 = 2 (x + 12)
⇒ 3x + 12 = 2x + 24
⇒ 3x - 2x = 24 - 12
∴ x = 12
১৪,০১৮.
The average age of 12 children is 15 years. If another child comes, the average age comes to 13. What is the age of the new child?
  1. ক
    5 years
  2. খ
    7 years
  3. গ
    9 years
  4. ঘ
    11 years
ব্যাখ্যা

Question: The average age of 12 children is 15 years. If another child comes, the average age comes to 13. What is the age of the new child?

Solution: 
Sum of 12 children ages = 12 × 15 = 180
Sum of the 13 children ages = 13 × 13 = 169
So age of new children = 180 - 169
= 11

[বাস্তবিকভাবে নতুন একজনের বয়স যুক্ত হওয়ার পর বয়সের গড় কম-বেশি হতে পারে তবে ১২ জনের মোট বয়স (১৮০ বছর) অপেক্ষা ১৩ জনের মোট বয়স (১৬৯ বছর) কম হতে পারে না।  এই প্রশ্নটি যেহেতু জব সল্যুশনের প্রশ্ন তাই গাণিতিক নিয়ম অনুযায়ী ১১ বছর উত্তর রাখা হয়েছে] 

১৪,০১৯.
A man is running at a speed of 3 km/hr in the direction of the train whose length is 500 meters. If the train is moving at a speed of 63 km/hr then how many seconds will this train take to cross the man?
  1. ক
    ক) 38 sec
  2. খ
    খ) 35 sec
  3. গ
    গ) 34 sec
  4. ঘ
    ঘ) 30 sec
ব্যাখ্যা
Question: A man is running at a speed of 3 km/hr in the direction of the train whose length is 500 meters. If the train is moving at a speed of 63 km/hr then how many seconds will this train take to cross the man?

Solution: 
ট্রেন ও মানুষের আপেক্ষিক গতি = (63 - 3) km/hr
= 60 km/hr
= (60 x 1000)/3600 m/sec
= 50/3 m/sec

 মানুষটি পার হতে সময় লেগেছে = 500 x (3/50) sec
= 30 sec
১৪,০২০.
What percent of 500 is 1.5?
  1. ক
    0.3%
  2. খ
    3%
  3. গ
    0.5%
  4. ঘ
    30%
ব্যাখ্যা

Question: What percent of 500 is 1.5?

Solution:
ধরি,
500 এর x% = 1.5
⇒ 500 এর (x/100) = 1.5
⇒ 5x = 1.5
⇒ x = 1.5/5
⇒ x = 0.3

​সুতরাং, 500 এর 0.3% হলো 1.5

১৪,০২১.
Speed of a boat along and against the current are 14 kms/hr and 8 kms/hr respectively. The speed of the current is?
  1. ক
    4 km/hr
  2. খ
    3 km/hr
  3. গ
    2.5 km/hr
  4. ঘ
    2 km/hr
ব্যাখ্যা
Question: Speed of a boat along and against the current are 14 kms/hr and 8 kms/hr respectively. The speed of the current is?

Solution: 
Let the speed of the boat is S
the speed of the current is W

S + W = 14 . . . . . . (i)
S - W = 8 . . . . . . . .(ii)
_________________
from equation (i) & (ii)
S = 11 km/hr, W = 3 km/hr
Speed of current = 3 km/hr
১৪,০২২.
A boat can travel with a speed of 12 km/hr in still water. If the speed of the stream is 5 km/hr, find the time taken by the boat to go 136 km downstream.
  1. ক
    ক) 10 hours
  2. খ
    খ) 8 hours
  3. গ
    গ) 6 hours
  4. ঘ
    ঘ) 4 hours
ব্যাখ্যা
Question: A boat can travel with a speed of 12 km/hr in still water. If the speed of the stream is 5 km/hr, find the time taken by the boat to go 136 km downstream.

Solution: 
Speed downstream = (12 + 5) km/hr = 17 km/hr

Time taken to travel 136 km downstream = 136/17 hr
= 8 hr
১৪,০২৩.
The true discount on a bill of Tk. 2700 is Tk. 200. What is the banker's discount?
  1. ক
    Tk. 210
  2. খ
    Tk. 212
  3. গ
    Tk. 216
  4. ঘ
    Tk. 218
ব্যাখ্যা
Question: The true discount on a bill of Tk. 2700 is Tk. 200. What is the banker's discount?

Solution:
Face value = Tk. 2700
TD = Tk. 200
PW (present worth) = FV (face value) - TD (true discount)
= 2700 - 200
= 2500

True discount is the simple interest on the present value for the unexpired time.

Now, simple interest on Tk. 2500 for unexpired time = Tk. 200
The rate of simple interest = (200/2500) × 100% = 8%

Banker's discount is the simple interest on the face value of the bill for unexpired time.

simple interest on Tk. 2700 for unexpired time or remaining time.
R = 8%
Banker's discount = 2700 × (8/100) = 216
১৪,০২৪.
(৩√৩)৩ = কত?
  1. ক
    ক) ২৭√৩
  2. খ
    খ) ৮১√৩
  3. গ
    গ) ৮১
  4. ঘ
    ঘ) ৯√৩
ব্যাখ্যা
প্রশ্ন: (৩√৩)৩ = কত?

সমাধান:
(৩√৩)৩
= ৩ × ৩ × ৩ × √৩× √৩× √৩
= ২৭ × ৩ × √৩
= ৮১√৩
১৪,০২৫.
The perimeter of a rectangle is 180 metres. If its length is twice its breadth, then its area is :
  1. ক
    1800 m2
  2. খ
    200 m2
  3. গ
    1200 m2
  4. ঘ
    1600 m2
ব্যাখ্যা

Let the breadth of the rectangle be x metres
Then, length of the rectangle = 2x metres

Therefore,
2(2x + x) = 180
⇒ 6x = 180
⇒ x = 30

So,
length = 60 m,
breadth = 30 m

∴ Area
= (60 × 30) m2
= 1800 m2
১৪,০২৬.
The price of an article was increased by p% . Later the new price was decreased by p%. If the latest price was TK. 1, The original price was:
  1. ক
    ক) 1
  2. খ
    খ) (1 - p2)/100
  3. গ
    গ) 10000/(1000-p2)
  4. ঘ
    ঘ) √{(1 - p2)/100}
  5. ঙ
    ঙ) None of above
ব্যাখ্যা

At p% profit, selling price = 100 + p
at p% loss, new selling price = (100 + p) - (100 + p) × p/100
= (100 + p) - {(100p + p2)/100}
= 10000 + 100p - 100p - p2
= (10000 - p2)/100

so, (10000 - p2)/100 is equal to 1
1 is equal to 1/(10000 - p2)/100
100 is equal to 1 × (100/ 10000 - p2) × 100
= 10000/(10000 - p2)

অপশন গ) (10000/10000-p^2) হওয়ার কথা ছিলো। সেক্ষেত্রে উত্তর ঠিক হয়।
লাইভ পরীক্ষার প্রশ্নে অপশন ভুল থাকায় উত্তর হিসাবে ঙ) None of above কে ধরা হয়েছে।

১৪,০২৭.
A committee is to consist of two members. If there are eight men and five women available to serve on the committee, how many different committees can be formed?
  1. ক
    78
  2. খ
    86
  3. গ
    98
  4. ঘ
    106
ব্যাখ্যা
Question: A committee is to consist of two members. If there are eight men and five women available to serve on the committee, how many different committees can be formed?

Solution:

Here,
Total members,
n = 8 + 5 = 13
r = 2

Number of committees can be formed
= 13C2 
= 13 × 12/2 × 1
= 156/2
= 78

∴ 78 different committees can be formed.
১৪,০২৮.
log23 × log32 = ?
  1. ক
    1
  2. খ
    2
  3. গ
    √2
  4. ঘ
    0
ব্যাখ্যা
Question: log23 × log32 = ?

