Bank Math

PrepBank · পাতা ৭৬ / ১৬১ · ৭,৫০১–৭,৬০০ / ১৬,১২৪

৭,৫০১.

Find the odd number/letters from the given alternatives.

ক
ক) PQXZ
খ
খ) CQBN
গ
গ) ABDF
ঘ
ঘ) PRMN

ব্যাখ্যা

Question: Find the odd number/letters from the given alternatives.

Solution:
PQXZ → No vowel.
CQBN → No vowel.
ABDF → One vowel.
PRMN → No vowel.

৭,৫০২.

What is 45 percent of (7/12) of 240?

ক
63
খ
90
গ
108
ঘ
140

ব্যাখ্যা

Question: What is 45 percent of (7/12) of 240?

Solution:
Here 7/12 of 240 is (7/12) × 240 = 7 × 20 = 140

Now 45 Percent of 140 we have to find out.
45% of 240 = (45/100) × 140 = 63.

৭,৫০৩.

A passenger train of 200 m runs at a speed of 55 km/hr. A person traveling in it observes that the goods train moving in opposite direction takes 10 seconds to cross him. Find the speed of the goods train, if it is 250 m long.

ক
ক) 30.23 m/s
খ
খ) 29.73 m/s
গ
গ) 42.11 m/s
ঘ
ঘ) 55 m/s

ব্যাখ্যা

Given: Speed of passenger train = 55 km/hr, length of goods train (P) = 250, length of passenger train (Q)= 200m
Hint:
Time = (P+Q)/(V1+V2) sec
Goods train and the passenger train move in opposite direction. Hence, the relative speed is the addition of two speeds.
Convert 55 km/hr into m/s
55 x (5/18) = 15.277 m/s
Therefore,
10 = (250+200)/(15.27+V2)
V2 = 29.73 m/s

৭,৫০৪.

The cost of a table and a chair are in the ratio of 5 : 7. If the cost of a chair and table is increased by 20% and 10% respectively, then what will be the new ratio?

ক
16 : 27
খ
60 : 77
গ
55 : 84
ঘ
None of these

ব্যাখ্যা

Question: The cost of a table and a chair are in the ratio of 5 : 7. If the cost of a chair and table is increased by 20% and 10% respectively, then what will be the new ratio?

Solution:
Let, the cost of the table and chair be Tk. 5x and Tk. 7x respectively.

New cost of chair = 120% of 7x
= (120 × 7x)/100
= 42x/5

New cost of table = 110% of 5x
= (110 × 5x)/100
= 55x/10

∴ New ratio = 55x/10 : 42x/5
= 55 : 84

৭,৫০৫.

The numbers 11, 12, 14, x - 2, x + 4, x + 9, 32, 38, 47 are arranged in ascending order and the median is 24; find x.

ক
ক) 18
খ
খ) 24
গ
গ) 22
ঘ
ঘ) 20

ব্যাখ্যা

দেয়া আছে,
সংখ্যাগুলো =11, 12, 14, x - 2, x + 4, x + 9, 32, 38, 47
এখানে সংখ্যাগুলো ক্রমানুযায়ী সাজানো আছে।

এখানে 9টি সংখ্যার মধ্যবর্তী সংখ্যা হলো (x + 4)
প্রশ্নমতে,
x + 4 = 24
x = 24 - 4
x = 20

৭,৫০৬.

Mr. Anis took a loan of Tk.1400 with simple interest for as many years as the rate of interest. If he paid Tk. 686 as interest at the end of the loan period, what was the rate of interest?

ক
ক) 4%
খ
খ) 5%
গ
গ) 6%
ঘ
ঘ) 7%

ব্যাখ্যা

Question: Mr. Anis took a loan of Tk.1400 with simple interest for as many years as the rate of interest. If he paid Tk. 686 as interest at the end of the loan period, what was the rate of interest?

Solution:
Given that n = r

We know,
S.I = (P × n × r)/100
⇒ 686 = (1400 × r × r)/100
⇒ 686 = 14r²⇒ r² = 686/14
⇒ r²= 49
∴ r = 7%

৭,৫০৭.

A motorboat, whose speed is 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is :

ক
ক) 4 km/hr
খ
খ) 5 km/hr
গ
গ) 6 km/hr
ঘ
ঘ) 10 km/hr

ব্যাখ্যা

Let the speed of the stream be x km/hr. Then,
Speed downstream = (15 + x) km/hr,
Speed upstream = (15 - x) km/hr

ATQ, 30/(15 + x) + 30/(15 - x) = 4(1/2)
Or, 900/(225 - X²) = 9/2
Or, 9X² = 225
Or, X² = 25
∴ X = 5 km/hr

৭,৫০৮.

