Bank Math

PrepBank · পাতা ১২০ / ১৬১ · ১১,৯০১–১২,০০০ / ১৬,১২৪

১১,৯০১.

The difference between the greatest and the least four-digit numbers that begins with 3 and ends with 5 is -

ক
ক) 900
খ
খ) 990
গ
গ) 999
ঘ
ঘ) 909

ব্যাখ্যা

Question: The difference between the greatest and the least four-digit numbers that begins with 3 and ends with 5 is -

Solution:
The greatest four-digit number that begins with 3 and ends with 5 = 3995
The least four-digit number that begins with 3 and ends with 5 = 3005

∴ Required difference = 3995 - 3005 = 990

১১,৯০২.

Today it is Thursday. After 132 days, it will be-

ক
Monday
খ
Sunday
গ
Wednesday
ঘ
Thursday

ব্যাখ্যা

Question: Today it is Thursday. After 132 days, it will be-

Solution:
132 ÷ 7 = 18, Reminder 6
∴ The day after 132 days = Thursday + 6 = Wednesday

Alternative Solution:
Since each day of the week is repeated after 7 days.
After 133 days,it will be thursday.
So one day before that would be Wednesday.

১১,৯০৩.

A grocer purchased a quantity of bananas at 3 pounds for $0.50 and sold the entire quantity at 4 pounds for $1.00. How many pounds did the grocer purchase if the profit from selling the bananas was $10.00?

ক
40
খ
60
গ
90
ঘ
120

ব্যাখ্যা

Question: A grocer purchased a quantity of bananas at 3 pounds for $0.50 and sold the entire quantity at 4 pounds for $1.00. How many pounds did the grocer purchase if the profit from selling the bananas was $10.00?

Solution:
Cost price of 3 pounds = $0.5
Selling price of 4 pounds = $1.00
Selling price of 3 pounds = (1/4) × 3 = $0.75
∴ Profit for every 3 pounds = 0.75 - 0.5 = $0.25
Total profit = $10

$0.25 profit in 3 pounds
∴ $1 profit in 3/0.25 pounds
∴ $10 profit in (3 × 10)/0.25 pounds
= 120 pounds

১১,৯০৪.

If sinA = cos2A, A =?

ক
30°
খ
40°
গ
50°
ঘ
60°

ব্যাখ্যা

প্রশ্ন: If sinA = cos2A, A =?

সমাধান:
sinA = cos2A
⇒ sinA = 1 - 2 sin²A
⇒ 2 sin²A + sinA - 1 = 0
⇒ 2 sin²A + 2 sinA - sinA -1 = 0
⇒ 2 sinA ( sinA + 1) -1 (sinA + 1) = 0
⇒ (sinA + 1) (2 sinA -1) = 0

হয়, sinA + 1 = 0
⇒ sinA = -1
⇒ A = 270°

অথবা 2 sinA - 1 = 0
⇒ sinA = 1/2
⇒ A = 30°

১১,৯০৫.

A triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is 100 m, then the altitude of the triangle is:

ক
50m
খ
100m
গ
125m
ঘ
200m

ব্যাখ্যা

Question: A triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is 100 m, then the altitude of the triangle is:

Solution:
In this question, we will denote ‘b’ as the base h1 and h2 as the altitudes of the triangle and parallelogram respectively.

Then, according to the data in the question:

½ × b × h1 = b × h2
⇒ h1 = 2 h2
⇒ h1 = 2 × 100 = 200m

∴ The altitude of the triangle is 200m.

১১,৯০৬.

On his daily commute Bill always crosses a certain toll bridge exactly two times. Bill can buy a discount pass for $60 which decreases the cost of the toll by 20%. If the toll costs $1.50 per crossing, after how many days of commuting will buying the discount pass result in a financial benefit for Bill?

ক
50 days
খ
60 days
গ
200 days
ঘ
100 days

ব্যাখ্যা

Question: On his daily commute Bill always crosses a certain toll bridge exactly two times. Bill can buy a discount pass for $60 which decreases the cost of the toll by 20%. If the toll costs $1.50 per crossing, after how many days of commuting will buying the discount pass result in a financial benefit for Bill?

Solution:
price of the discount pass = 60 dollars
price of toll per day = 1.5 × 2 = 3 dollars
giving 20% discount on 3 dollars,
the discount is = 20% of 3 = 0.6 dollars

let,
after x days he will get financial benefit.
so,
0.6x = 60
x = 100 days

১১,৯০৭.

What will be the least number which when tripled will be exactly divisible by 8, 12, 15?

ক
30
খ
45
গ
40
ঘ
32

ব্যাখ্যা

Question: What will be the least number which when tripled will be exactly divisible by 8, 12, 15?

Solution:
Prime factorization of,
8 = 2 × 2 × 2
12 = 2 × 2 × 3
15 = 3 × 5

LCM = 2 × 2 × 2 × 3 × 5 = 120
So the smallest, 3n = 120
⇒ n = 120/3
∴ n = 40

So the least number which when tripled will be exactly divisible by 8, 12, and 15 is 40.

১১,৯০৮.

A committee of 4 members is to be formed by selecting out of 7 men and 6 women. In how many different ways can the committee be formed if it should have 3 men and 1 woman?

ক
110 different ways
খ
210 different ways
গ
100 different ways
ঘ
150 different ways

ব্যাখ্যা

Question: A committee of 4 members is to be formed by selecting out of 7 men and 6 women. In how many different ways can the committee be formed if it should have 3 men and 1 woman?

Solution:
3 men can be selected out of 7 men in
⁷C₃ = 7!/[3!(7 - 3)!]
= (7 × 6 × 5)/(3 × 2 × 1)
= 35 ways

1 woman can be selected out of 6 women in
⁶C₁ = 6 ways

∴ Required number of ways = 35 × 6 = 210

∴ 210 different ways to form the committee with 3 men and 1 woman.

১১,৯০৯.

What is the next term in the sequence: 3, 9, 6, 11, 9, 13, ....?

ক
11
খ
12
গ
15
ঘ
14

ব্যাখ্যা

Question: What is the next term in the sequence: 3, 9, 6, 11, 9, 13, ....?

Solution:
Here,
Split into two alternating sub-sequences:

Odd positions (1st, 3rd, 5th):
3, 6, 9 ⇒ increases by 3 each time

Even positions (2nd, 4th, 6th):
9, 11, 13 ⇒ increases by 2 each time

Since 13 was the 6th term (even position),
So, the 7th term (odd position) continues the first sub-sequence:
3, 6, 9 ⇒ next is 12

১১,৯১০.

The product of two consecutive even numbers is 168. What are the numbers?

ক
12 and 14
খ
14 and 16
গ
16 and 18
ঘ
22 and 24

ব্যাখ্যা

Question: The product of two consecutive even numbers is 168. What are the numbers?

Solution:
Let the smaller number be x,
so the next even number is = x + 2

According to the question,
x(x + 2) = 168
⇒ x² + 2x = 168
⇒ x² + 2x -168 = 0
⇒ x² + 14x - 12x - 168 = 0
⇒ x(x + 14) - 12(x + 14) = 0
⇒ (x + 14)(x - 12) = 0

⇒ x = - 14 and x = 12

If x = 12,
then the next even number =
12 + 2 = 14
The two numbers are: 12 and 14.

Again, If x = - 14, then the next even number = - 14 + 2 = - 12
So, the numbers are 12 and 14 or
- 14 and - 12

১১,৯১১.

If the average of p numbers is 2q² and the average of q numbers is 2p², what is the average of the combined (p + q) numbers?

ক
p + q
খ
2pq
গ
(p² + q²)/(p +q)
ঘ
2(p² + q²)/pq

ব্যাখ্যা

Question: If the average of p numbers is 2q² and the average of q numbers is 2p², what is the average of the combined (p + q) numbers?

Solution:
দেওয়া আছে,
p সংখ্যার গড় = 2q²
∴ p সংখ্যার সমষ্টি = p × 2q²

q সংখ্যার গড় = 2p²
∴ q সংখ্যার সমষ্টি = q × 2p²

∴ মোট সমষ্টি = (p × 2q²) + (q × 2p²)
= 2pq(q + p)

∴ তাদের গড় = মোট সমষ্টি / (p + q)
= 2pq(p + q)/(p + q)
= 2pq

১১,৯১২.

X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?

ক
10 days
খ
12 days
গ
15 days
ঘ
16 days

ব্যাখ্যা

Question: X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?

Solution:
work done by X in 4 days = (1/20) × 4
= 1/5

∴ Remaining work = 1 - (1/5)
= 4/5

(X + Y)'s 1day's work = (1/20) + (1/12)
= 8/60 = 2/15

Now,
2/15 work is done by X and Y in 1 day.
So, 4/5 work will be done by X and Y in = (15/2) × (4/5)
= 6 days

Hence, total time taken = (6 + 4) days
= 10 days

১১,৯১৩.

How many years will it take for an investment of Tk. 8000 to earn Tk. 1920 in simple interest at a rate of 8% per annum?