Solution:
log23 × log32
= log23 × (1/log23)
= log23 / log23
= 1
১৪,০২৯.
A motorcyclist covers the first 40 km in 20 minutes and the second 60 km in 30 minutes. Between these two segments, the motorcyclist stopped for 10 minutes for a rest. What is the average speed of the motorcycle in km/h?
  1. ক
    80 km/h
  2. খ
    90 km/h
  3. গ
    100 km/h
  4. ঘ
    120 km/h
ব্যাখ্যা

Question: A motorcyclist covers the first 40 km in 20 minutes and the second 60 km in 30 minutes. Between these two segments, the motorcyclist stopped for 10 minutes for a rest. What is the average speed of the motorcycle in km/h?

Solution:
মোট দূরত্ব = 40 কিমি + 60 কিমি = 100 কিমি।

প্রথম অংশের সময় = 20 মিনিট।
দ্বিতীয় অংশের সময় = 30 মিনিট।
বিশ্রামের জন্য বিরতি = 10 মিনিট।
মোট সময় = 20 + 30 + 10 মিনিট = 60 মিনিট = 1 ঘন্টা

গড় গতিবেগ = 100 কিমি/1 ঘন্টা
= 100 কিমি/ঘন্টা
∴ মোটরসাইকেলটির গড় গতিবেগ হলো 100 কিমি/ঘন্টা।

১৪,০৩০.
A die is thrown twice. What is the probability that the product of the numbers appearing both times is odd?
  1. ক
    1/9
  2. খ
    1/4
  3. গ
    1/2
  4. ঘ
    2/3
  5. ঙ
    3/5
ব্যাখ্যা
For an odd product, both of those numbers have to be odd.
The probability of getting an odd number in a single throw is  1/2 , because there are 3 (out of 6) possibilities.
Therefore, for two throws of the die, the probability of getting an odd product is  1/4 .
You can verify this if you list the possibilities “manually”:
 [(1,1), (1,3), (3,1), (3,3), (1,5), (5,1), (3,5), (5,3), (5,5)]  which makes 9 out of 36 cases (pairs) for both throws of the die, or 9/36 =1/4
১৪,০৩১.
For what percentage of profit per annum by which Tk. 12000 will be Tk. 17760 as profit-principal in 6 years?
  1. ক
    3%
  2. খ
    5%
  3. গ
    8%
  4. ঘ
    10%
ব্যাখ্যা

Question: For what percentage of profit per annum by which Tk. 12000 will be Tk. 17760 as profit-principal in 6 years?

Solution: 
Principal, P = Tk. 12000
Total Amount, A = Tk. 17760
Time, n = 6 years
Simple Interest SI = A - P = 17760 - 12000 = Tk. 5760

We know, 
SI = Prn/100
⇒ 5760 = (12000 × r × 6)/100
⇒ r × 720 = 5760
⇒ r = 5760/720
∴ r = 8

So the profit percentage of per annum is 8%.

১৪,০৩২.
A man completes a journey in 8 hours. He travels the first half of the journey at the rate of 40 km/hr and the second half at the rate of 60 km/hr. Find the total distance of the journey in km. 
  1. ক
    290 km.
  2. খ
    304 km.
  3. গ
    354 km.
  4. ঘ
    384 km.
ব্যাখ্যা

Question: A man completes a journey in 8 hours. He travels the first half of the journey at the rate of 40 km/hr and the second half at the rate of 60 km/hr. Find the total distance of the journey in km. 

Solution:
Let the total distance of the journey be d km.
Then, the first half of the journey = d/2 km and the second half = d/2 km.

Time taken for the first half,
= (d/2) / 40 hours
= d/80 hours

And,
Time taken for the second half,
= (d/2) / 60 hours
= d/120 hours

According to the question,
(d/80) + (d/120) = 8
⇒ (3d + 2d)/240 = 8
⇒ 5d/240 = 8
⇒ 5d = 8 × 240
⇒ 5d = 1920
⇒ d = 1920/5
⇒ d = 384 km

∴ The total distance of the journey is 384 km.

১৪,০৩৩.
Rony and Jony invest in a business in the ratio 7 : 5. If 4% of the total profit goes to charity and Rony's share is Tk. 224, what is the total profit?
  1. ক
    ক) Tk. 200
  2. খ
    খ) Tk. 300
  3. গ
    গ) Tk. 400
  4. ঘ
    ঘ) Tk. 500
ব্যাখ্যা
Question: Rony and Jony invest in a business in the ratio 7 : 5. If 4% of the total profit goes to charity and Rony's share is Tk. 224, what is the total profit?

Solution:
Let,
The total profit be Tk. 100.
Sum of their ratios = 7 + 5 = 12
After paying 4% to charity,
Rony's share = 96 × (7/12)  = Tk. 56

If Rony's share is Tk. 56, total profit = Tk. 100.
If Rony's share is Tk. 1, total profit = Tk. 100/56
∴ If Rony's share is Tk. 224, total profit = Tk. (100 × 224)/56
= Tk. 400
১৪,০৩৪.
A sum of money amounts to Tk. 6690 after 3 years and to Tk 10035 after 6 years on compound interest. Find the sum.
  1. ক
    ক) Tk 4360
  2. খ
    খ) Tk 4560
  3. গ
    গ) Tk 4660
  4. ঘ
    ঘ) Tk 4460
ব্যাখ্যা

Let the sum be P
then,
P(1 + r/100)3 = 6690 .......(i)
and
P(1 + r/100)6 = 10035 .......(ii)
On dividing (ii) by )i),
(1 + r/100)3 = 10025/6690 = 3/2
Substituting this value in (i) we find, P×(3/2) = 6690
⇒ P = (6690×2/3) = 4460

১৪,০৩৫.
At what percentage profit must an article be sold such that selling it at two-thirds of that price results in a 20% loss?
  1. ক
    20%
  2. খ
    20.50%
  3. গ
    17.50%
  4. ঘ
    35%
  5. ঙ
    15%
ব্যাখ্যা

Question: At what percentage profit must an article be sold such that selling it at two-thirds of that price results in a 20% loss?
​
​Solution:
Let,
Cost Price be x .
Selling Price be y.
​
​Selling at 2/3 of y, causes 20% loss,
So, 2y/3 = x - 20% of x
⇒ 2y/3 = x - (20x/100)
⇒ 2y/3 = x{(1 - (20/100)}
⇒ 2y/3 = x × (80/100)
∴ y = 6x/5
​
​Profit = Selling Price - Cost Price
= (6x/5) - x
= (6x - 5x)/5
= x/5
​
​∴ Profit Percentage = (Profit/Cost Price) × 100%
= {(x/5)/x} × 100%
= 20%

১৪,০৩৬.
The second and third terms of a geometric series are 9 and 3 respectively. The fifth term of the series is –
  1. ক
    ক) 0
  2. খ
    খ) 1/3
  3. গ
    গ) 1
  4. ঘ
    ঘ) 1/9
ব্যাখ্যা

ATQ, ar2-1 = ar = 9 ......(i)
ar3-1 = 3 ..... (ii)  
(ii)/(i) = r = 1/3
from (i) we get, a = 9×3 = 27
∴ ar5-1 = 27×(1/3)4 
= 27×(1/81)
= 1/3 

১৪,০৩৭.
If cosecθ - cotθ = 1/5, then find the value of sinθ + 5cosθ. 
  1. ক
    √5
  2. খ
    1/5
  3. গ
    5
  4. ঘ
    1/√5
ব্যাখ্যা

Question: If cosecθ - cotθ = 1/5, then find the value of sinθ + 5cosθ.