If n is a whole number greater than 1, then n²(n² - 1) is always divisible by-

ক
16
খ
12
গ
10
ঘ
8

ব্যাখ্যা

Question: If n is a whole number greater than 1, then n²(n² - 1) is always divisible by-

Solution:
If n = 2 then n²(n² - 1) = 2²(2² - 1) = 12, which is divisible by 12.
If n = 3 then n²(n² - 1) = 3²(3² - 1) = 72, which is divisible by 12.
If n = 4 then n²(n² - 1) = 4²(4² - 1) = 240, which is divisible by 12.

Hence, n²(n² - 1) is always divisible by 12.

৭,৫০৯.

For the word 'MAGIC' how many different types of arrangement are possible so that the vowels are always together?

ক
24 words
খ
44 words
গ
48 words
ঘ
60 words

ব্যাখ্যা

Question: For the word 'MAGIC' how many different types of arrangement are possible so that the vowels are always together?

Solution:
In the Word MAGIC
There are 2 vowels: A, I
They can be arranged in 2! = 2 ways

There are three consonants: M, G, C
As the vowels are always together, we consider them as 1 letter.
So, 4 letter can be arranged in 4! = 24 ways

∴ Total number of arrangement is 2 × 24 = 48 words

৭,৫১০.

A garden of 50 meter length and 40 meter width has a walkway of 2 meter width on every side. What is the area of the garden, in square meters, excluding the walkway?

ক
ক) 5376 sq m
খ
খ) 1656 sq m
গ
গ) 2556 sq m
ঘ
ঘ) 7874 sq m

ব্যাখ্যা

The area of the garden, excluding the walkway, is
= {(50 - 2×2) × (40 - 2×2)}
= 46×36
= 1656 m²

৭,৫১১.

A sum of Tk. 10 is given as a loan, to be returned in six monthly installments of Tk. 3.What is the simple interest rate?

ক
ক) 820%
খ
খ) 620%
গ
গ) 640%
ঘ
ঘ) 720%

ব্যাখ্যা

Let the rate of interest be R%
Amount due in 6 months
= 10 + simple interest on Tk. 10 for six months.
= {10 + 10 × R × (1/2)}/100
= 10 + (R/20)
With the formula mentioned,
3 = 100(10 + 9R/20)/{(100 × 6) + R × 6(6 - 1)}/(2 × 12)
⇒ 3 = (1000 + 5R)/{600 + (5R/4)}
⇒ 1800 + 15R/4 = 1000 + 5R
⇒ 5R/4 = 800
⇒ R = 640.
Hence interest rate is 640%

৭,৫১২.

Rina bought 40 shares at Tk 75 each. After 3 months, she bought 20 more shares at Tk 70 each. At what price should she buy 40 additional shares so that the average price per share becomes Tk 72?

ক
68
খ
70
গ
72
ঘ
75

ব্যাখ্যা

Question: Rina bought 40 shares at Tk 75 each. After 3 months, she bought 20 more shares at Tk 70 each. At what price should she buy 40 additional shares so that the average price per share becomes Tk 72?

Solution:
Let,
She wants to buy 40 more shares at = Tk x
∴ Total = 40 × x = Tk 40x

First,
40 shares at Tk 75
∴ Total = 40 × 75 = Tk 3000

Then,
20 shares at Tk 70
∴ Total = 20 × 70 = Tk 1400

Here, total shares = 40 + 40 + 20 = 100
∴ Total cost = 100 × 72 = Tk 7200

ATQ,
40x + 3000 + 1400 = 7200
⇒ 40x + 4400 = 7200
⇒ 40x = 7200 - 4400
⇒ 40x = 2800
⇒ x = 2800 ÷ 40
∴ x = 70

৭,৫১৩.

Rahul, Amin, and Akash started a business. Rahul invested 1/2 part, Amin 1/3 part and rest of the capital was invested by Akash. The ratio of their profit will be?

ক
ক) 2 : 3 : 1
খ
খ) 3 : 2 : 1
গ
গ) 2 : 3 : 6
ঘ
ঘ) 3 : 2 : 5

ব্যাখ্যা

Let the total capital be Tk. x.
Then, Rahul's share = Tk. x/2
Amin's share = Tk. x/3
Akash's share = [x - {(x/2) + (x/3)}]
= Tk. x/6
∴ Required ratio = x/2 : x/3 : x/6 = 1/2 : 1/3 : 1/6
= 3 : 2 : 1

৭,৫১৪.

(x - 35) is divisible by 36, 48, 60. Find the value of x.