ক
4 years
খ
4.5 years
গ
3 years
ঘ
2.5 years

ব্যাখ্যা

Question: How many years will it take for an investment of Tk. 8000 to earn Tk. 1920 in simple interest at a rate of 8% per annum?

Solution:
Given that,
Principal, P = 8000
Simple Interest, SI = 1920
Rate of interest, r = 8%
Time, n = ?

We know,
n = I/Pr
= 1920/(8000 × 8%)
= (1920 × 100)/(8000 × 8)
= 3

So, it will take 3 years for the investment to earn Tk. 1920 at 8% simple interest.

১১,৯১৪.

In the figure ABCD is a square. If the length of the square is 10ft, then what will be the area of the triangle OCD?

ক
ক) 12.5 sft
খ
খ) 25 sft
গ
গ) 37.22 sft
ঘ
ঘ) Cannot be determined

ব্যাখ্যা

Question: In the figure ABCD is a square. If the length of the square is 10ft, then what will be the area of the triangle OCD?

Solution:

length of square 10 ft
area of square = 10² sq.ft
= 100 sq.ft

area of triangle OCD = (1/4) × 100 sq.ft
= 25 sq.ft

১১,৯১৫.

The volume of a rectangle with length, breadth, and height as 5x, 3x² and 7x⁴

ক
ক) 105x⁷
খ
খ) 105x²
গ
গ) 105x⁴
ঘ
ঘ) 105x

ব্যাখ্যা

The volume of the rectangle = 5x × 3x² × 7x⁴
= 105x^{(1 + 2 + 4)} = 105x⁷

১১,৯১৬.

Find the number of triangles which can be formed by joining the angular points of a polygon of 7 sides as vertices.

ক
12 ways
খ
20 ways
গ
35 ways
ঘ
40 ways

ব্যাখ্যা

Question: Find the number of triangles which can be formed by joining the angular points of a polygon of 7 sides as vertices.

Solution:
the number of triangles which can be formed by joining the angular points of a polygon of 7 sides as vertices
= ⁷C₃
= 7!/(3! × 2!)
= 35 ways

১১,৯১৭.

What is the logarithm of (1/256) with base 2√2?

ক
4
খ
8
গ
- 16/3
ঘ
16/3

ব্যাখ্যা

Question: What is the logarithm of (1/256) with base 2√2?

Solution:
log_2√2 (1/256)
= log_2√2 256^-1
= (- 1) log_2√2 2⁸
= (- 8) log_{(2 × 2^1/2)} 2
= (- 8) log_2^3/2 2
= - 8/(3/2) log₂ 2
= - 8 × (2/3) × 1 [ log_a a = 1 ]
= - 16/3

১১,৯১৮.

The difference between the circumference and the radius of a circle is 111 cm. Find the radius of a circle is -

ক
ক) 14 cm
খ
খ) 21 cm
গ
গ) 28 cm
ঘ
ঘ) 35 cm

ব্যাখ্যা

Let r be the radius of circle

Given that,
2πr - r = 111
⇒ r(2π - 1) = 111
⇒ r{(44/7) - 1} = 111
⇒ r (44 - 7)/7 }=111
⇒ r(37/7) = 111
⇒ r = 111 (7/37)
r = 21

১১,৯১৯.

The ratio of A's and B's salaries is 2 : 3 respectively. When A's salary is increased by 10%, it becomes Tk 13200. What is the salary of B?

ক
ক) 15000 Tk
খ
খ) 16000 Tk
গ
গ) 18000 Tk
ঘ
ঘ) 21000 Tk

ব্যাখ্যা

Question: The ratio of A's and B's salaries is 2 : 3 respectively. When A's salary is increased by 10%, it becomes Tk 13200. What is the salary of B?

Solution:
Let the salaries of A and B be Tk 2x and 3x respectively.

Then,
110% of 2x = 13200
⇒ (110/100) × 2x = 13200
⇒ x = (13200 × 100)/(110 × 2)
⇒ x = 6000

So, salary of B is = 3 × 6000 = 18000 Tk

১১,৯২০.

A mixture contains copper, zinc, and tin in the ratio 2 : 3 : 5. If the total weight of the mixture is 50 grams, how many grams of tin are there in the mixture?

ক
20 grams
খ
15 grams
গ
10 grams
ঘ
25 grams

ব্যাখ্যা

Question: A mixture contains copper, zinc, and tin in the ratio 2 : 3 : 5. If the total weight of the mixture is 50 grams, how many grams of tin are there in the mixture?

Solution:
Given,
Copper : Zinc : Tin = 2 : 3 : 5

Total parts = 2 + 3 + 5 = 10

Weight of tin = (5/10) × 50 = 25 grams

১১,৯২১.

A heap of pebbles when made up into group of 32, 40, 72, leaves the remainder 10, 18 and 50 respectively. Find least number of pebbles in the heaps.

ক
1418
খ
1430
গ
1510
ঘ
1521
ঙ
None of these

ব্যাখ্যা

Question: A heap of pebbles when made up into group of 32, 40, 72, leaves the remainder 10, 18 and 50 respectively. Find least number of pebbles in the heaps.

Solution:
In this type of problem we find the difference of divisors and their remainders.
Here difference,
32 - 10 = 22
40 - 18 = 22
72 - 50 = 22
Here, in each case difference is same = 22

Then, required number of pebbles is given by,
32 = 2 × 2 × 2 × 2 × 2
40 = 2 × 2 × 2 × 5
72 = 2 × 2 × 2 × 3 × 3

Hence,
LCM = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 5 = 1440

∴ Required number of pebbles,
= (1440 - 22)
= 1418

১১,৯২২.

Scoring 86 runs, a batsman smashed 8 fours and 3 sixes. How much of his score was contributed by running?

ক
41.86%
খ
31.86%
গ
26.72%
ঘ
32.78%

ব্যাখ্যা

Question: Scoring 86 runs, a batsman smashed 8 fours and 3 sixes. How much of his score was contributed by running?

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

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

১১,৯২৩.

ক
1
খ
32
গ
52
ঘ
64

ব্যাখ্যা

Question:

Solution:

১১,৯২৪.

A train 240m long passed a pole in 24 seconds. How long will it take to pass a platform 650m long?

ক
ক) 65 s
খ
খ) 89 s
গ
গ) 100 s
ঘ
ঘ) 130 s

ব্যাখ্যা

ট্রেনের দৈর্ঘের তুলনায় খুটির দৈর্ঘ্য নগণ্য বলে 24 সেকেন্ডে ট্রেনটি মূলত নিজের দৈর্ঘ্য অতিক্রম করবে ।
240 মিটার অতিক্রম করে = 24 সেকেন্ডে
∴ (650 + 240) বা 890 মিটার অতিক্রম করে = (24 × 890)/240
= 89 সেকেন্ডে ।

১১,৯২৫.

A mixture of 20kg of spirit and water contains 10% water. How much water must be added to this mixture to raise the percentage of water to 25%?

ক
4
খ
8
গ
12
ঘ
16
ঙ
None of the above

ব্যাখ্যা

Question: A mixture of 20kg of spirit and water contains 10% water. How much water must be added to this mixture to raise the percentage of water to 25%?

Solution:
In 1st mixture, water = 20 of 10%
= 20 of 10/100
= 2 kg

So, Spirit = 20 - 2
= 18 kg

Let,
The volume of water has to be mixed x litre

ATQ,
18/(2 + x) = 75/25
⇒ 18/(2 + x) = 3/1
⇒ 3(2 + x) = 18
⇒ 6 + 3x = 18
⇒ 3x = 18 - 6
⇒ 3x =12
⇒ x = 4

১১,৯২৬.

There are two filling pipes taking 20 min and 24 min to fill a tank and a drain pipe removing 3 gallons per minute. When used simultaneously, the tank fills in 15 minutes. What is the tank’s volume?

ক
70 gallons
খ
80 gallons
গ
100 gallons
ঘ
110 gallons
ঙ
120 gallons

ব্যাখ্যা

Question: There are two filling pipes taking 20 min and 24 min to fill a tank and a drain pipe removing 3 gallons per minute. When used simultaneously, the tank fills in 15 minutes. What is the tank’s volume?

Solution:
Let the waste pipe empty the tank in x minutes.

According to the question,
(1/20 + 1/24) - 1/x = 1/15
⇒ 1/x = (1/20 + 1/24) - 1/15
⇒ 1/x = 1/40
∴ x = 40 minutes

A waste pipe can empty 3 gallons per minute
In 40 minutes it can empty = 3 × 40 = 120 gallons.

∴ Capacity of the tank = 120 gallons.

১১,৯২৭.

5 mat-weavers can wave 5 mats in 5 days. At the same rate, how many mats would be woven by 10 mat-weavers in 10 days?

ক
ক) 15
খ
খ) 20
গ
গ) 25
ঘ
ঘ) 30

ব্যাখ্যা

Question: 5 mat-weavers can wave 5 mats in 5 days. At the same rate, how many mats would be woven by 10 mat-weavers in 10 days?