Solution:
cosecθ - cotθ = 1/5
⇒ (1/sinθ) - (cosθ/sinθ) = 1/5
⇒ (1 - cosθ)/sinθ = 1/5
⇒ sinθ = 5(1 - cosθ)
∴ sinθ = 5 - 5cosθ

∴ sinθ + 5cosθ = (5 - 5cosθ) + 5cosθ
= 5 - 5cosθ + 5cosθ
= 5

১৪,০৩৮.
The equation  is only possible when?
  1. ক
    x = - 2y
  2. খ
    x > y
  3. গ
    x = y
  4. ঘ
    x < y
ব্যাখ্যা

Question: The equation  is only possible when?

Solution:
cos2θ = (x + y)2/4xy

Maximum value of cos2θ = 1. So,
⇒ 1 = (x + y)2/4xy
⇒ 4xy = (x + y)2
⇒ 4xy = x2 + y2 + 2xy
⇒ 0 = x2 + y2 - 2xy
⇒ 0 = (x - y)2
⇒ 0 = x - y
∴ x = y

১৪,০৩৯.
What least number must be added to 1056, so that the sum is completely divisibly by 23?
  1. ক
    2
  2. খ
    3
  3. গ
    18
  4. ঘ
    21
ব্যাখ্যা

Question: What least number must be added to 1056, so that the sum is completely divisibly by 23?

Solution:
1056 কে 23  দ্বারা ভাগ করলে 21 অবশিষ্ট থাকে।

এখানে
23 - 21 = 2
2, 1056 এর সাথে যোগ করলে যোগফল 23 দ্বারা বিভাজ্য ।

১৪,০৪০.
In how many ways can a football team be chosen out of 14 players?
  1. ক
    182
  2. খ
    246
  3. গ
    364
  4. ঘ
    448
ব্যাখ্যা
Question: In how many ways can a football team be chosen out of 14 players?

Solution:

A football team contains 11 players.

Required number of ways
= nCr 
= nCn - r
= 14C14-11
= 14C3
= (14 × 13 × 12)/(3 × 2 × 1)
= 364

∴ A football team be chosen out of 14 players in 364 ways.
১৪,০৪১.
A 180-meter-long train takes 18 seconds to pass a pole. How long will it take to pass a 330-meter-long platform?
  1. ক
    30 seconds
  2. খ
    33 seconds
  3. গ
    42 seconds
  4. ঘ
    51 seconds
ব্যাখ্যা
Question: A 180-meter-long train takes 18 seconds to pass a pole. How long will it take to pass a 330-meter-long platform?

Solution:
আমরা জানি,
কোনো ট্রেন একটি খুঁটিকে অতিক্রম করলে ট্রেনটি তার নিজের দৈর্ঘ্যকে অতিক্রম করে।
আবার,
কোনো প্ল্যাটফর্মকে অতিক্রম করতে হলে ট্রেনকে নিজের দৈর্ঘ্য এবং প্ল্যাটফর্মের দৈর্ঘ্যের সমান দূরত্ব অতিক্রম করতে হয়।

∴ প্ল্যাটফর্ম অতিক্রম করলে ট্রেনের অতিক্রান্ত দূরত্ব = (ট্রেনের দৈর্ঘ্য + প্ল্যাটফর্মের দৈর্ঘ্য) = (180 + 330) মিটার = 510 মিটার 

এখন,
180 মিটার অতিক্রম করে = 18 সেকেন্ডে
∴ 1 মিটার অতিক্রম করে = 18/180 সেকেন্ডে
∴ 510 মিটার অতিক্রম করে = (18 × 510)/180 = 51 সেকেন্ডে
১৪,০৪২.
Find the greatest number that exactly divides each of the numbers 48, 72, and 108.
  1. ক
    16
  2. খ
    9
  3. গ
    12
  4. ঘ
    18
ব্যাখ্যা

Question: Find the greatest number that exactly divides each of the numbers 48, 72, and 108.

Solution:
We know,
The HCF (Highest Common Factor) of two or more numbers is the greatest number that divides each of them exactly.

Now,
Prime factorization of 48 = 2 × 2 × 2 × 2 × 3

Prime factorization of 72 = 2 × 2 × 2 × 3 × 3

Prime factorization of 108 = 2 × 2 × 3 × 3 × 3

∴ HCF of 48, 72, and 108 = 2 × 2 × 3 = 12

Therefore, the greatest number is 12.

১৪,০৪৩.
A sum of money amounts to Tk. 5200 in 5 years and to Tk. 5680 in 7 years at simple interest. The rate of interest per annum is?
  1. ক
    ক) 3%
  2. খ
    খ) 4%
  3. গ
    গ) 5%
  4. ঘ
    ঘ) 6%
ব্যাখ্যা
Question: A sum of money amounts to Tk. 5200 in 5 years and to Tk. 5680 in 7 years at simple interest. The rate of interest per annum is?

Solution:
Simple interest for 2 years = (5680 - 5200) Tk.
= Tk. 480
∴ Simple Interest for 2 years =  Tk. 480
∴ Simple Interest for 5 years =  Tk. (480 × 5/2)
= Tk. 1200
∴ Principal = 5200 - 1200 = Tk. 4000.

We know, 
I = Pnr
⇒ r = I/Pn
 ⇒ r = (1200 × 100)/(4000 × 5)
∴ r = 6%
১৪,০৪৪.
Which of the following is a leap year?
  1. ক
    1982
  2. খ
    1984
  3. গ
    1998
  4. ঘ
    2002
ব্যাখ্যা

Question: Which of the following is a leap year?

Solution:
অধিবর্ষ বা লিপ ইয়ার নির্ণয়ের দুটি প্রধান নিয়ম রয়েছে:
১. সাধারণ বছর: বছরটি 4 দ্বারা নিঃশেষে বিভাজ্য হতে হবে।
২. শতাব্দী বছর (100 দ্বারা বিভাজ্য): বছরটি 400 দ্বারা নিঃশেষে বিভাজ্য হতে হবে।

এখন,
1982 ÷ 4 = 495.5 → বিভাজ্য নয় → Leap year নয়। 
1984 ÷ 4 = 496 → বিভাজ্য → Leap year. 
1998 ÷ 4 = 499.5 → বিভাজ্য নয় → Leap year নয়। 
2002 ÷ 4 = 500.5 → বিভাজ্য নয় → Leap year নয়। 

অতএব, 1984 সালটি অধিবর্ষ।

১৪,০৪৫.
In a sequence of 10 consecutive integers, how much greater is the sum of the last five integers than the sum of the first five integers?
  1. ক
    22
  2. খ
    25
  3. গ
    30
  4. ঘ
    32
ব্যাখ্যা
ধরি, সংখ্যাগুলো x - 4, x - 3, x - 2, x - 1, x, x + 1, x + 2, x + 3, x +  4, x + 5
শেষ 5টি সংখ্যার যোগফল = 5x + 15
প্রথম 5টি সংখ্যার যোগফল = 5x - 10
∴ পার্থক্য = 5x + 15 - ( 5x - 10) = 25
১৪,০৪৬.
Find the number of the divisors of 72
  1. ক
    10
  2. খ
    11
  3. গ
    12
  4. ঘ
    13
ব্যাখ্যা
Question:  Find the number of the divisors of 72

Solution: 
72
= 32 × 23 

the number of the divisors of 72 is = (2 + 1) × (3 + 1)
= 3 × 4 
= 12
১৪,০৪৭.
A bottle of whisky contains 40% alcohol. If we replace a part of this whisky by another whisky containing 20% alcohol, the percentage of alcohol becomes 28%. What quantity of whisky is replaced?
  1. ক
    3/5
  2. খ
    3/4
  3. গ
    4/5
  4. ঘ
    2/5
ব্যাখ্যা
Question: A bottle of whisky contains 40% alcohol. If we replace a part of this whisky by another whisky containing 20% alcohol, the percentage of alcohol becomes 28%. What quantity of whisky is replaced?