ক
695
খ
720
গ
755
ঘ
None of them

ব্যাখ্যা

Question: (x - 35) is divisible by 36, 48, 60. Find the value of x.

Solution:
Find the LCM of 36, 48, and 60.
Prime factorization
36 = 2² × 3²
48 = 2⁴ × 3¹
60 = 2² × 3¹ × 5¹

LCM formula
LCM = 2⁴ × 3² × 5 = 16 × 9 × 5 = 720
Let
x - 35 = 720
x = 720 + 35
x = 755

৭,৫১৫.

In a school, the ratio of boys to girls is 7 : 5. If 20 more girls join and 14 boys leave, the new ratio becomes 6 : 5. How many boys were there?

ক
250
খ
310
গ
180
ঘ
290
ঙ
266

ব্যাখ্যা

Question: In a school, the ratio of boys to girls is 7 : 5. If 20 more girls join and 14 boys leave, the new ratio becomes 6 : 5. How many boys were there?

Solution:
Given that,
the ratio of the boys and girls is 7 : 5
Let the number of the boys and girls be ,
boys = 7x
girls = 5x

After changing the number of the students,
Number of boys = 7x - 14
Number of girls = 5x + 20

Now the ratio becomes,
⇒ (7x - 14)/(5x + 20) = 6/5
⇒ 35x - 70 = 30x + 120
⇒ 35x - 30x = 120 + 70
⇒ 5x = 190
∴ x = 38

So the number of the boys = 7x = 7 × 38 = 266

৭,৫১৬.

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

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

৭,৫১৭.

If x is an integer and y = - 2x - 8 what is the least value of x for which y is less than 9?

ক
- 9
খ
- 8
গ
- 7
ঘ
- 6

ব্যাখ্যা

প্রশ্ন: If x is an integer and y = - 2x- 8, what is the least value of x for which y is less than 9?

সমাধান:
y < 9
∴ - 2x - 8 < 9
বা, - 2x < 17
বা, -x < 17/2
বা, -x < 8.5
∴ x > - 8.5

সুতরাং, x এর সর্বনিম্ন মান - 8 হবে।

৭,৫১৮.

In a camp, meals are prepared for 120 men or 200 children. If 150 children have already eaten, how many men can be served with the leftover food?

ক
20 men
খ
40 men
গ
30 men
ঘ
45 men

ব্যাখ্যা

Question: In a camp, meals are prepared for 120 men or 200 children. If 150 children have already eaten, how many men can be served with the leftover food?

Solution:
Camp has = 200 children
Already have taken meal = 150 children

Remaining children to take meal = 200 - 150 = 50 children

The camp has meal for 200 children = 120 men
The camp has meal for 1 children = 120/200 men
The camp has meal for 50 children = (120 × 50)/200 men
= 30 men

৭,৫১৯.

Half of the water tank is filled manually. Tap A can fill the tank in 20 minutes and B can empty the tank in 12 minutes. If A and B are opened together, then the time taken to empty or fill the tank is -

ক
ক) 30 minutes
খ
খ) 15 minutes
গ
গ) 60 minutes
ঘ
ঘ) 45 minutes

ব্যাখ্যা

Given that,
A takes 20 minutes to fill and B takes 12 minutes to empty
Clearly,
tap B is faster than tap A.
And so, the tank will be emptied.
Half of the tank or 1/2 part of the tank is already filled.
Therefore,
we have to find the time taken to empty that 1/2 part.
Part filled by A in 1 minute = 1/20
Part emptied by B in 1 minute = 1/12.
Part emptied by (A + B) in 1 minute
= (1/12) – (1/20)
= (5 - 3)/60
= 1/30.
Therefore,
The time taken by (A + B) to empty the full tank is 30 minutes.
Time taken to empty 1/2 part of the tank is
= 30/2
= 15 minutes.

৭,৫২০.

Find the smallest positive integer that must be added to 11356 so that it becomes divisible by both 18 and 22.

ক
70
খ
128
গ
108
ঘ
116
ঙ
None of these

ব্যাখ্যা

Question: Find the smallest positive integer that must be added to 11356 so that it becomes divisible by both 18 and 22.

Solution:
Since the number must be divisible by both 18 and 22, it must be divisible by their Least Common Multiple (LCM).

LCM of 18 and 22:
18 = 2 × 3²
22 = 2 × 11
∴ LCM = 2 × 3² × 11 = 198

Now, dividing 11356 by 198:
11356 = (198 × 57) + 70
Here, the remainder is 70.