Solution:
5 mat weavers in 5 days wave = 5 mats
∴ 1 mat weavers in 1 day wave = 5/(5 × 5) mats
∴ 10 mat weavers in 10 days wave = (5 × 10 × 10)/(5 × 5) = 20 mats

১১,৯২৮.

60% of a number added to 60 gives the result as the number itself, then the number is:

ক
ক) 175
খ
খ) 200
গ
গ) 150
ঘ
ঘ) 125

ব্যাখ্যা

Question: 60% of a number added to 60 gives the result as the number itself, then the number is:

Solution:
Let x be the number which is added to 60.
Now,
60% of x = 0.6x

ATQ,
⇒ 60 + 0.6x = x
⇒ x - 0.6x = 60
⇒ 0.4x = 60
⇒ x = 60/0.4
∴ x = 150

১১,৯২৯.

Rahim and Karim enter into a partnership with capitals in the ratio of 10 : 12. At the end of 8 months, Rahim withdraws. If they receive profits in the ratio of 10 : 18. Find how long Karim's capital was used.

ক
7 months
খ
8 months
গ
10 months
ঘ
12 months

ব্যাখ্যা

Question: Rahim and Karim enter into a partnership with capitals in the ratio of 10 : 12. At the end of 8 months, Rahim withdraws. If they receive profits in the ratio of 10 : 18. Find how long Karim's capital was used.

Solution:
Let the capital of Rahim (C₁) = 10
And the capital of Karim is (C₂) = 12

Time period spend by Rahim (T₁) = 8 months
Let, time period spend by Karim (T₂) = x months

The ratio of their profit (p₁ : p₂) is 10 : 18
Apply formula:
(C₁ × T₁)/ (C₂ × T₂) = p₁/p₂
⇒ (10 × 8)/ (12 × x) = (10/18)
⇒ (80/12x) = (5/9)
⇒ 20/3x = 5/9
⇒ 180 = 15x
Hence, x = 12 months

১১,৯৩০.

a, b, c, d চারটি ক্রমিক স্বাভাবিক সংখ্যা হলে নিচের কোনটি পূর্ণবর্গ সংখ্যা?

ক
abcd
খ
ab × cd
গ
abcd + 1
ঘ
abcd - 1

ব্যাখ্যা

প্রশ্ন: a, b, c, d চারটি ক্রমিক স্বাভাবিক সংখ্যা হলে নিচের কোনটি পূর্ণবর্গ সংখ্যা?

সমাধান:
আমরা জানি,
যে কোনাে চারটি ক্রমিক স্বাভাবিক সংখ্যার গুণফলের সাথে 1 যােগ করলে যােগফল একটি পূর্ণবর্গ সংখ্যা হবে।
a, b, c, d চারটি ক্রমিক স্বাভাবিক সংখ্যা।
a, b, c, d এর গুণফল = abcd

abcd গুণফলের সাথে 1 যােগ করলে যােগফল = abcd + 1
abcd + 1 একটি পূর্ণবর্গ সংখ্যা হবে।

১১,৯৩১.

Akash ranks 19th in the class of 55 students. There are 9 students below Rasel rankwise. How many students are there between Akash and Rasel?

ক
25
খ
26
গ
27
ঘ
28

ব্যাখ্যা

Question: Akash ranks 19th in the class of 55 students. There are 9 students below Rasel rankwise. How many students are there between Akash and Rasel?

Solution:
মোট শিক্ষার্থী = ৫৫ জন
আকাশ তাদের মধ্যে ১৯তম

রাসেলের পেছনে ৯ জন আছে।
অর্থাৎ, রাসেল শেষ থেকে ১০ম।

তাই, আকাশ ও রাসেলের মধ্যে আছে = ৫৫ - (১৯ + ১০) = ২৬জন

১১,৯৩২.

রাজেশ সাইকেলে ৬কি.মি./ঘণ্টা গতিতে ৫০ মিনিটে একটি নির্দিষ্ট দূরত্ব অতিক্রম করে। যদি সে ঘণ্টায় ১০ কি.মি. গতিতে হাঁটে, তাহলে একই দূরত্ব হেঁটে অতিক্রম করতে তার কত মিনিট লাগবে?

ক
ক) ৪০ মিনিট
খ
খ) ৫০ মিনিট
গ
গ) ৪৫ মিনিট
ঘ
ঘ) ৩০ মিনিট

ব্যাখ্যা

৬০ মিনিটে অতিক্রম করে ৬০০০ মিটার
১ মিনিটে অতিক্রম করে ৬০০০/৬০ মিটার
৫০মিনিটে অতিক্রম করে (৬০০০ × ৫০)/৬০ মিটার
= ৫০০০ মিটার
= ৫ কি.মি.

সময় = ৫/১০ ঘণ্টা
= ১/২ ঘণ্টা
= (১/২) × ৬০ মিনিট
= ৩০ মিনিট

১১,৯৩৩.

A sum of Tk. 1600 is invested at 15% simple interest per annum for 10 months. What will be the interest?

ক
Tk. 150
খ
Tk. 180
গ
Tk. 200
ঘ
Tk. 240

ব্যাখ্যা

Question: A sum of Tk. 1600 is invested at 15% simple interest per annum for 10 months. What will be the interest?

Solution:
দেওয়া আছে,
আসল, P = Tk. 1600
সুদের হার, r = 15%
সময়, n = 10 months = 10/12 year = 5/6 year

আমরা জানি,
সুদ (I) = Pnr/100
= 1600 × (5/6) × 15/100
= (16 × 5 × 15)/6
= 1200/6
= 200 Taka

∴ 10 মাসে মোট মুনাফা হবে 200 টাকা।

১১,৯৩৪.

If ROSE is coded *#@& and PEOPLE is coded ^&#^$&. What will be the code of SLEEP?

ক
$@&&^
খ
&$@@^
গ
@$&&^
ঘ
^$&&@

ব্যাখ্যা

Question: If ROSE is coded *#@& nad PEOPLE is coded ^&#^$&. What will be the code of SLEEP?

Solution:
here,
R = *
O = #
S = @
E = &
P = ^
L = $

so, SLEEP = @$&&^

১১,৯৩৫.

A fort has enough food for 180 soldiers for 60 days. After 20 days, 60 soldiers leave. For how many more days will the remaining food last

ক
40
খ
50
গ
60
ঘ
20

ব্যাখ্যা

Question: A fort has enough food for 180 soldiers for 60 days. After 20 days, 60 soldiers leave. For how many more days will the remaining food last-

Solution:
After 20 days: 180 soldiers had food for 40 days. Suppose 120 soldiers had food for x days.
Now, fewer soldiers, more days (Indirect Proportion):
120 : 180 : : 40 : x
⇒ 120/180 = 40/x
⇒ 120x = 180 × 40
⇒ x = (180 × 40)/120
∴ x = 60

১১,৯৩৬.

Mr. A multiplies a number by 3 instead of dividing by 3. Resultant number is what percentage of the correct value?

ক
900
খ
400
গ
300
ঘ
200

ব্যাখ্যা

Question: Mr. A multiplies a number by 3 instead of dividing by 3. Resultant number is what percentage of the correct value?

Solution:
মনে করি, সংখ্যাটি x
সঠিকভাবে সমাধান করলে সংখ্যাটিকে 3 দিয়ে ভাগ করতে হবে।
তাহলে, সঠিক মান হবে = x/3

ভুলবশত সংখ্যাটিকে 3 দিয়ে গুণ করা হলে প্রাপ্ত সংখ্যাটি = 3x

∴ ভুল মানটি সঠিক মানের শতকরা = 3x/(x/3) × 100%
= 3x × (3/x) × 100%
= 900%

১১,৯৩৭.

The marked price of a Footwear is Tk. 200, and it is sold after applying two successive 20% discounts. What is the final price at which it is sold?

ক
Tk. 128
খ
Tk. 120
গ
Tk. 116
ঘ
Tk. 108
ঙ
None of the above

ব্যাখ্যা

Question: The marked price of a Footwear is Tk. 200, and it is sold after applying two successive 20% discounts. What is the final price at which it is sold?

Solution:
Discount 1 = 200 × (20/100) = Tk. 40

Selling price after 1^st discount = 200 - 40 = Tk. 160

Discount 2 = 160 × (20/100) = Tk. 32

∴ Selling price after 2^nd discount = 160 - 32 = Tk. 128

১১,৯৩৮.

By selling an article for Tk 100 Rakib gains Tk 20. Then, his gain% is-

ক
15%
খ
20%
গ
25%
ঘ
30%

ব্যাখ্যা

Question: By selling an article for Tk 100 Rakib gains Tk 20. Then, his gain% is-

Solution:
ক্রয়মূল্য = ১০০ - ২০ টাকা
= ৮০ টাকা

এখন,
৮০ টাকায় লাভ হয় = ২০ টাকা
১ টাকায় লাভ হয় = ২০/৮০ টাকা
∴ ১০০ টাকায় লাভ হয় = (২০ × ১০০)/৮০ টাকা
= ২৫ টাকা বা ২৫%

১১,৯৩৯.