Solution:

∴ Ratio of first and second whisky in the mixture
= 8 : 12 = 2 : 3

Now, the quantity of whisky replaced is equal to the quantity of the second whisky added.
∴ The quantity of whisky replaced = 3/5
১৪,০৪৮.
A box contains 24 electric bulbs, out of which 6 are defective. Two bulbs are chosen at random from this box. The probability that at least one of them is defective is:
  1. ক
    41/92
  2. খ
    27/119
  3. গ
    51/92
  4. ঘ
    41/119
  5. ঙ
    None of the above
ব্যাখ্যা

Question: A box contains 24 electric bulbs, out of which 6 are defective. Two bulbs are chosen at random from this box. The probability that at least one of them is defective is:

Solution:
Given that,
Total bulbs = 24
Defective bulbs = 6
Non-defective bulbs = 24 - 6 = 18
Two bulbs are chosen at random (without replacement)

Now,
P(both non-defective) = (18/24) × (17/23)
= 306/552
= 51/92

And,
∴ P(at least one defective)
= 1 - P(both non-defective)
= 1 - (51/92)
= (92 - 51)/92
= 41/92

১৪,০৪৯.
The sum of age of a family consisting of a father, a mother and their only son is 70. Mother is four times the age of the son and father is five times the age of the son. What is the age of the mother?
  1. ক
    24 years
  2. খ
    26 years
  3. গ
    28 years
  4. ঘ
    32 years
ব্যাখ্যা
Question: The sum of age of a family consisting of a father, a mother and their only son is 70. Mother is four times the age of the son and father is five times the age of the son. What is the age of the mother?

Solution: 
let, 
the age of the son is x 
so,
mother's age = 4x
father's age = 5x

∴ x + 4x + 5x = 70
or, 10x = 70
∴ x = 7

mother's present age is = (4 × 7) = 28 years
১৪,০৫০.
In how many different ways can the letters of the word 'EXTRA' be arranged so that the vowels are never together?
  1. ক
    120 ways
  2. খ
    72 ways
  3. গ
    144 ways
  4. ঘ
    48 ways
  5. ঙ
    320 ways
ব্যাখ্যা

Question: In how many different ways can the letters of the word 'EXTRA' be arranged so that the vowels are never together?

Solution:
Taking the vowels (EA) as one letter, the given word has
the letters X T R (EA) = 4 letters.
∴ These letters can be arranged in = 4! = 24 ways.
∴ The letters EA may be arranged amongst themselves in = 2! = 2 ways.

∴ Number of arrangements having vowels together = (24 × 2) = 48 ways.

∴ Total arrangements of all letters = 5! = (5 × 4 × 3 × 2 × 1) = 120.

∴ Number of arrangements not having vowels together = (120 - 48) = 72

So number of arrangements where vowels are never together = 72

১৪,০৫১.
3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?
  1. ক
    ক) 10
  2. খ
    খ) 11
  3. গ
    গ) 12
  4. ঘ
    ঘ) 13
ব্যাখ্যা

Let the required number of working hours per day be x
More pumps, Less working hours per day (Indirect proportion)
Less days, More working hours per day (Indirect proportion)
Pumps 4:3 & Days 1:2 } :: 8:x
∴ 4×1×x = 3×2×8
⇔ x = (3×2×8)/(4)
⇔ x = 12

১৪,০৫২.
5 times a positive number is less than its square by 24. What is the integer?
  1. ক
    5
  2. খ
    8
  3. গ
    7.5
  4. ঘ
    9
ব্যাখ্যা
Question: 5 times a positive number is less than its square by 24. What is the integer?

Solution:
Let the unknown number be x.
5 times a positive number = 5x
5 times a positive number is less than its square by 24
x2 - 5x = 24
⇒ x2 + 3x - 8x - 24 = 0
⇒ x(x + 3) - 8(x + 3) = 0
⇒ (x - 8)(x + 3) = 0
∴ x = 8

8 is the required integer.
১৪,০৫৩.
If |x + 2| = |x - 1| then what is the value of x?
  1. ক
    ক) 1/2
  2. খ
    খ) 2
  3. গ
    গ) - 1
  4. ঘ
    ঘ) - 1/2
ব্যাখ্যা
Quesion: If |x + 2| = |x - 1| then what is the value of x?

Solution:
|x + 2| = |x - 1|
⇒ |x + 2|2 = |x - 1|2
⇒ (x + 2)2 = (x - 1)2
⇒ x2 + 4x + 4 = x2 - 2x + 1
⇒ 6x = - 3
∴ x = - 1/2
১৪,০৫৪.
Four persons are chosen at random from a group of 3 men, 2 women and 4 children. The chance that exactly 2 of them are children, is-
  1. ক
    1/9
  2. খ
    1/5
  3. গ
    1/12
  4. ঘ
    10/21
ব্যাখ্যা

n(S) = number of ways of choosing 4 persons out of 9
= 9C4 = (9 × 8 × 7 × 6)/(4 × 3 × 2 × 1) = 126

n(E) = number of ways of choosing 2 children out of 4 and 2 persons out of (3 + 2) personal
n(E) = 4C2 × 5C2 = {(4 × 3)/(2 × 1) × (5 × 4)/(2 × 1)} = 60

∴P(E) = n(E)/n(S) = 60/126 = 10/21.

১৪,০৫৫.
৮টি ধারাবাহিক বিজোড় সংখ্যার ৬ষ্ঠ সংখ্যাটি হল - ১৭, সবগুলো সংখ্যার সমষ্টি কত?
  1. ক
    ১১২
  2. খ
    ১২২
  3. গ
    - ১২২
  4. ঘ
    - ১১২
  5. ঙ
    কোনটিই নয়
ব্যাখ্যা

প্রশ্ন: ৮টি ধারাবাহিক বিজোড় সংখ্যার ৬ষ্ঠ সংখ্যাটি হল - ১৭, সবগুলো সংখ্যার সমষ্টি কত?

সমাধান:
৮টি ধারাবাহিক বিজোড় সংখ্যার সিরিজটি হলো: - ২৭, - ২৫, - ২৩ - ২১, - ১৯, - ১৭, - ১৫, - ১৩
সবগুলো সংখ্যার সমষ্টি = - (২৭ + ২৫ + ২৩ + ২১ + ১৯ + ১৭ + ১৫ + ১৩)
= - ১৬০

আবার
৮টি ধারাবাহিক বিজোড় সংখ্যার সিরিজটি হলো: - ৭, - ৯, - ১১, - ১৩, - ১৫, - ১৭, - ১৯, - ২১
সবগুলো সংখ্যার সমষ্টি = - (৭ + ৯ + ১১ + ১৩ + ১৫ + ১৭ + ১৯ + ২১)
= - ১১২

এখানে দুইভাবে সমাধান করলে উত্তর আসে - ১১২ এবং - ১৬০
অপশনে যেহেতু  - ১১২ আছে তাই সঠিক উত্তর হিসেবে  - ১১২ নেওয়া হয়েছে।

১৪,০৫৬.
60% of 500 is what percent of 400?
  1. ক
    80%
  2. খ
    75%
  3. গ
    70%
  4. ঘ
    65%
ব্যাখ্যা
Question: 60% of 500 is what percent of 400?

Solution:
Let
60% of 500 be x percent of 400.

That means,
60% of 500 = x% of 400.
⇒ 60 × 500/100 = 400x/100
⇒ 300 = 4x
⇒ 4x = 300
⇒ x = 75
১৪,০৫৭.
A man spends 45% of his salary on rent, 25% on food, and saves the rest. If his salary is Tk. 60000. how much does he save?
  1. ক
    Tk. 21500
  2. খ
    Tk. 18000
  3. গ
    Tk. 15300
  4. ঘ
    Tk. 12000
ব্যাখ্যা

Question: A man spends 45% of his salary on rent, 25% on food, and saves the rest. If his salary is Tk. 60000. how much does he save?
 