Since we need to add a number to make it divisible by 198,
∴ Smallest integer to be added = Divisor - Remainder
= 198 - 70
= 128

Therefore, 128 must be added to 11356 to make it divisible by both 18 and 22.

৭,৫২১.

If a/b = 4/5 and b/c = 15/16, Then (c² - a²)/(c² + a²) is-

ক
ক) 1/7
খ
খ) 7/25
গ
গ) 3/4
ঘ
ঘ) None of these

ব্যাখ্যা

a/b = 4/5
b/c= 15/16
এখানে
(a/b)(b/c) = (4/5)(15/16)
a/c = 3/4
c/a = 4/3
c²/a² = 16/9
(c² - a²)/(c² + a²) = (16 - 9)/(16 + 9)
= 7/25

৭,৫২২.

Piyal and Belal together can complete a work in 3 days. They start together but after 2 days, Belal left the work. If the work is completed after two more days, Belal alone could do the work in how many days?

ক
3 days
খ
4 days
গ
5 days
ঘ
6 days

ব্যাখ্যা

Question: Piyal and Belal together can complete a work in 3 days. They start together but after 2 days, Belal left the work. If the work is completed after two more days, Belal alone could do the work in how many days?

Solution:
(Piyal + Belal)'s one day's work = 1/3 part
(Piyal + Belal) works 2 days together = 2/3 part
Remaining work = 1- 2/3
= 1/3 part

1/3 part of work is completed by Piyal in two days
Hence, one day's work of Piyal = 1/6 part

Then, one day's work of Belal = 1/3 - 1/6 = 1/6
So, Belal alone can complete the whole work in 6 days.

৭,৫২৩.

Karim started a business with Tk. 80,000. After some months, Rahim joined with Tk. 60,000. At the end of the year, the profit was divided in the ratio 8 : 3. For how many months was Rahim in the business?

ক
4 months
খ
6 months
গ
8 months
ঘ
10 months

ব্যাখ্যা

Question: Karim started a business with Tk. 80,000. After some months, Rahim joined with Tk. 60,000. At the end of the year, the profit was divided in the ratio 8 : 3. For how many months was Rahim in the business?

Solution:
Let, Rahim joined for x months.

ATQ,
(80,000 × 12)/(60,000 × x) = 8/3
⇒ (80,000 × 12 × 3) = (60,000 × x × 8)
⇒ 2,880,000 = 480,000x
⇒ x = 2,880,000/480,000
⇒ x = 6

∴ Rahim joined for 6 months.

৭,৫২৪.

A train 110 m long is running at the speed of 60 km/hr. In what time will it pass a man who is running at the speed of 6 km/hr in the opposite direction in which the train is moving?

ক
ক) 3 sec
খ
খ) 5 sec
গ
গ) 6 sec
ঘ
ঘ) 9 sec

ব্যাখ্যা

Question: A train 110 m long is running at the speed of 60 km/hr. In what time will it pass a man who is running at the speed of 6 km/hr in the opposite direction in which the train is moving?

Solution:
Relative speed = 60 km/hr + 6 km/hr
= 66 km/hr
= 66 ×1000/3600 m/sec
= 66 × 5/18 m/sec
= 55/3 m/sec

time needed = 110 /55/3 sec
= 110 × 3/55 sec
= 6 sec

৭,৫২৫.

n(A\B) + n(A ∩ B) = ?

ক
n(A)
খ
n(B)
গ
n(A\B)
ঘ
n(A ∪ B)

ব্যাখ্যা

Question: n(A\B) + n(A ∩ B) = ?

Solution:
We know that,
A\B = {x : x ∈ A and x ∉ B}

Example: A = {a, b, c} and B = {c, d},
then A ∩ B = {a, b, c} ∩ {c, d} = {c}
and A\B = {a, b, c} \ {c, d} = {a, b}

We can say that,
n(A\B) = n(A) - n(A ∩ B)

Now,
n(A\B) + n(A ∩ B) = n(A) - n(A ∩ B) + n(A ∩ B) = n(A)

৭,৫২৬.

The positive integers m and n leave remainders of 2 and 3, respectively, when divided by 6. m > n. What is the remainder when m - n is divided by 6?

ক
ক) 2
খ
খ) 3
গ
গ) 4
ঘ
ঘ) 5

ব্যাখ্যা

We are given that the numbers m and n, when divided by 6, leave remainders of 2 and 3, respectively,
Hence, we can represent the numbers m and as 6p +2 and 6q + 3, respectively, where p and q are suitable integers.
Now, m - n = (6p + 2) - (6q + 3) = 6p - 6q - 1 = 6(p-q) - 1.
A remainder must be positive, so let's add 6 to this expression and compensate by subtracting 6 :
6(p - q) - 1 =
6 (p - q) - 6 + 6 - 1 =
6 (p - q) - 6 = 5 =
6 (p - q - 1) + 5
Thus, the remainder is 5,
and the answer is 5

৭,৫২৭.