A hemispherical bowl of internal radius 9 cm contains a liquid. This liquid is to be filled into cylindrical shaped small bottles of diameter 3 cm and height 8 cm. How many bottles will be needed to empty the bowl?

ক
ক) 20
খ
খ) 27
গ
গ) 38
ঘ
ঘ) 54

ব্যাখ্যা

Question: A hemispherical bowl of internal radius 9 cm contains a liquid. This liquid is to be filled into cylindrical shaped small bottles of diameter 3 cm and height 8 cm. How many bottles will be needed to empty the bowl?

Solution:
অর্ধগোলকের আয়তন = (1/2)× 4πr³/3
= (2/3) π9³ ঘনসেমি

প্রতি সিলিন্ডার আকৃতির বোতলের আয়তন = π (3/2)² × 8
= 18π ঘনসেমি
ধরি, n সংখ্যক বোতল লাগবে।

n × 18π = (2/3) π9³
⇒ n = (2/3) π9³/18π
∴ n = 27

১১,৯৪০.

If A = 1, B = 4, C = 7, and so on, what is the meaning of the following numbers: 46, 13, 1, 52, 34?

ক
P, L, A, N, E
খ
P, A, P, E, R
গ
R, E, P, E, L
ঘ
P, E, A, R, L

ব্যাখ্যা

Question: If A = 1, B = 4, C = 7, and so on, what is the meaning of the following numbers: 46, 13, 1, 52, 34?

Solution:
দেয়া আছে, A = 1, B = 4, C = 7, .....

∴ প্রতিটি কোড = (অক্ষরের অবস্থান × 3) - 2
∴ ডিকোডিং নিয়মটি হবে: অক্ষরের অবস্থান = (কোড + 2)/3

এখন,
(46 + 2)/3 = 48/3 = 16 → P
(13 + 2)/3 = 15/3 = 5 → E
(1 + 2)/3 = 3/3 = 1 → A
(52 + 2)/3 = 54/3 = 18 → R
(34 + 2)/3 = 36/3 = 12 → L

∴ সংখ্যাগুলির অর্থ হলো PEARL

১১,৯৪১.

A woman saves 25% of her salary. If her monthly income is Tk. 12000, how much does she spend?

ক
Tk. 7200
খ
Tk. 8550
গ
Tk. 8000
ঘ
Tk. 9000

ব্যাখ্যা

Question: A woman saves 25% of her salary. If her monthly income is Tk. 12000, how much does she spend?

Solution:
Total income = Tk.12,000
Saving = 25% of income
So, Spending = (100 - 25)% = 75%

∴ Spending = (75/100) × 12000 = 75 × 120 = Tk. 9000

১১,৯৪২.

একটি ব্যবসায়ে A, B এবং C তিনজন অংশীদার। তারা সবাই মিলে মোট ১৪০০০ টাকা বিনিয়োগ করলো। বছর শেষে A ৩৩৭.৫০ টাকা, B ১১২৫ টাকা এবং C ৬৩৭.৫ টাকা মুনাফা পেলো। B এবং A এর বিনিয়োগের পার্থক্য কত?

ক
৪০৫৬ টাকা
খ
৪৮৯০ টাকা
গ
৫০৩৬ টাকা
ঘ
৫২৫০ টাকা
ঙ
৬৪২৮ টাকা

ব্যাখ্যা

প্রশ্ন: একটি ব্যবসায়ে A, B এবং C তিনজন অংশীদার। তারা সবাই মিলে মোট ১৪০০০ টাকা বিনিয়োগ করলো। বছর শেষে A ৩৩৭.৫০ টাকা, B ১১২৫ টাকা এবং C ৬৩৭.৫ টাকা মুনাফা পেলো। B এবং A এর বিনিয়োগের পার্থক্য কত?

সমাধান:
A, B এবং C এর বিনিয়োগের অনুপাত = A, B এবং C এর লাভের অনুপাত
= ৩৩৭.৫০ : ১১২৫ : ৬৩৭.৫
= ৯ : ৩০ : ১৭

∴ যোগফল = (৯ + ৩০ + ১৭) = ৫৬

এখন,
A এর বিনিয়োগ = {১৪০০০ × (৯/৫৬)} = ২২৫০ টাকা
B এর বিনিয়োগ = {১৪০০০ × (৩০/৫৬)} = ৭৫০০ টাকা

∴ A এবং B এর বিনিয়োগের পার্থক্য = (৭৫০০ - ২২৫০) টাকা
= ৫২৫০ টাকা

১১,৯৪৩.

If the universal set consists of two sets A and B, then the complementary set of A is-

ক
A ∩ B
খ
A
গ
B
ঘ
A ∪ B

ব্যাখ্যা

Question: If the universal set consists of two sets A and B, then the complementary set of A is-

Solution:
U সার্বিক সেট এবং A সেটটি U এর উপসেট।
A সেটের বহির্ভূত সকল উপাদান নিয়ে গঠিত সেটকে A সেটের পূরক সেট বলে।
A এর পূরক সেটকে A^c বা A' দ্বারা প্রকাশ করা হয়।
গাণিতিকভাবে A^c = U - A

দেওয়া আছে
U সার্বিক সেট A ও B এর উপাদান নিয়ে গঠিত।
ধরি
A = {2, 4, 6, 7} এবং B = {1, 3, 5}
U = A ∪ B
= {2, 4, 6, 7} ∪ {1, 3, 5}
= {1, 2, 3, 4, 5, 6, 7}

A এর পূরক সেটকে A^c বা A' = U - A
= {1, 2, 3, 4, 5, 6, 7} - {2, 4, 6, 7}
= {1, 3, 5}
= B

১১,৯৪৪.

The radius of circle A is r, and the radius of circle B is 3r/4 . What is the ratio of the area of circle A to the area of circle B ?

ক
ক) 16 to 9
খ
খ) 9 to 16
গ
গ) 1 to 4
ঘ
ঘ) 4 to 3

ব্যাখ্যা

Question: The radius of circle A is r, and the radius of circle B is 3r/4 . What is the ratio of the area of circle A to the area of circle B ?

Solution:
A বৃত্তের ব্যাসার্ধ = r
A বৃত্তের ক্ষেত্রফল = πr²

B বৃত্তের ব্যাসার্ধ = 3r/4
B বৃত্তের ক্ষেত্রফল = π(3r/4)² = 9π²/16

A বৃত্তের ক্ষেত্রফল : B বৃত্তের ক্ষেত্রফল = πr² : 9π²/16
= 1 : 9/16
= 16 × 1 : (9/16)16
= 16 : 9

১১,৯৪৫.

A reduction of 10% in the price of tea enables a dealer to purchase 25 kg more tea for Tk 22500. What is the reduced price per kg of tea?

ক
81 tk
খ
90 Tk
গ
93 Tk
ঘ
97 Tk

ব্যাখ্যা

Question: A reduction of 10% in the price of tea enables a dealer to purchase 25 kg more tea for Tk 22500. What is the reduced price per kg of tea?

Solution:
Let 10% of 22500 = 2250
Now,
25 kg = 2250
⇒ 1kg = 2250/25
∴ 1kg = 90

১১,৯৪৬.

A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions made by the larger wheel is:

ক
ক) 8
খ
খ) 9
গ
গ) 10
ঘ
ঘ) 11

ব্যাখ্যা

Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
14 : 6 :: 21 : x
or, 14 x x = 6 x 21
or, x = (6 x 21)/14
so, x = 9.

১১,৯৪৭.

The sum of two numbers is 18. The greatest product of these two number can be-

ক
80
খ
17
গ
81
ঘ
Can't determined

ব্যাখ্যা

Question: The sum of two numbers is 18. The greatest product of these two number can be-

Solution:
Given that,
a + b = 18
So, maximum of (a × b) will be only when a = b
Thus, a = b = 9
∴ Maximum of (a × b) = 9 × 9 = 81.

So the greatest product is 81.

১১,৯৪৮.

If (p/q)^n-1=(q/p)^n-3, the value of n is -

ক
ক) 2
খ
খ) 1
গ
গ) 1/2
ঘ
ঘ) 7/2

ব্যাখ্যা

Given that,
(p/q)^n-1 = (q/p)^n-3
⇒ (p/q)^n-1 = (p/q)^-(n-3)
⇒ n-1 = -(n-3)
⇒ n-1 =-n +3
⇒ n + n = 3 + 1
⇒ 2n = 4
⇒ n = 4/2
∴ n = 2

১১,৯৪৯.

How many numbers from 1 to 225 inclusive are equal to the cube of an integer?

ক
4
খ
5
গ
6
ঘ
7

ব্যাখ্যা

Question: How many numbers from 1 to 225 inclusive are equal to the cube of an integer?