Solution: 
Given that, 
Total salary = Tk. 60000

Now, 
Spends on rent = 45% of 60000
= (45/100) × 60000
= Tk. 27000 

And spends on food = 25% of 60000
= (25/100) × 60000
= Tk. 15000

∴ Total expenditure = rent + food
= 27000 + 15000
= Tk. 42000

∴ Savings = Total salary - Total expenditure
= 60000 - 42000
= Tk. 18000

He saves Tk. 18000

Shortcut method:
Percentage saved = 100% - (45% + 25%)
= 100% - 70%
= 30%

∴ Savings = 30% of 60000
= 0.30 × 60,000
= Tk. 18000

১৪,০৫৮.
In a class average age of 15 boys is 11. If 5 boys each of age 9 years are added, what would be the new average?
  1. ক
    15 years
  2. খ
    12.5 years
  3. গ
    10.5 years
  4. ঘ
    16 years
ব্যাখ্যা

Question: In a class average age of 15 boys is 11. If 5 boys each of age 9 years are added, what would be the new average?

Solution:
Sum of ages of 15 boys = 15 × 11= 165
Sum of ages of 5 boys = 5 × 9 = 45
Total age of 20 boys = 165 + 45 = 210
∴ Average of ages of 20 boys = 210/20 = 10.5 years

১৪,০৫৯.
How long does a train 110 metres long running at the speed of 72 km/hr take to cross a bridge 132 metres in length?
  1. ক
    9.8 sec
  2. খ
    12.1 sec
  3. গ
    12.42 sec
  4. ঘ
    14.3 sec
ব্যাখ্যা
Question: How long does a train 110 metres long running at the speed of 72 km/hr take to cross a bridge 132 metres in length?

Solution:
Speed = 72 km/hr
= (72 × 1000)/3600 m/s
= 20 m/s

Train has to be treavelled = (110 + 132) metres = 242 metres

Required time = 242/20 seconds 
= 12.1 seconds
১৪,০৬০.
A cake is divided into 24 pieces. If Kamal takes 1/4 of the cake and Jamal takes 1/3 of the rest that are left, how many pieces are still left?
  1. ক
    18
  2. খ
    16
  3. গ
    12
  4. ঘ
    8
ব্যাখ্যা
Question: A cake is divided into 24 pieces. If Kamal takes 1/4 of the cake and Jamal takes 1/3 of the rest that are left, how many pieces are still left?

Solution:
The cake is divided into 24 pieces, and Kamal takes 1/4 of the cake is = (1/4) × 24 = 6 pieces
After Kamal takes 6 pieces, there are,
24 − 6 = 18 pieces.

Jamal takes 1/3 of the remaining pieces,
(1/3) × 18 = 6 pieces.
So Jamal takes 6 pieces.

So the cake are left = 24 - 6 - 6 = 12 pieces.

∴ After Kamal and Jamal take their portions, 12 pieces of the cake are still left.
১৪,০৬১.
The monthly incomes of A and B are in the ratio 4 : 3. Each saves Tk.600. If their expenditures are in the ratio 3 : 2, then what is the monthly income of A?
  1. ক
    ক) 1800 taka
  2. খ
    খ) 2400 taka
  3. গ
    গ) 3000 taka
  4. ঘ
    ঘ) 1200 taka
ব্যাখ্যা
প্রশ্ন: The monthly incomes of A and B are in the ratio 4 : 3. Each saves Tk.600. If their expenditures are in the ratio 3 : 2, then what is the monthly income of A?

সমাধান:
ধরি,
A  এর মাসিক আয় ৪ক টাকা 
B এর মাসিক আয় ৩ক টাকা

A এর খরচ (৪ক - ৬০০) টাকা 
B এর খরচ (৩ক - ৬০০) টাকা

শর্তমতে,
(৪ক - ৬০০)/(৩ক - ৬০০) = ৩/২
বা, ৮ক - ১২০০ = ৯ক - ১৮০০
বা, ৯ক - ৮ক = ১৮০০ - ১২০০
বা, ক = ৬০০

A এর মাসিক আয় = ৪ × ৬০০ টাকা = ২৪০০ টাকা
১৪,০৬২.
A sample of 50 liters of glycerine is found to be adulterated to the extent of 20%. How much pure glycerine should be added to it so as to bring down the percentage of impurity to 5%?
  1. ক
    150 liters
  2. খ
    160.5 liters
  3. গ
    164 liters
  4. ঘ
    176 liters
ব্যাখ্যা

Question: A sample of 50 liters of glycerine is found to be adulterated to the extent of 20%. How much pure glycerine should be added to it so as to bring down the percentage of impurity to 5%?

Solution: 
Initially, the 50 liters of glycerine is 20% adulterated. So, the pure glycerine in it is 80% of 50 liters.

Amount of pure glycerine initially = 80% of 50 liters
= 0.8 × 50
= 40 liters

Let 'x' represent the amount of pure glycerine that needs to be added to reduce the percentage of impurity to 5%.

The total volume of glycerine after adding pure glycerine will be 50 + x liters

After adding 'x' liters of pure glycerine, the total amount of pure glycerine in the mixture will be 40  + x liters (added).

Now, this total amount of pure glycerine should be 95% of the new total volume (50 liters original + x liters added), as the impurity percentage is to be reduced to 5%.

So, we can set up an equation:

Total amount of pure glycerine = 95% of total volume after adding pure glycerine

40 + x = 0.95 × 50 + 0.95 × x
⇒ 40 + x = 47.5 + 0.95x
⇒ x - 0.95x = 47.5 - 40
⇒ 0.05x = 7.5
⇒ x = 7.5 / 0.05
⇒ x = 150 liters

১৪,০৬৩.
Find the least number which when divided by 20, 25, 35, and 40 leaves remainders 14, 19, 29 and 34 respectively. 
  1. ক
    ক) 1400
  2. খ
    খ) 1394
  3. গ
    গ) 1406
  4. ঘ
    ঘ) 1384
ব্যাখ্যা
Here
20 − 14 = 6
25 − 19 = 6
35 − 29 = 6
40 − 34= 6

Required number (L.C.M of 20, 25, 35, and 40) - 6

L.C.M of 20, 25, 35, and 40 = 1400
Required number= 1400 - 6 = 1394
১৪,০৬৪.
If one-fifth of one-half of a number is 12, then two-thirds of that number is: 
  1. ক
    72
  2. খ
    80
  3. গ
    84
  4. ঘ
    96
ব্যাখ্যা

Question: If one-fifth of one-half of a number is 12, then two-thirds of that number is: 

Solution:
Let the number be X.
(1/5) × (1/2) × X = 12
⇒ X = 12 × 5 × 2
⇒ X = 120
Two-thirds of the number:
(2/3) × 120 = 80

১৪,০৬৫.
Three taps P, Q and R can fill a tank in 6 hours. After working together for 2 hours, tap R is closed, and P and Q can fill the rest of the tank in 7 hours. The number of hours taken by R alone to fill the tank is –
  1. ক
    7 hours
  2. খ
    8 hours
  3. গ
    14 hours
  4. ঘ
    10 hours
ব্যাখ্যা

Questions: Three taps P, Q, and R can fill a tank in 6 hours. After working together for 2 hours, tap R is closed, and P and Q can fill the rest of the tank in 7 hours. The number of hours taken by R alone to fill the tank is –

Solution:
Three taps P, Q and R can fill a tank in 6 hours.
Three taps can fill in one hour 1/6 part of the tank
Three taps can fill in 2 hours 1/3 part of the tank.

Rest part 1 - 1/3 = 2/3 part
2/3 part can be filled in 7 hours by P and Q

∴ In 1 hour P and Q can fill 2/21 part
∴ In 1 hour P, Q and R can fill 1/6 part

∴ in 1 hour R can fill (1/6 - 2/21) = 1/14 part
Hence, R alone fills the tank in 14 hours.