A train 150 meters long passes a signal post in 15 seconds. How long will it take to pass a bridge that is 450 meters long?

ক
1 minute
খ
3 minute
গ
2 minute
ঘ
1.5 minute

ব্যাখ্যা

Question: A train 150 meters long passes a signal post in 15 seconds. How long will it take to pass a bridge that is 450 meters long?

Solution:
Train's speed = Distance/Time
= 150/15 = 10 m/s

Total distance to pass the bridge,
= Length of train + Length of bridge
= 150 m + 450 m
= 600 m

∴ Required time = Distance/Speed
= 600/10
= 60 seconds
= 1 minute

∴ The train will take 60 seconds or 1 minute to pass platform.

৭,৫২৮.

Find the number of the divisors of 540.

ক
18
খ
20
গ
22
ঘ
24

ব্যাখ্যা

Question: Find the number of the divisors of 540.

Solution:
540
= 1 × 540
= 2 × 270
= 3 × 180
= 4 × 135
= 5 × 108
= 6 × 90
= 9 × 60
= 10 × 54
= 12 × 45
= 15 × 36
= 18 × 30
= 20 × 27

the number of the divisors of 540 is 24

৭,৫২৯.

The average of 9 numbers is 40. If 60 is added, what is the new average?

ক
ক) 40
খ
খ) 41
গ
গ) 42
ঘ
ঘ) 43

ব্যাখ্যা

Question: The average of 9 numbers is 40. If 60 is added, what is the new average?

Solution:
৯ টি সংখ্যার গড় = ৪০
সমষ্টি = (৪০ × ৯) = ৩৬০

৬০ যোগ করার পর মোট = ৩৬০ + ৬০ = ৪২০

গড় = ৪২০/ ১০ = ৪২

৭,৫৩০.

Alim was hired for a job for 7 days. Each day, he was paid Tk. 10 more than what he was paid for the previous day of work. The total amount he was paid in the first 4 days of work equaled the total amount he was paid in the last 3 days. What was his starting pay?

ক
ক) TK. 90
খ
খ) Tk. 138
গ
গ) Tk. 153
ঘ
ঘ) Tk. 160
ঙ
ঙ) None

ব্যাখ্যা

তার প্রথমদিনের আয় x টাকা।
প্রশ্নমতে, x+x+10+x+20+x+30 = x+40+x+50+x+60
বা,4x + 60 = 3x + 150
বা, x = 90

৭,৫৩১.

Find the HCF of 3/4, 5/6 and 6/7 = ?

ক
1/48
খ
1/60
গ
1/84
ঘ
None of these

ব্যাখ্যা

Question: Find the HCF of 3/4, 5/6 and 6/7 = ?

Solution:
For the HCF of fractions, it has to be taken the HCF of numerators and LCM denominators.

HCF of 3, 5, 6 = 1
LCM of 4, 6, 7 = 84

HCF of numerators/LCM of denominators = 1/84

Hence, the HCF of 3/4, 5/6 and 6/7 = 1/84

৭,৫৩২.

How many integers from 1 to 100 are divisible by 3 but not by 8?

ক
ক) 29
খ
খ) 30
গ
গ) 31
ঘ
ঘ) 32

ব্যাখ্যা

এখানে,
3 দ্বারা বিভাজ্য সংখ্যা = 100/3
ভাগফল 33 এবং ভাগশেষ 1
সুতরাং 3 দ্বারা বিভাজ্য সংখ্যা = 33 টি
3 ও 8 এর ল, সা, গু = 24
এখন 100/24 =
ভাগফল 4 এবং ভাগশেষ 4
∴ 3 ও 8 দ্বারা বিভাজ্য সংখ্যা = 4 টি
সুতরাং, (33 - 4) = 29 টি সংখ্যা 3 দ্বারা বিভাজ্য কিন্তু 8 দ্বারা বিভাজ্য নয়।

৭,৫৩৩.

Find the HCF of 210, 385, and 735.

ক
45
খ
35
গ
55
ঘ
27

ব্যাখ্যা

Question: Find the HCF of 210, 385, and 735.

Solution:
HCF of 210, 385, and 735.

Factor of 210 = 2 × 3 × 5 × 7
Factor of 385 = 5 × 7 × 11
Factor of 735 = 3 × 5 × 7 × 7
∴ HCF of (210, 385 and 735) = 35

৭,৫৩৪.