Solution:
1³ = 1
2³= 8
3³= 27
4³= 64
5³= 125
6³ = 216
7³ = 343, যা 225 থেকে বড়।

সুতরাং,
1 থেকে 225 এর মধ্যবর্তী মোট 6 টি সংখ্যা (1, 8, 27, 64, 125, 216) আছে যেগুলো পূর্ণসংখ্যার ঘনফল।

১১,৯৫০.

By error, a student used 7/10 in place of 7/5 to multiply a number. Determine the percent error in the computation.

ক
40%
খ
45%
গ
50%
ঘ
60%

ব্যাখ্যা

Question: By error, a student used 7/10 in place of 7/5 to multiply a number. Determine the percent error in the computation.

Solution:
Let
the number be 100.

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

∴ Difference = 140 - 70 = 70

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

১১,৯৫১.

Tk. 180 is to be divided among 66 persons (men and women). The ratio of the total amount of money received by men and women is 5 : 4. But the ratio of the money received by each man and woman is 3 : 2. The number of men is:

ক
22
খ
26
গ
30
ঘ
36

ব্যাখ্যা

Question: Tk. 180 is to be divided among 66 persons (men and women). The ratio of the total amount of money received by men and women is 5 : 4. But the ratio of the money received by each man and woman is 3 : 2. The number of men is:

Solution:
Let, amount received by men = 5x.
and amount received by women = 4x

ATQ,
5x + 4x = 180
⇒ 9x = 180
⇒ x = 20

Amount received by men = TK.100
Amount received by women = TK.80

Suppose, the number of men be y and that of women be = (66 - y).
∴ (100/y)/{80/(66 - y)} = 3/2
⇒ (100/y) × {(66 - y)/80} = 3/2
⇒ {5(66 - y)}/4y = 3/2
⇒ 660 - 10y = 12y
⇒ 22y = 660
⇒ y = 30

১১,৯৫২.

A train 250m long passes a pole in 25 seconds. How long will it take to pass a platform 480m long?

ক
ক) 89 sec
খ
খ) 73 sec
গ
গ) 75 sec
ঘ
ঘ) 85 sec

ব্যাখ্যা

Question: A train 250m long passes a pole in 25 seconds. How long will it take to pass a platform 480m long?

Solution:
সমাধান:
ট্রেনটির মোট দূরত্ব অতিক্রম করতে হবে = (250 + 480) মিটার = 730 মিটার

ট্রেনটি 250 মিটার অতিক্রম করতে সময় নেয় = 25 সেকেন্ড
ট্রেনটি 1 মিটার অতিক্রম করতে সময় নেয় = 25/250 সেকেন্ড
ট্রেনটি 730 মিটার অতিক্রম করতে সময় নেয় = (25 × 730)/250 সেকেন্ড
= 73 সেকেন্ড

১১,৯৫৩.

In a simultaneous throw of two dice, what is the probability of getting a total of 7?

ক
1/6
খ
1/36
গ
1/12
ঘ
5/36

ব্যাখ্যা

Question: In a simultaneous throw of two dice, what is the probability of getting a total of 7?

Solution:
If two dices are thrown total events = 6² = 36
Event of getting a total of 7 = {(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)}
Expected events = 6

∴ Probability = 6/36 = 1/6

১১,৯৫৪.

There is a bag that contains 4 yellow balls, 5 black balls and 7 pink balls. The number of ways in which three balls can be drawn from the box so that at least one of the balls is black is:

ক
395
খ
390
গ
345
ঘ
200

ব্যাখ্যা

Question: There is a bag that contains 4 yellow balls, 5 black balls and 7 pink balls. The number of ways in which three balls can be drawn from the box so that at least one of the balls is black is:

Solution:
Total number of balls = 16
The required number of ways
Case 1:
1 black and 2 others = ⁵C₁ × ¹¹C₂
= 5 × 55
= 275

Case 2:
2 black and 1 other = ⁵C₂ × ¹¹C₁
= 10 × 11
= 110

Case 3:
All the three black = ⁵C₃ = 10

Total = 275 + 110 + 10 = 395 ways
Hence option number (1) is the right answer

১১,৯৫৫.

In the given figure, AB is the diameter of the circle with center O. If ∠BOD = 15° & ∠EOA = 85°, then find the value of ∠ECA.

ক
20°
খ
25°
গ
35°
ঘ
Can’t be determined

ব্যাখ্যা

Question: In the given figure, AB is the diameter of the circle with center O. If ∠BOD = 15° & ∠EOA = 85°, then find the value of ∠ECA.

Solution:
∠EOA = 85°, ∠BOD = 15°
∠EOD = 180° - (85° + 15°) = 80°
In ΔOED,
OE = OD (radii)
∠OED = ∠ODE = 50°

In ΔOEC,
∠EOC = 80°+15° = 95°, ∠OEC =50°
∴ ∠ECA = 180°- (95 + 50°) = 35°

১১,৯৫৬.

The average age a family consists of six members is 20 years. If one person is removed, the average becomes 15 years. Find the age of the person removed?

ক
45 years
খ
40 years
গ
42 years
ঘ
None of these

ব্যাখ্যা

Question: The average age a family consists of six members is 20 years. If one person is removed, the average becomes 15 years. Find the age of the person removed?

Solution:
The average age of a family consists of 6 members is 20 years.
The total age of all family members 20 × 6 = 120

one person is removed then the average becomes 15 years.
The sum of the age of 5 members 15 × 5 = 75 years.

The age of the person removed 120 - 75 = 45 years.
∴ The average age of the person removed is 45 years.

১১,৯৫৭.

A delivery cart went from Candle ford to Lark Rise and back at an average speed of 2/3 miles per hour. If the distance from Candle ford to Lark Rise is 1 mile and the trip back took half as much time as the trip there, what was the average speed of the delivery cart on the way to Lark Rise?

ক
ক) 1/3
খ
খ) 3/4
গ
গ) 1/2
ঘ
ঘ) 2/3

ব্যাখ্যা

Question: A delivery cart went from Candle ford to Lark Rise and back at an average speed of 2/3 miles per hour. If the distance from Candle ford to Lark Rise is 1 mile and the trip back took half as much time as the trip there, what was the average speed of the delivery cart on the way to Lark Rise?

Solution:
Total distance = Average speed × total time
So, 2 = 2/3×T
⇒ T = 3 hours
So, the whole journey took 3 hours
Since trip back took half as much time as the trip there, it took 2 hours to reach there and 1 hour to come back.
So, speed of the delivery cart while going to Lark Rise = distance/time = 1/2 mph

১১,৯৫৮.

ক
0
খ
- 1
গ
4
ঘ
8

ব্যাখ্যা

Question:

Solution:

১১,৯৫৯.

The pair of co-prime numbers is ____?

ক
ক) 2, 3
খ
খ) 2, 4
গ
গ) 2, 6
ঘ
ঘ) 2, 110

ব্যাখ্যা

2, 3 এর মধ্যে ১ ব্যতিত আর কোন সাধারণ উৎপাদক নেই।
∴ (2, 3) সহমৌলিক (co-prime) সংখ্যা।

১১,৯৬০.

A train takes 18 sec to pass completely through a station 162m long and 15 seconds through another station 120m long.The length of the train-

ক
ক) 70m
খ
খ) 80m
গ
গ) 90m
ঘ
ঘ) 100m

ব্যাখ্যা

Let length of the train be x m
Speed of train,
(x+162)/18 = (x+120)/15
∴ x = 90 m

১১,৯৬১.

Mr. Kamal travelled from P to Q at a speed of 4 km/hr and returned from Q to P at a speed of 6 km/hr. If the entire trip required 10 hours, what is the distance between P and Q in km?

ক
15 km
খ
18 km
গ
24 km
ঘ
30 km
ঙ
45 km

ব্যাখ্যা

Question: Mr. Kamal travelled from P to Q at a speed of 4 km/hr and returned from Q to P at a speed of 6 km/hr. If the entire trip required 10 hours, what is the distance between P and Q in km?

Solution:
ধরা যাক, P থেকে Q এর দূরত্ব হলো x কিমি।
সুতরাং, P থেকে Q তে যেতে সময় লাগে = x/4 ঘন্টা
Q থেকে P তে ফিরে আসতে সময় লাগে = x/6 ঘন্টা

প্রশ্ন অনুযায়ী, মোট সময় লেগেছে 10 ঘন্টা।
∴ (x/4) + (x/6) = 10
⇒ (3x + 2x)/12 = 10
⇒ 5x/12 = 10
⇒ 5x = 10 × 12
⇒ 5x = 120
⇒ x = 120 / 5
⇒ x = 24

সুতরাং, P এবং Q এর মধ্যবর্তী দূরত্ব হলো 24 কিমি।

১১,৯৬২.

If 3^{x + 2} = 117, then 3^2x =?

ক
13
খ
91
গ
169
ঘ
196

ব্যাখ্যা

Question: If 3^{x + 2} = 117, then 3^2x =?

Solution:
3^{x + 2} = 117
⇒ 3^{x + 2} = 9 × 13
⇒ 3^{x + 2} = 3² × 13
⇒ (3^x . 3²) /3² = 13
⇒ 3^x = 13
⇒ (3^x)² = 13²
⇒ 3^2x = 169

১১,৯৬৩.