১৪,০৬৬.
The speed of P and Q are in the ratio 5 : 8. Q takes 24 minutes less than P to reach a destination. Time in which Q reaches the destination?
  1. ক
    32 minutes
  2. খ
    40 minutes
  3. গ
    48 minutes
  4. ঘ
    36 minutes
ব্যাখ্যা

Question: The speed of P and Q are in the ratio 5 : 8. Q takes 24 minutes less than P to reach a destination. Time in which Q reaches the destination?

Solution:
Given, speed of P and Q = 5 : 8

So, ratio of time taken = 8 : 5 [Time ∝ 1/Speed]

Let time taken by P and Q be 8x and 5x minutes respectively.

According to the question,
8x - 5x = 24
⇒ 3x = 24
⇒ x = 8

Hence, time taken by Q = 5 × 8 = 40 minutes

১৪,০৬৭.
A pipe was used to fill a cistern in 6 hours but after working for 4 hours it stopped. another pipe that can fill the tank in 10 hours was replaced to fill the rest of the tank. How much time will it take to fill the rest of the tank by the second pipe?
  1. ক
    2 hours
  2. খ
    6 hours
  3. গ
    10/3 hours
  4. ঘ
    3 hours
ব্যাখ্যা
Question: A pipe was used to fill a cistern in 6 hours but after working for 4 hours it stopped. another pipe that can fill the tank in 10 hours was replaced to fill the rest of the tank. How much time will it take to fill the rest of the tank by the second pipe?

Solution: 
in 4 hours,
fill-up = 4/6 = 2/3
remaining = 1/3

২য় পাইপ 
1 অংশ পানি পূর্ণ করতে পারে = 10 ঘণ্টায়
1/3 অংশ পানি পূর্ণ করতে পারে = 10/3 ঘণ্টায়
১৪,০৬৮.
A man bought some rice and wheat for Tk. 490. The ratio of weight of rice and wheat is 8 : 5 and the price equal amount of rice and wheat is in the ratio 3 : 5. The price of total rice = ?
  1. ক
    Tk. 320
  2. খ
    Tk. 240
  3. গ
    Tk. 280
  4. ঘ
    Tk. 200
ব্যাখ্যা
Question : A man bought some rice and wheat for Tk. 490. The ratio of weight of rice and wheat is 8 : 5 and the price equal amount of rice and wheat is in the ratio 3 : 5. The price of total rice = ?

Solution :
Given,
The ratio of weight of rice and wheat is = 8 : 5
The ratio of equal amount of rice and wheat is = 3 : 5

So the ratio of total price of rice and wheat is = 24 : 25
∴Total = 24 + 25
= 49

According to the question,
49 unit = Tk. 490
∴ 1 unit = Tk. 10

∴ Price of total rice = 24 × 10
= Tk. 240
১৪,০৬৯.
If logm(81) = 4, what is the value of m?
  1. ক
    3
  2. খ
    4
  3. গ
    8
  4. ঘ
    6
ব্যাখ্যা

Question: If logm(81) = 4, what is the value of m?

Solution:
logm(81) = 4
⇒ m4 = 81 [logb(a) = c ⇒ bc = a]
⇒ m4 = 34
∴ m = 3

 

১৪,০৭০.
An 84 kg metal sphere is melted down and reshaped into 4,000 nails of equal size. Find the weight of one nail in grams.
  1. ক
    21 grams
  2. খ
    0.21 grams
  3. গ
    2.4 grams
  4. ঘ
    24 grams
ব্যাখ্যা

Question: An 84 kg metal sphere is melted down and reshaped into 4,000 nails of equal size. Find the weight of one nail in grams.

Solution:
দেওয়া আছে,
ধাতুর বলের ওজন = 84 কেজি = 84 × 1000 = 84000 গ্রাম
পেরেকের সংখ্যা = 4000 টি 

এখন,
4000 পেরেকের ওজন = 84000 গ্রাম
∴ 1 টি পেরেকের ওজন = (84000/4000) গ্রাম = 21 গ্রাম

১৪,০৭১.
The area of a rhombus is 91 cm2 and the length of one of the diagonals is 14 cm. The length of the other diagonal is -
  1. ক
    ক) 15
  2. খ
    খ) 12
  3. গ
    গ) 13
  4. ঘ
    ঘ) 16
ব্যাখ্যা

We know, Area of rhombus = 1/2 × x × y [Here, x and y are two diagonals of the rhombus]
Or, x = (91 × 2) / 14 = 13 cm

১৪,০৭২.
In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 15000, the number of valid votes that the other candidate got, was-
  1. ক
    5000
  2. খ
    5400
  3. গ
    5800
  4. ঘ
    6200
ব্যাখ্যা
Question: In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 15000, the number of valid votes that the other candidate got, was-

Solution:
Total number of votes = 15000
Given that 20% of Percentage votes were invalid
⇒ Valid votes = 80%
∴ Total valid votes = 15000 × (80/100) = 12000
 
1st candidate got 55% of the total valid votes. 
Hence the 2nd candidate should have got 45% of the total valid votes 

∴ Valid votes that 2nd candidate got = total valid votes × (45/100) 
= 12000 × (45/100) = 5400
১৪,০৭৩.
A person takes 20 minutes more to cover a certain distance by decreasing his speed by 20%. What is the time taken to cover the distance at his original speed?
  1. ক
    1 hr
  2. খ
    1 hr 20 min
  3. গ
    1 hr 10 min
  4. ঘ
    50 min
ব্যাখ্যা
Question: A person takes 20 minutes more to cover a certain distance by decreasing his speed by 20%. What is the time taken to cover the distance at his original speed?

Solution:
Let the distance and original speed be 'd' km and 'k' kmph respectively.
d/0.8k - d/k = 20/60
⇒ 5d/4k - d/k = 1/3
⇒ (5d - 4d)/4k = 1/3
⇒ d = (4/3)k

Time taken to cover the distance at original speed
= d/k = 4/3 hours = 1 hour 20 minutes
১৪,০৭৪.
What is the total interest on Tk. 800 at 12.5% per annum for 9 months in Taka?
  1. ক
    75
  2. খ
    110
  3. গ
    88
  4. ঘ
    22
ব্যাখ্যা
Question: What is the total interest on Tk. 800 at 12.5% per annum for 9 months in Taka?

Solution: 
আসল, P = Tk. 800
সুদের হার, r = 12.5% = 0.125 
বছর, n = 9 months = 9/12 year

সুদ = Pnr 
= 800 × (9/12) × 0.125
= 75 Taka 
১৪,০৭৫.
If the three numbers are added in pairs , the sum is equal to 10, 16, 24. What is the difference between third and first number?
  1. ক
    ক) 5
  2. খ
    খ) 6
  3. গ
    গ) 7
  4. ঘ
    ঘ) 8
ব্যাখ্যা
Let,
the numbers are a, b and c
According to the question,
⇒ a + b = 10
⇒ b + c = 16
⇒ c + a = 24

From above question,
⇒ 2(a + b + c) = 50
⇒ (a + b + c) = 25
Value of a = 25 - (b + c) = 25 - 16 = 9
Value of c = 25 - (a + b) = 25 - 10 = 15

Required difference = (15 - 9) = 6
∴ Difference is 6
১৪,০৭৬.
Which of the following is the largest?
  1. ক
    9/12
  2. খ
    10/15
  3. গ
    5/8
  4. ঘ
    7/10
ব্যাখ্যা

Question: Which of the following is the largest?

Solution: 
ক) 9/12 = 0.75

খ) 10/15 = 0.66

গ) 5/8 = 0.62

ঘ) 7/10 = 0.70

So 9/12 = 0.75 is clearly the biggest.