Four years ago a man was 6 times as old as his son. After 16 years he will be twice as old as his son. What is the present age of man and his son?

ক
34, 9
খ
33, 7
গ
35, 5
ঘ
36, 6

ব্যাখ্যা

Question: Four years ago a man was 6 times as old as his son. After 16 years he will be twice as old as his son. What is the present age of man and his son?

Solution:
Let age of son 4 years ago be = X
So, age of man 4 years ago would be = 6X

As per question after 16 years;
2 × age of son = age of man
2(X + 4 +16) = (6X + 4 + 16)
⇒ 2X + 40 = 6X + 20
⇒ 2X - 6X = 20 - 40
⇒ - 4X = - 20
∴ X = 5 years

∴ Present age of son = 5 + 4 = 9 years
∴ Present age of man = 6X + 4 = 6 × 5 + 4 = 30 + 4 = 34 years

৭,৫৩৫.

A man's salary was reduced by 30%, again the reduce salary was increased by 30%. Find the loss of in term of percentage.

ক
ক) 9%
খ
খ) 15%
গ
গ) 20%
ঘ
ঘ) 25%

ব্যাখ্যা

Let the salary was Tk. 100

A man's salary was reduced by 30%.
So, salary will be Tk. (100 - 30) = Tk. 70

Again the reduce salary was increased by 30%.
So, salary will be Tk. (70 + 30% of 70) = Tk. (70 + 21) = Tk. 91

Loss of in term of percentage = Tk. (100 - 91) = Tk. 9

৭,৫৩৬.

30% of 50 is what fraction of 75% of 80?

ক
ক) 1/2
খ
খ) 1/4
গ
গ) 1/5
ঘ
ঘ) 1/7

ব্যাখ্যা

Question: 30% of 50 is what fraction of 75% of 80?

Solution:
30% of 50 = 50 × .3
= 15

75% of 80 = 80 × 0.75
= 60

fraction = 15/60
= 1/4

৭,৫৩৭.

The length, breadth and height of a room in the shape of a cuboid are increased by 10%, 20% and 50% respectively. Find the percentage change in the volume of the cuboid.

ক
ক) 98%
খ
খ) 99%
গ
গ) 93%
ঘ
ঘ) 91%

ব্যাখ্যা

Question: The length, breadth and height of a room in the shape of a cuboid are increased by 10%, 20% and 50% respectively. Find the percentage change in the volume of the cuboid.

Solution:
Let each side of the cuboid be 10 unit initially.
Initial Volume of the cuboid,
= Length × Breadth × Height
= (10 × 10 × 10)
= 1000 cubic unit.

After increment dimensions become,
Length = (10 + 10% of 10) = 11 unit.
Breadth = (10 + 20% of 10) = 12 unit.
Height = (10 + 50% of 10) = 15 unit.

Now, New volume = (11 × 12 × 15) = 1980 cubic unit.

∴ Increase in volume = 1980 - 1000 = 980 cubic unit.
Increase in volume percent = (980/1000) × 100
= 98%

৭,৫৩৮.

A man covers half of his journey at 12 km/h and the remaining half at 6 km/h. His average speed is-

ক
10 km/h
খ
8 km/h
গ
7 km/h
ঘ
9 km/h

ব্যাখ্যা

Question: A man covers half of his journey at 12 km/h and the remaining half at 6 km/h. His average speed is-

Solution:
Given,
Man covers half of his journey at 12 km/h
The remaining half at 6 km/h

His average speed is = (2 × 12 × 6)/(12 + 6)
= 144/18
= 8 km/h

৭,৫৩৯.

sin(180° + θ) = ?

ক
- sinθ
খ
- cosθ
গ
sinθ
ঘ
cosθ

ব্যাখ্যা

Question: sin(180° + θ) = ?

Solution:

sin(180° + θ) হলে sin তৃতীয় ভাগে পরবে।
তাই sin এর মান ঋণাত্নক হবে।
∴ sin(180° + θ) = - sinθ

৭,৫৪০.

A tank has a leak which would empty the completely filled tank in 10 hours. If the tank is full of water and a tap is opened which admits 4 litres of water per minute in the tank , the leak takes 15 hours to empty the tank. How many litres of water does the tank hold?

ক
ক) 2400 litters
খ
খ) 1200 litters
গ
গ) 4500 litters
ঘ
ঘ) 7200 litters

ব্যাখ্যা

Question: A tank has a leak which would empty the completely filled tank in 10 hours. If the tank is full of water and a tap is opened which admits 4 litres of water per minute in the tank , the leak takes 15 hours to empty the tank. How many litres of water does the tank hold?