The average age of a class of 29 students is 20 years. If the age of the teacher is included, then the average increases by 3 months. Find the age of the teacher.

ক
ক) 25.2 years
খ
খ) 27.5 years
গ
গ) 29 years
ঘ
ঘ) 31.5 years

ব্যাখ্যা

Average = Sum of Quantities/Number of Quantities

1) First calculate the total age of 40 students
Total age of 29 students = ( Average age x No. of students)
= (20 x 29) = 580 years

2) Average age of 29 students + 1 teacher = 20 years + 3 months = 81/4 years

3) Finally the total age of 29 students + 1 teacher = 81/4 × 30 = 607.5 years

Therefore, age of teacher = (Total age of 30 members - Total age of 29 students)
= (607.5 – 580)
= 27.5 years.

১১,৯৬৪.

The compound interest on a certain sum for 2 years at 10% per annum is Tk. 525. The simple interest on the same sum for double the time at half the rate percent per annum is:

ক
Tk. 1000
খ
Tk. 800
গ
Tk. 500
ঘ
Tk. 400

ব্যাখ্যা

Question: The compound interest on a certain sum for 2 years at 10% per annum is Tk. 525. The simple interest on the same sum for double the time at half the rate percent per annum is:

Solution:
Let the sum be Tk. P.

ATQ,
P {1 + (10/100)}² - p = 525
⇒ P[{1 + (1/10)}² - 1] = 525
⇒ P{(11/10)² - 1} = 525
⇒ P{(121/100) - 1} = 525
⇒ P(21/100) = 525
⇒ P = (525 × 100)/21
∴ P = 2500

We know,
Simple interest, I = Pnr
= (2500 × 4 × 5)/100
= Tk. 500

১১,৯৬৫.

Cost of 3 cricket balls = cost of 2 pairs of leg pads
Cost of 3 pairs of leg pads = cost of 2 pairs of gloves.
Cost of 3 pairs of gloves = cost of 2 cricket bats.
If a cricket bat costs Tk. 5400, what is the cost of a cricket ball?

ক
Tk. 1200
খ
Tk. 1400
গ
Tk. 1600
ঘ
Tk. 1800

ব্যাখ্যা

Question: Cost of 3 cricket balls = cost of 2 pairs of leg pads.
Cost of 3 pairs of leg pads = cost of 2 pairs of gloves.
Cost of 3 pairs of gloves = cost of 2 cricket bats.
If a cricket bat costs Tk. 5400, what is the cost of a cricket ball?

Solution:
3 pairs of gloves = 2 × 5400 = 10800
∴ 1 pairs of gloves = 10800/3 = 3600

3 pairs of leg pads = 2 × 3600 = 7200
∴ 1 pairs of leg pads = 7200/3 = 2400

3 cricket balls = 2 × 2400 = 4800
∴ cost of 1 cricket ball = 4800/3 = 1600

১১,৯৬৬.

A assigns B to do a task in 3 days. After 3 days A finds that 3/5 of the work has been done. How many days will B take to complete the rest of the work?

ক
ক) 5 days
খ
খ) 2 days
গ
গ) 3 days
ঘ
ঘ) 4 days

ব্যাখ্যা

Question: A assigns B to do a task in 3 days. After 3 days A finds that 3/5 of the work has been done. How many days will B take to complete the rest of the work?

Solution:
B ৩/৫ অংশ কাজ করে ৩ দিনে।
সম্পূর্ণ কাজ করে ৩/(৩/৫) দিনে
= ৫ দিনে।

অর্থাৎ B এর সম্পূর্ণ কাজ শেষ করতে আরো (৫ - ৩) বা, ২ দিন লাগবে।

১১,৯৬৭.

If the probability that event S will not occur is 1 - y, then the probability that event S will occur is-

ক
y² - 1
খ
y²
গ
y/2
ঘ
y - 1
ঙ
y

ব্যাখ্যা

Question: If the probability that event S will not occur is 1 - y, then the probability that event S will occur is-

Solution:
If the probability that an event S occurs is given by P(S), then the probability that the same event will not occur, denoted as P(S') = 1 - P(S).

Therefore P(S) + P(S') = 1
Here P(S') = 1 - y

⇒ P(S) + 1 - y = 1
∴ P(S) = 1 - 1 + y = y

১১,৯৬৮.

A tank can be filled with water by two pipes A and B together in 36 minutes. If the pipe B was stopped after 30 minutes, the tank is filled in 40 minutes. The pipe B can alone fill the tank in:

ক
ক) 90 minutes
খ
খ) 91 minutes
গ
গ) 92 minutes
ঘ
ঘ) 95 minutes

ব্যাখ্যা

Let the pipes fill the tank in x minutes.
Part of tank filled by pipes A and B in one minute:
1/36 Part of the tank filled by pipe A in 1 minute = 1/36−1/x
According to the question,
30×1/x + 40(1/36−1/x) = 1
⇒30/x + 40/36 − 40/x = 1
⇒30/x + 10/9 − 40/x = 1
⇒10/x = 1/9
Hence, x = 90 minutes.

১১,৯৬৯.

Two brands of detergent are to be combined. Detergent A contains 30 percent bleach and 70 percent soap, while Detergent B contains 50 percent bleach and 50 percent soap. If the combined mixture is to be 40 percent bleach, what percent of the final mixture should be Detergent A?

ক
35%
খ
45%
গ
50%
ঘ
60%

ব্যাখ্যা

Question: Two brands of detergent are to be combined. Detergent A contains 30 percent bleach and 70 percent soap, while Detergent B contains 50 percent bleach and 50 percent soap. If the combined mixture is to be 40 percent bleach, what percent of the final mixture should be Detergent A?

Solution:
ধরি, মিশ্রণে Detergent A এর অংশ x%
∴ Detergent B এর অংশ হবে (100 - x%)

এখানে,
ডিটারজেন্ট A থেকে প্রাপ্ত ব্লিচের পরিমাণ হলো (x% এর 30%)।
ডিটারজেন্ট B থেকে প্রাপ্ত ব্লিচের পরিমাণ হলো (100 - x)% এর 50%।
চূড়ান্ত মিশ্রণে ব্লিচের মোট পরিমাণ হলো (100% এর 40%)।

প্রশ্নমতে,
0.30x + 0.50 × (100 - x) = 0.40 × 100
⇒ 0.30x + 50 - 0.50x = 40
⇒ - 0.20x = - 10
⇒ x = - 10/(- 0.20)
∴ x = 50

অর্থাৎ, মিশ্রণের 50% হবে Detergent A।

১১,৯৭০.

What will come in the place of the question mark in the following question- 40% of 50% of 3/4 of 2400 = ?

ক
360
খ
280
গ
520
ঘ
300

ব্যাখ্যা

Question: What will come in the place of the question mark in the following question- 40% of 50% of 3/4 of 2400 = ?

Solution:
40% of 50% of 3/4 of 2400 = ?
⇒ 40% × 50% × (3/4) × 2400 = ?
⇒ (40/100) × (50/100) × 3/4 × 2400 = ?
⇒ (2/5) × (1/2) × (3/4) × 2400 = ?
⇒ (6/40) × 2400 = ?
⇒ ? = 360

∴ The value of ? is 360

১১,৯৭১.

A train 250 meters long is running at a speed of 90 km/h. How long will it take to cross a platform 150 meters long?

ক
24 seconds
খ
28 seconds
গ
16 seconds
ঘ
30 seconds

ব্যাখ্যা

Question: A train 250 meters long is running at a speed of 90 km/h. How long will it take to cross a platform 150 meters long?

Solution:
speed = 90 km/h = 90 × (5/18) m/s
= 25 m/s

To cross the platform have to travel = (250 + 150) m
= 400 m

∴ Required time = 400/25 seconds
= 16 seconds

১১,৯৭২.

If the annual rate of simple interest increases from 10% to 12.5%, a man's yearly income increases by Tk 1250. His principal is -

ক
ক) 25000 Tk
খ
খ) 40000 Tk
গ
গ) 50000 Tk
ঘ
ঘ) 75000 Tk

ব্যাখ্যা

Question: If the annual rate of simple interest increases from 10% to 12.5%, a man's yearly income increases by Tk 1250. His principal is -

Solution:
Let the principal be Tk x

Then,
(x × 25 × 1}/(2 × 100)} - {(x × 25 × 1}/100} = 1250
⇒ x/8 - x/10 = 1250
⇒ x/40 = 1250
⇒ x = 50000

১১,৯৭৩.

If 1 - 2x ≤ 3, then -

ক
ক) x ≤ -2
খ
খ) x ≥ -2
গ
গ) x ≤ -1
ঘ
ঘ) x ≥ -1

ব্যাখ্যা

1 - 2x ≤ 3
⇒ 1 - 2x -1 ≤ 3 - 1
⇒- 2x ≤ -2
⇒ -2x/2 ≥ 2/-2 [-2 দ্বারা ভাগ করে]
∴ x ≥ -1

১১,৯৭৪.

sin²60° + 2tan45° - cos²30° - 2 =?