১৪,০৭৭.
  1. ক
    144
  2. খ
    142
  3. গ
    136
  4. ঘ
    138
ব্যাখ্যা
Question:

Solution: 
১৪,০৭৮.
If 0.13 ÷ p2 = 13, then p equals:
  1. ক
    0.1
  2. খ
    0.01
  3. গ
    0.001
  4. ঘ
    0.3
ব্যাখ্যা

Question: If 0.13 ÷ p2 = 13, then p equals:

Solution:
0.13 ÷ p2 = 13
⇒ p2 = 0.13/13
⇒ p2 = 1/100
⇒ p = √1/100
⇒ p = 1/10
⇒ p = 0.1

১৪,০৭৯.
Alloy A contains 40% gold and 60% silver. Alloy B contains 35% gold and 40% silver and 25% copper. Alloys A and B are mixed in the ratio of 1:4 .What is the ratio of gold and silver in the newly formed alloy?
  1. ক
    11:9
  2. খ
    9:11
  3. গ
    3:6
  4. ঘ
    6:3
  5. ঙ
    None of the above
ব্যাখ্যা

A:: - G:S = 40:60
B:: - G:S:C = 35:40:25
New,
G:S= (1×40 + 4×35) : (40×4 + 1×60)
= 180:220
= 18:22
= 9:11

১৪,০৮০.
A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Tk. 1000 more than D, what is B's share?
  1. ক
    Tk. 500
  2. খ
    Tk. 1500
  3. গ
    Tk. 2000
  4. ঘ
    None of these
ব্যাখ্যা

Question: A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Tk. 1000 more than D, what is B's share?

Solution: 
let, they get 5x, 2x, 4x, 3x 

4x - 3x = 1000 
⇒ x = 1000 

∴ B's share is = 2x 
= 2 × 1000 
= 2000 taka 

১৪,০৮১.
Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?
  1. ক
    ক) 5 : 2
  2. খ
    খ) 4 : 3
  3. গ
    গ) 2 : 3
  4. ঘ
    ঘ) 3 : 2
ব্যাখ্যা
(20 × 16) women can complete the work in 1 day
1 woman's 1day's work = 1/ 320
(16 × 15) men can complete the work in 1 day
1 man's 1day's work = 1/240
So, required ratio = 1/240 : 1/320
= 1/3 : 1/4
= 4:3
১৪,০৮২.
If Z = 52 and BAT = 46, then RAT will be equal to-
  1. ক
    78 
  2. খ
    36
  3. গ
    24
  4. ঘ
    120
ব্যাখ্যা
Question: If Z = 52 and BAT = 46, then RAT will be equal to-

Solution:

Here,
The Position number of Z is 26 which is re-write as 26 × 2 = 52.
Now,
BAT = (2 × 2) + (1 × 2) + (20 × 2) 
= 4 + 2 + 40
= 46

Similarly,
RAT = (18 × 2) + (1 × 2) + (20 × 2)
= 36 + 2 + 40
= 78
১৪,০৮৩.
A man buys a cycle for Tk. 1400 and sells it at a loss of 15%. What is the selling price of the cycle?
  1. ক
    Tk. 1220
  2. খ
    Tk. 1808
  3. গ
    Tk. 1190
  4. ঘ
    Tk. 1197
ব্যাখ্যা
At 15% loss, selling price = 85% of Tk. 1400
= Tk. 85 x 1400/100 = Tk. 1190
--------------------------------
Alternative way:
Selling price = 1400 - 15% of Tk. 1400 = 1400 - 210 = Tk. 1190
১৪,০৮৪.
A cloth merchant sold half of his cloth at 20% profit, half of the remaining at 20% loss and the rest was sold at the cost price. Calculate the overall profit% or loss%?
  1. ক
    8% profit
  2. খ
    6.5% loss
  3. গ
    5% profit
  4. ঘ
    9% loss
ব্যাখ্যা
Question: A cloth merchant sold half of his cloth at 20% profit, half of the remaining at 20% loss and the rest was sold at the cost price. Calculate the overall profit% or loss%?

Solution:
Let the CP of the whole cloth be x
CP of 1/2 cloth = x/2

CP of half of the remaining = x/4

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

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

SP of the remaining half = x/4

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

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

Gain % = (x/20)/x × 100% = 5%
১৪,০৮৫.
230 + 230 + 230 + 230 = ?
  1. ক
    ক) 830
  2. খ
    খ) 8120
  3. গ
    গ) 232
  4. ঘ
    ঘ) 230
ব্যাখ্যা

Question: 230 + 230 + 230 + 230 = ?

Solution
230 + 230 + 230 + 230
= 4 × 230
= 22 × 230
= 22 + 30
= 232

১৪,০৮৬.
Interest obtained on a sum of Tk. 5000 for 3 years is Tk. 1500. Find the rate percent.
  1. ক
    20%
  2. খ
    15%
  3. গ
    10%
  4. ঘ
    25%
  5. ঙ
    None
ব্যাখ্যা
Question: Interest obtained on a sum of Tk. 5000 for 3 years is Tk. 1500. Find the rate percent.

Solution:
Here,
p = Tk. 5000
n = 3 years
I = Tk. 1500

Now,
I = pn(r/100)
⇒ 1500 = 5000 × 3 × (r/100)
⇒ r = 10%
১৪,০৮৭.
A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in  6 seconds. The speed of the second train is-
  1. ক
    48 km/hr
  2. খ
    54 km/hr
  3. গ
    82 km/hr
  4. ঘ
    66 km/hr
ব্যাখ্যা
Question: A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in  6 seconds. The speed of the second train is-

Solution:
Distance covered = (108 + 112)
= 220 meter.
Time = 6 seconds.

Relative speed = 220/6 = 110/3 m/s.
= (110 × 3600)/(3 × 1000) km/hr
= 132 km/hr.

Now,
50 + Speed of second train = 132 km/hr.
∴ Speed of second train = (132 - 50) km/hr.
= 82 km/hr.
১৪,০৮৮.
If a man were to sell his chair for Tk. 720, he would lose 25%. To gain 25% he should sell it for:
  1. ক
    ক) Tk. 1200
  2. খ
    খ) Tk. 1000
  3. গ
    গ) Tk. 1300
  4. ঘ
    ঘ) Tk. 960
ব্যাখ্যা
Question: If a man were to sell his chair for Tk. 720, he would lose 25%. To gain 25% he should sell it for:

Solution:
Let the Cost price of the Chair is x.
Selling price = x - 25% of x
⇒ 720 = x - (25x/100)
⇒ 720 = 75x/100
⇒ 75x = 72000
∴ x = 960

To gain 25% = 960 + 25% of 960
= Tk. 1200
১৪,০৮৯.
Alif is shorter than Meena but taller than Zara. Pial is taller than Alif. Meena is the second-tallest person among them. Sumon is shorter than Zara. Who is the third-tallest person among them?
  1. ক
    Alif
  2. খ
    Pial
  3. গ
    Meena
  4. ঘ
    Zara
ব্যাখ্যা

Question: Alif is shorter than Meena but taller than Zara. Pial is taller than Alif. Meena is the second-tallest person among them. Sumon is shorter than Zara. Who is the third-tallest person among them?

Solution:
First statement: Meena > Alif > Zara

Second statement: Pial > Alif

Third statement: Meena is the second-tallest, meaning one person is taller than Meena. Since Pial is taller than Alif and Meena is taller than Alif, Pial must be taller than Meena.
Therefore, Pial > Meena > Alif

Fourth statement: Zara > Sumon

Putting everyone together: Pial > Meena > Alif > Zara > Sumon

∴ The third-tallest person is Alif.

১৪,০৯০.
Tina works four times as fast as Rina. If Rina can complete a work in 20 days alone, how many days will Tina and Rina together take to complete the work? 
  1. ক
    2 days 
  2. খ
    4 days 
  3. গ
    5 days 
  4. ঘ
    6 days 
  5. ঙ
    None
ব্যাখ্যা

Question: Tina works four times as fast as Rina. If Rina can complete a work in 20 days alone, how many days will Tina and Rina together take to complete the work?