Solution:
Let the total capacity of the tank is 30 units.
The efficiency of Leakage(Pipe A) will be 30/10 = 3
And the efficiency of the leakage (Pipe A) and another Pipe (B) which is filling the tank will be 30/15 = 2

Pipe A is emptying at 3 units/hr and when filling pipe B started then the emptying rate will come down to 2 units/hr.
∴ Filling Pipe B efficiency is 3 - 2 = 1 unit/hr
Pipe B will be fill the tank in 30/1 = 30 hrs.

The filling rate of Pipe B per minute is 4 litter
∴ Total Capacity of tank will be = (4 × 60) × 30 = 7200 litters.

৭,৫৪১.

How many terms are there in the geometric progression,
3, 6, 12, 24, …, 1536

ক
10
খ
8
গ
11
ঘ
9

ব্যাখ্যা

Question: How many terms are there in the geometric progression,
3, 6, 12, 24, …, 1536

Solution:
First term, a = 3
Common ratio, r = 6/3 = 2

Last term or nth term of GP = ar^{n - 1}
⇒ 1536 = 3 × (2^{n - 1})
⇒ 2^{n - 1} = 1536/3
⇒ 2^{n - 1} = 512
⇒ 2^{n - 1} = 2⁹
So, comparing the power,
Thus, n - 1 = 9
∴ n = 10

∴ Number of terms = 10

৭,৫৪২.

How many years will it take for an investment of Tk.1000 to earn Tk. 200 in simple interest rate of 5%?

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

ব্যাখ্যা

Question: How many years will it take for an investment of Tk.1000 to earn Tk. 200 in simple interest rate of 5%?

Solution:
Given that,
Principal, P = 1000
Simple Interest, SI = 200
Rate of interest, r = 5%
Time, n = ?

We know,
n = I/Pr
= 200/(1000 × 5%)
= (200 × 100)/(1000 × 5)
= 4

So, it will take 4 years for the investment to earn Tk. 200 at 5% simple interest.

৭,৫৪৩.

If x and y are two positive integers and x + y = 4 then, what is the probability of x equals to 1?

ক
ক) 1/3
খ
খ) 1/4
গ
গ) 1/5
ঘ
ঘ) 1/6

ব্যাখ্যা

Question: If x and y are two positive integers and x + y = 4 then, what is the probability of x equals to 1?

Solution:
total possible ways = (1, 3), (2, 2), (3, 1) = 3
favorable event = (1, 3) = 1

∴ probability = 1/3

৭,৫৪৪.

Using the digits 2, 5, and 7 exactly once each, three-digit numbers are formed. One number is selected at random. What is the probability that it is divisible by 4?

ক
1/6
খ
1/4
গ
1/3
ঘ
1/2
ঙ
2/3

ব্যাখ্যা

Question: Using the digits 2, 5, and 7 exactly once each, three-digit numbers are formed. One number is selected at random. What is the probability that it is divisible by 4?

Solution:
Total numbers = 3! = 6
Numbers are 257, 275, 527, 572, 725, 752

We know,
A number is divisible by 4 if the number formed by its last two digits is divisible by 4.

∴ Check last two digits are 72 and 52 divisible by 4.

∴ Favourable outcomes = 572 and 752 = 2

∴ Probability = 2/6 = 1/3

৭,৫৪৫.

The difference between the greatest and least prime numbers which are less than 80 is

ক
ক) 67
খ
খ) 72
গ
গ) 75
ঘ
ঘ) 77

ব্যাখ্যা

Greatest prime number = 97
Least prime number = 2
So, their difference = 79 - 2 = 77

৭,৫৪৬.

A man travels from his home to the office at 4 km/hr and reaches his office 5 min late. If the speed had been 5 km/hr he would have reached 10 min early. Find the distance from his home to the office?

ক
3 km
খ
5 km
গ
6 km
ঘ
10 km

ব্যাখ্যা

Question: A man travels from his home to the office at 4 km/hr and reaches his office 5 min late. If the speed had been 5 km/hr he would have reached 10 min early. Find the distance from his home to the office?

Solution:
ধরি, বাড়ি থেকে অফিসের দূরত্ব = d কিমি।
4 কিমি/ঘণ্টা বেগে সময় লাগে = d/4 ঘণ্টা
5 কিমি/ঘণ্টা বেগে সময় লাগে = d/5 ঘণ্টা

সময়ের পার্থক্য = 5 মিনিট (দেরি) + 10 মিনিট (আগে) = 15 মিনিট
= 15/60 = 1/4 ঘণ্টা

প্রশ্নমতে,
(d/4) - (d/5) = 1/4
⇒ (5d - 4d) / 20 = 1/4
⇒ d / 20 = 1/4
⇒ d = 20 / 4
∴ d = 5

সুতরাং, বাড়ি থেকে অফিসের দূরত্ব 5 কিমি।

৭,৫৪৭.