ক
ক) 1
খ
খ) - 2
গ
গ) 0
ঘ
ঘ) 2

ব্যাখ্যা

Question: sin²60° + 2tan45° - cos²30° - 2 =?

Solution:
sin²60° + 2tan45° - cos²30° - 2
= (sin60°)² + 2 × 1 - (cos30°)² - 2
= (√3/2)² + 2 - (√3/2)² - 2
= 0

১১,৯৭৫.

There are 7 non-collinear points. How many triangles can be drawn by joining these points?

ক
35
খ
37
গ
33
ঘ
45
ঙ
43

ব্যাখ্যা

Question: There are 7 non-collinear points. How many triangles can be drawn by joining these points?

Solution:
A triangle is formed by joining any three non-collinear points in pairs.
There are 7 non-collinear points.

∴ The number of triangles formed =
⁷C₃
= 35

১১,৯৭৬.

A triangular plot with sides of 25 feet, 40 feet and 55 feet is to be surrounded by a fence built on pillars set 5 feet apart. How many pillars will be required to surround the plot?

ক
ক) 21
খ
খ) 22
গ
গ) 23
ঘ
ঘ) 24

ব্যাখ্যা

Question: A triangular plot with sides of 25 feet, 40 feet and 55 feet is to be surrounded by a fence built on pillars set 5 feet apart. How many pillars will be required to surround the plot?

Solution:
ত্রিভুজ ক্ষেত্রটির পরিসীমা
= (25 + 40 + 55) ফুট
= 120 ফুট

একটি পিলার থেকে অন্য পিলারের দূরত্ব = 5 মিটার

মোট পিলার লাগবে
= (120/5) টি
= 24 টি

১১,৯৭৭.

The present age of the son is half of the present age of his mother. Ten years ago, his mother's age was thrice the age of her son. What is the present age of the son?

ক
ক) 20 years
খ
খ) 18 years
গ
গ) 36 years
ঘ
ঘ) 40 years

ব্যাখ্যা

Question: The present age of the son is half of the present age of his mother. Ten years ago, his mother's age was thrice the age of her son. What is the present age of the son?

Solution:
Let the mother's age be 2x years
Then, Son's age = x years

ATQ,
2x - 10 = 3(x - 10)
⇒ 2x - 10 = 3x - 30
⇒ x = 20

১১,৯৭৮.

The price of a pen is 25% more than the price of a book. The price of a pen holder is 50% more than the price of the book. How much is the price of the pen holder more than the price of the pen?

ক
20%
খ
35%
গ
25%
ঘ
30%

ব্যাখ্যা

Let price of book = 100tk
Price of pen = 100 + 100 × 25%
= 125 tk
Price of pen-holder = 100 + 100 × 50%
= 150 tk

Difference is = 150 -125 = 25 tk

∴ Percentage = (25 × 100)/125
= 20%

১১,৯৭৯.

Mr. Karim sold his cow for Tk. 30,000 at a 20% gain. Find the cost price.

ক
ক) 20,000
খ
খ) 22,000
গ
গ) 25,000
ঘ
ঘ) 28,000

ব্যাখ্যা

Question: Mr. Karim sold his cow for Tk. 30,000 at a 20% gain. Find the cost price.

Solution:
20% লাভে,
বিক্রয়মূল্য 120 টাকা হলে ক্রয়মূল্য = 100 টাকা
∴ বিক্রয়মূল্য 30000 টাকা হলে ক্রয়মূল্য = (100 x 30000)/120 টাকা
= 25000 টাকা

১১,৯৮০.

The monthly sales of a grocer for five months are Tk. 6435, Tk. 6927, Tk. 6855, Tk. 7230 and Tk. 6562. How much must he sell in the sixth month to ensure his average over six months is exactly Tk. 6500?

ক
Tk. 4560
খ
Tk. 4991
গ
Tk. 6251
ঘ
Tk. 7135

ব্যাখ্যা

Question: The monthly sales of a grocer for five months are Tk. 6435, Tk. 6927, Tk. 6855, Tk. 7230 and Tk. 6562. How much must he sell in the sixth month to ensure his average over six months is exactly Tk. 6500?

Solution:
ধরি,
6-তম মাসে বিক্রির পরিমাণ = ক টাকা

প্রথম ৫ মাসে মোট বিক্রি = (6435 + 6927 + 6855 + 7230 + 6562) টাকা = 34009 টাকা

প্রশ্নমতে,
(34009 + ক)/6 = 6500
⇒ 34009 + ক = 6500 × 6
⇒ 34009 + ক = 39000
⇒ ক = 39000 - 34009
⇒ ক = 4991

∴ 6-তম মাসে বিক্রির পরিমাণ হতে হবে = 4991 টাকা

১১,৯৮১.

What is the sum of first 20 terms of the series 7 + 12 + 17 +.............. ?

ক
1350
খ
1260
গ
1195
ঘ
1090

ব্যাখ্যা

Question: What is the sum of first 20 terms of the series 7 + 12 + 17 +.............. ?

Solution:
Given series: 7 + 12 + 17 +................

Here,
First term of the series a = 7
common difference d = 12 - 7 = 5
and number of terms n = 20

∴ It is an arithmetic series.

We know
the sum of first n-terms of an arithmetic series, S_n = (n/2){2a + (n - 1)d}

∴ So, the sum of 20 terms S₂₀ = (20/2){2 × 7 + (20 - 1)5}
= 10(14 + 19 × 5)
= 10(14 + 95)
= 10 × 109
= 1090

১১,৯৮২.

The ratio of men : women working in a company is 3 : 5. What proportion of the employees are women?

ক
3/5
খ
3/8
গ
5/8
ঘ
5/3
ঙ
None of these

ব্যাখ্যা

Question: The ratio of men : women working in a company is 3 : 5. What proportion of the employees are women?

Solution:
In this company, the ratio of men : women is 3 : 5
so for every 3 men there are 5 women.
This means that for every 8 employees, 5 of them are women.
Therefore 5/8 of the employees are women.

১১,৯৮৩.

Which of the following is a leap year?

ক
1996
খ
1982
গ
2003
ঘ
2005

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,
1996 ÷ 4 = 499 → নিঃশেষে বিভাজ্য → Leap year।
1982 ÷ 4 = 495.5 → বিভাজ্য নয় → Leap year নয়।
2003 ÷ 4 = 500.75 → নিঃশেষে বিভাজ্য নয় → Leap year নয়।
2005 ÷ 4 = 501.25 → নিঃশেষে বিভাজ্য নয় → Leap year নয়।

অতএব, 1996 সাল অধিবর্ষ।

১১,৯৮৪.

Abul, Billal and Rahim start together from the same place to walk round a circular path of length 24km. Abul walks at the rate of 6 km/h, Billal 3 km/h and Rahim (3/2) km/h. After how many hours will they meet again at the starting point together?

ক
16
খ
12
গ
14
ঘ
48
ঙ
None

ব্যাখ্যা

Question: Abul, Billal and Rahim start together from the same place to walk round a circular path of length 24km. Abul walks at the rate of 6 km/h, Billal 3 km/h and Rahim (3/2) km/h. After how many hours will they meet again at the starting point together?

Solution:
Abul এর সময় লাগবে = 24/6 = 4 ঘণ্টা
Billal এর সময় লাগবে = 24/3 = 8 ঘণ্টা
Rahim এর সময় লাগবে = 24 ÷ (3/2)
= 24 × (2/3)
= 16 ঘণ্টা

4, 8, 16 এর লসাগু = 16

অতএব,
Abul, Billal এবং Rahim 16 ঘণ্টা পর মিলিত হবে।

১১,৯৮৫.

Two alloys contain zinc and copper in the ratio of 2 : 1 and 4 : 1.In what ratio the two alloys should be added together to get a new alloy having zinc and copper in the ratio of 3 : 1?

ক
ক) 3 : 5
খ
খ) 5 : 9
গ
গ) 7 : 5
ঘ
ঘ) None of these

ব্যাখ্যা

Zinc in first allow = 2/3 units;
Zinc in second alloy = 4/5 units.
copper in first alloy = 1/3 units;
copper in second alloy = 1/5 units.
Let the first and second alloys be mixed in the ratio 1 : y.
Then, {(2/3) + (4y/5)}/{(1/3 + (y/5)) = 3/1
⇒ 10 + 12y = 3 (5 + 3y)
⇒ 10 + 12y = 15 + 9y
⇒ 3y = 5
⇒ y = 5/3.
∴ Required ratio = 1 : 5/3
= 3:5

১১,৯৮৬.

A retailer bought 100 Bluetooth speakers at a cost of BDT 1,800 each. He sold each at a 30% markup. After a month, 20 speakers remained unsold, and he returned them to the supplier for a 50% refund of the cost price. What is the retailer’s approximate profit margin as a percentage of the total acquisition cost?