Solution:
Tina : Rina work ratio = 4 : 1
∴ Time taken ratio = 1 : 4

Since Rina takes 20 days, Tina takes = 20 / 4 = 5 days

∴ (Tina + Rina)'s 1 day work = (1/5) + (1/20)
= (4 + 1)/20
= 5/20
= 1/4

∴ Total days to finish the work = 1 ÷ (1/4) = 4 days

∴ Tina and Rina together can complete the work in 4 days.

১৪,০৯১.
Simplify: log104+log1025
  1. ক
    ক) 6
  2. খ
    খ) 2
  3. গ
    গ) 4
  4. ঘ
    ঘ) 100
ব্যাখ্যা

log104+log1025
= log10(4×25)
= log10100
= log10102
= 2log1010
= 2

১৪,০৯২.
Currently, a mother’s age is five times that of her son. After 10 years, her age will be three times her son’s age. What is the son’s present age?
  1. ক
    8 years
  2. খ
    12 years
  3. গ
    10 years
  4. ঘ
    7 years
ব্যাখ্যা

Question: Currently, a mother’s age is five times that of her son. After 10 years, her age will be three times her son’s age. What is the son’s present age?

Solution:
Let,
The son’s present age = x years
Then, mother’s present age = 5x years

According to the question,
5x + 10 = 3(x + 10)
⇒ 5x + 10 = 3x + 30
⇒ 5x - 3x = 30 - 10
⇒ 2x = 20
⇒ x = 10

∴ The son’s present age is 10 years.

১৪,০৯৩.
If a coin is tossed once, what is the probability of getting a tail?
  1. ক
    0.5
  2. খ
    1
  3. গ
    0.25
  4. ঘ
    0
ব্যাখ্যা

Question: If a coin is tossed once, what is the probability of getting a tail?

Solution: Here, the total outcome is 2 (Head and Tail) 
The favorable outcome is 1 (Tail)

Therefore, Probability = Favorable outcome/Total outcome
= 1/2
= 0.5

১৪,০৯৪.
If the price of a commodity is decreased by 25% and its consumption is increased by 25%, what will be the increase or decrease in expenditure on the commodity?
  1. ক
    4% increase
  2. খ
    8.25% decrease
  3. গ
    6.25% decrease
  4. ঘ
    8% increase
  5. ঙ
    10% increase
ব্যাখ্যা

Question: If the price of a commodity is decreased by 25% and its consumption is increased by 25%, 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 25%,
∴ Current Price = (100 - 25% of 100) = Tk. 75

Same time due to decrements in price 25% consumption has been increased.
So, Current expenses on commodity = (75 + 25% of 75) = Tk. 93.75

Here,
The initial expenditure was Tk. 100 which became Tk. 93.75 at the end, it means there is 6.25% decrements in the expenditure of the commodity.

So the expenditure decreases by 6.25%

১৪,০৯৫.
Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other, is:
  1. ক
    11.6 sec
  2. খ
    12.5 sec
  3. গ
    10.8 sec
  4. ঘ
    12.8 sec
  5. ঙ
    None
ব্যাখ্যা
Question: Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other, is:

Solution: 
Relative speed = (60 + 40) km/hr = 100 km/hr = 250/9 m/sec
Distance covered in crossing each other = (140 + 160) m = 300 m.

Required time = 300 × (9/250) sec
= 10.8 sec
১৪,০৯৬.
Tea worth Tk.126 per kg and Tk.135 per kg are mixed with a third variety in the ratio 1 : 2 : 2. If the mixture is worth Tk.153 per kg, the price of the third variety per kg will be:
  1. ক
    ক) 84.5 tk 
  2. খ
    খ) 184.5 tk 
  3. গ
    গ) 194.5 tk 
  4. ঘ
    ঘ) 224.5 tk 
ব্যাখ্যা
Question: Tea worth Tk. 126 per kg and Tk. 135 per kg are mixed with a third variety in the ratio 1 : 2 : 2. If the mixture is worth Tk. 153 per kg, the price of the third variety per kg will be:

Solution: 
let, price of third variety x tk per kg 
126y + 135 × 2y + x × 2y = 153 (y + 2y + 2y)
⇒ 126 + 270 + 2x = 765
⇒ 2x = 369
∴ x = 184.5 tk
১৪,০৯৭.
The average weight of 3 friends is 33 kg. None of the friends weights less than 31 kg. What can be the maximum weight of any three friends?
  1. ক
    32
  2. খ
    33
  3. গ
    35
  4. ঘ
    37
ব্যাখ্যা
Question: The average weight of 3 friends is 33 kg. None of the friends weights less than 31 kg. What can be the maximum weight of any three friends?

Solution: 
তিনজনের গড় ওজন ৩৩ কেজি 
মোট ওজন ৩৩ × ৩ কেজি 
= ৯৯ কেজি 

প্রতিজনের ওজন সর্বনিম্ন ৩১ কেজি হতে পারে
∴ দুজনের সর্বনিম্ন ওজন হবে ৩১ × ২ কেজি 
= ৬২ কেজি 

∴ একজনের সর্বোচ্চ ওজন হতে পারে = ৯৯ - ৬২ কেজি 
= ৩৭ কেজি 
১৪,০৯৮.
If p + q + r = 10 and p2 + q2 + r2 = 38, then what is the value of pq + qr + rp? 
  1. ক
    26
  2. খ
    31
  3. গ
    48
  4. ঘ
    12
ব্যাখ্যা

Question: If p + q + r = 10 and p2 + q2 + r2 = 38, then what is the value of pq + qr + rp?

Solution:
We know the identity:
(p + q + r)2 = p2 + q2 + r2 + 2(pq + qr + rp)
⇒ 102 = 38 + 2(pq + qr + rp)
⇒ 100 = 38 + 2(pq + qr + rp)
⇒ 2(pq + qr + rp) = 100 - 38 = 62
⇒ pq + qr + rp = 62/2
∴ pq + qr + rp = 31

১৪,০৯৯.
If the sum of two numbers is 20 and the sum of their squares is 208, then what is the product of the two numbers?
  1. ক
    90
  2. খ
    96
  3. গ
    100
  4. ঘ
    104
ব্যাখ্যা

Question: If the sum of two numbers is 20 and the sum of their squares is 208, then what is the product of the two numbers?

Solution:
ধরি, সংখ্যা দুটি যথাক্রমে x এবং y।
দেওয়া আছে,
x + y = 20
x2 + y2 = 208

আমরা জানি,
(x + y)2 = x2 + y2 + 2xy
⇒ (20)2 = 208 + 2xy
⇒ 400 = 208 + 2xy
⇒ 2xy = 400 - 208
⇒ 2xy = 192
⇒ xy = 192 / 2
∴ xy = 96

সুতরাং, সংখ্যা দুটির গুণফল হলো 96.

১৪,১০০.
Two bags together contain 900 marbles. If one-sixth of the marbles in the second bag are moved to the first bag, both bags have the same number of marbles. How many marbles are in the second bag initially?
  1. ক
    360
  2. খ
    480
  3. গ
    540
  4. ঘ
    380
ব্যাখ্যা
Question: Two bags together contain 900 marbles. If one-sixth of the marbles in the second bag are moved to the first bag, both bags have the same number of marbles. How many marbles are in the second bag initially?

Solution:
Let the first bag have x marbles and the second bag have y marbles.
Than,
x + y = 900 ..........(1)
And
After transferring one-sixth of the marbles from the second bag to the first. than,
⇒ x + (y/6) = y - (y/6)
⇒ x + (y/6) = 5y/6
⇒ x = (5y/6) - (y/6)
⇒ x = 4y/6
∴ x = 2y/3

From (1),
⇒ (2y/3) + y = 900
⇒ 5y/3 = 900
⇒ y = (900 × 3)/5
∴ y = 540

So the second bag initially contains 540 marbles.