ক
10%
খ
12%
গ
14%
ঘ
20%
ঙ
None

ব্যাখ্যা

Question: A retailer bought 100 Bluetooth speakers at a cost of BDT 1,800 each. He sold each at a 30% markup. After a month, 20 speakers remained unsold, and he returned them to the supplier for a 50% refund of the cost price. What is the retailer’s approximate profit margin as a percentage of the total acquisition cost?

Solution:
Given,
Purchased = 100 speakers
∴ Total Cost = 100 × 1,800 = BDT 180,000

Sold = (100 - 20) = 80 units
Selling price (30% markup) = 1,800 × 1.30 = BDT 2,340
∴ Revenue from sold units = 80 × 2,340 = BDT 187,200

Refund for returns (50%) = 1,800 × 0.5 = BDT 900 per speaker
∴ Refund from unsold units = 20 × 900 = BDT 18,000

Total Income = 187,200 + 18,000 = BDT 205,200

Profit = 205,200 − 180,000 = BDT 25,200

Profit Margin % = (25,200/180,000) × 100 = 14%

১১,৯৮৭.

The difference of squares of two consecutive odd integers is divisible by which of the following integers?

ক
3
খ
6
গ
7
ঘ
8

ব্যাখ্যা

Question: The difference of squares of two consecutive odd integers is divisible by which of the following integers?

Solution:
Let
The two consecutive odd integers be (2n + 1) and (2n + 3).

Now
(2n + 3)² - (2n - 1)²=(2n + 3 + 2n + 1)(2n + 3 - 2n - 1)
=(4n + 4) × 2
= 4(n + 1) × 2
= 8(n + 1), which is divisible by 8.

১১,৯৮৮.

When the speed is increased by 4 kmph, it takes 4 hours less to cover a distance of 32km. Find the previous speed.

ক
ক) 2kmph
খ
খ) 4kmph
গ
গ) 8kmph
ঘ
ঘ) 12kmph

ব্যাখ্যা

ধরি
প্রকৃত গতিবেগ ছিল = x kmph

প্রশ্নমতে,
(32/x) - {32/(x + 4)} = 4
⇒ (32x + 128 - 32x)/{x(x + 4)}= 4
⇒ 128/{x(x + 4)} = 4
⇒ (x + 4)x = 32
⇒ x² + 4x - 32 = 0
⇒ x² + 8x - 4x - 32 = 0
⇒ (x + 8) (x - 4) = 0
এখানে অথবা
x + 8 = 0 x - 4 = 0
x= - 8 x = 4

প্রকৃত গতিবেগ ছিল = 4 kmph

১১,৯৮৯.

P and O invested in a business. The profit earned was divided in the ratio 2: 3. If P invested Tk. 40,000 the amount invested by Q is

ক
ক) Tk. 40,000
খ
খ) Tk. 50,000
গ
গ) Tk. 70,000
ঘ
ঘ) Tk. 60,000

ব্যাখ্যা

ধরি, P বিনিয়োগ করেছিল 2x টাকা এবং Q বিনিয়োগ করেছিল 3x টাকা
প্রশ্নমতে, 2x = 40,000
∴ x = 20,000
অতএব, Q বিনিয়োগ করেছিল = 3x = 3 × 20,000
= 60,000 টাকা।

১১,৯৯০.

If tan3A = √3, then A = ?

ক
20°
খ
30°
গ
45°
ঘ
60°

ব্যাখ্যা

Question: If tan3A = √3, then A = ?

Solution:
tan3A = √3
⇒ tan3A = tan60°
⇒ 3A = 60°
⇒ A = 60°/3
∴ A = 20°

১১,৯৯১.

A copper sphere of radius 3 cm is beaten and drawn into a wire of diameter 0.2 cm. The length of the wire is-

ক
36 m
খ
18 m
গ
12 m
ঘ
9 m

ব্যাখ্যা

Question: A copper sphere of radius 3 cm is beaten and drawn into a wire of diameter 0.2 cm. The length of the wire is-

Solution:
ব্যাসার্ধ, r = 3 সেমি
গোলকটির আয়তন = (4/3) × π × r³
= (4/3) × π × 3³
= 36π

তারটি ব্যাসার্ধ = 0.2/2 = 0.1 সেমি
তারটির আয়তন = πr²l
= π × (0.1)² × l
= 0.01πl

শর্তমতে,
0.01πl = 36π
⇒ l = 36/0.01
⇒ l = 3600 cm
⇒ l = 36 m

১১,৯৯২.

The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is?

ক
121
খ
98
গ
111
ঘ
115
ঙ
None of these

ব্যাখ্যা

Question: The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is?

Solution:
Given,
The product of two numbers = 4107
The H.C.F. of the two numbers = 37

We know that,
⇒ HCF × LCM = Product of the numbers
⇒ 37 × LCM = 4107
∴ LCM = 4107/37 = 111

∴ Smaller Number=37
∴ Greater Number=111

১১,৯৯৩.

Find the minimum number of straight lines required to make the given figure.

ক
11
খ
14
গ
16
ঘ
17

ব্যাখ্যা

Question: Find the minimum number of straight lines required to make the given figure.

Solution:

Required straight lines: AB, KL, DC, AC, BD, AD, EF, GH, IJ, BC, GK, GL, HK, HL = 14

১১,৯৯৪.

A boatman goes 1 km against the current of the stream in 1/2 hour and goes 1 km along the current in 20 minutes. How long will it take to go 5 km in stationary water?

ক
1 hour 15 min
খ
2 hour
গ
2 hour 15 min
ঘ
2 hour 30 min

ব্যাখ্যা

Question: A boatman goes 1 km against the current of the stream in 1/2 hour and goes 1 km along the current in 20 minutes. How long will it take to go 5 km in stationary water?

Solution:
Speed upstream = 1/(1/2) = 2 km/hr

Speed downstream = 1/(20/60) = 3 km/hr

Speed in still water = (1/2)(3 + 2) = 2.5 km/hr

Time taken to travel 5 km in still water = 5/2.5 hr
= 2 hr

১১,৯৯৫.

ক
5/9
খ
2/7
গ
10/9
ঘ
10/7

ব্যাখ্যা

Question:

Solution:

১১,৯৯৬.

In how many different ways can the letters of the word ‘DAUGHTER’ be arranged so that the vowels always come together?

ক
ক) 3400
খ
খ) 4320
গ
গ) 5670
ঘ
ঘ) 6800

ব্যাখ্যা

The given word contains 8 different letters.
When the vowels AUE are taken together, we may treat them as 1 letter.
Then,
The letters to be arranged are DGHTR (AUE)
The letters can be arranged in ⁶P₆ = 6!
= 720 ways.
The vowels AUE may be arranged in 3! = 6 ways.
Required number of ways = (720 × 6)
= 4320 ways.

১১,৯৯৭.

A’s age after 15 years would be equal to 5 times his age 5 years ago. Find his age 3 years hence.

ক
10 years
খ
13 years
গ
15 years
ঘ
17 years

ব্যাখ্যা

Question: A’s age after 15 years would be equal to 5 times his age 5 years ago. Find his age 3 years hence.

Solution:
Let A’s present age be ‘n’ years.
According to the question,
n + 15 = 5(n - 5)
⇒ n + 15 = 5 n – 25
⇒ 4n = 40
⇒ n = 10

∴ A’s present age = 10 years
Therefore, A’s age 3 years hence = 10 + 3 = 13 years

১১,৯৯৮.

A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. Find the average speed for first 320 km of tour.

ক
ক) 70.11 km/hr
খ
খ) 71.11 km/hr
গ
গ) 72.11 km/hr
ঘ
ঘ) 73.11 km/hr

ব্যাখ্যা

We know Time = Distance/speed
So total time taken = (160/64) + (160/80)
Time taken for 320 Km = 320× (2/9) = 71.11km/hr

১১,৯৯৯.

x is a two digit number. The digits of the number differ by 6 and the square of the digits differ by 60. Which one of the following could x equal?

ক
ক) 16
খ
খ) 24
গ
গ) 28
ঘ
ঘ) 93

ব্যাখ্যা

8 - 2 = 6 অর্থাৎ অঙ্কদ্বয়ের পার্থক্য 6 এবং
8²- 2²= 64 - 4 = 60 অর্থাৎ অক্ষদ্বয়ের বর্গের অন্তর 60
x এর মান হবে 28

১২,০০০.

If the radius of the base of a right circular cylinder is halved, keeping the height same, what is the ratio of the volume of the reduced cylinder to that of the original one?

ক
1 : 8
খ
1 : 4
গ
1 : 2
ঘ
8 : 1

ব্যাখ্যা

Question: If the radius of the base of a right circular cylinder is halved, keeping the height same, what is the ratio of the volume of the reduced cylinder to that of the original one?

Solution:
Let original radius = R
Then, new radius = R/2

Volume of reduced cylinder/Volume of original cylinder = π(R/2)²h/πR²h
= 1/4
= 1 : 4