A fort had arrangements for 150 boys for 45 days. After 10 days, 25 boys left the fort. Then after how much time the food will be consumed completely if the consumption of food remains the same for the remaining boys?

ক
45 days
খ
47 days
গ
42 days
ঘ
None of these

ব্যাখ্যা

Question: A fort had arrangements for 150 boys for 45 days. After 10 days, 25 boys left the fort. Then after how much time the food will be consumed completely if the consumption of food remains the same for the remaining boys?

Solution:
ATQ,
25 people left the fort after 10 days, but still, the remaining food will be consumed at the same rate.
That means if the 150 boys continue till the end, then the remaining food would last for 150 boys for (45 - 10) = 35 days.
Now
After 10 days the remaining food will be (boys × days) 150 × 35 = 5250 unit
But the 25 boys left the for after 10 days
i.e., 125 boys will consume the 5250 unit food in x days
Now,
x = 5250/125 = 42 days.
That means the remaining food will last for 42 days.

৭,৫৪৮.

ক
2/5
খ
√3/2
গ
1/2
ঘ
4

ব্যাখ্যা

Question:

Solution:

৭,৫৪৯.

In a certain code, AXIOM is written as ZWHNL. How is WAXED written in that code?

ক
VYXDC
খ
VZWED
গ
WZXDC
ঘ
VZWDC

ব্যাখ্যা

Question: In a certain code, AXIOM is written as ZWHNL. How is WAXED written in that code?

সমাধান:
এই কোডিং প্যাটার্নটি হলো প্রতিটি অক্ষরের পূর্ববর্তী অক্ষর ব্যবহার করা।
A ⇒ Z
X ⇒ W
I ⇒ H
O ⇒ N
M ⇒ L
এই নিয়ম অনুযায়ী, WAXED শব্দটির কোড হবে:
W ⇒ V
A ⇒ Z
X ⇒ W
E ⇒ D
D ⇒ C

সুতরাং, WAXED এর কোড হবে: VZWDC

৭,৫৫০.

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

ক
35.55 km/hr
খ
36 km/hr
গ
71.11 km/hr
ঘ
71 km/hr

ব্যাখ্যা

Question: A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is-

Solution:
Total time taken = (160/64 + 160/80)hrs
= 9/2 hrs.

Average speed = 320 × (2/9) km.hr
= 71.11 km/hr.

৭,৫৫১.

Mahi was facing east. he walked 7 km forward and then after turning to his right walked 5 km. Again he turned to his right and walked 7 km. After this he turned back. Which direction was he facing at that time?

ক
East
খ
West
গ
North
ঘ
South

ব্যাখ্যা

Question: Mahi was facing east. he walked 7 km forward and then after turning to his right walked 5 km. Again he turned to his right and walked 7 km. After this he turned back. Which direction was he facing at that time?

Solution:
Mahi's Movement-

∴ If Mahi turned back from final position he must be facing in the direction of East.

৭,৫৫২.

If 1 < p < 3, then which of the following could be true?
(I) p² < 2p
(II) p² = 2p
(III) p² > 2p

ক
I only
খ
II only
গ
I and II only
ঘ
I and III only
ঙ
I, II, and III

ব্যাখ্যা

Question: If 1 < p < 3, then which of the following could be true?
(I) p² < 2p
(II) p² = 2p
(III) p² > 2p

Solution:
Given: 1 < p < 3

Since p > 0,

(I) p² < 2p
⇒ p < 2
True for 1 < p < 2
Example: p = 1.5 gives 2.25 < 3.0
So, condition (I) could be true.

(II) p² = 2p
⇒ p = 2
Since 2 is within the given range (1< 2 < 3), condition (II) could be true.

(III) p² > 2p
⇒ p > 2
Example: p = 2.5, gives 6.25 > 5.0
So, condition (III) could be true.

Conclusion: Since values of p in the range 1< p < 3 satisfy conditions (I), (II), and (III), the correct choice is: (E) I, II, and III.

৭,৫৫৩.

The next number of the sequence is-
1, 1, 4, 8, 9, 27, 16, ?

ক
ক) 32
খ
খ) 64
গ
গ) 25
ঘ
ঘ) 36

ব্যাখ্যা

Question:
The next number of the sequence is-
1, 1, 4, 8, 9, 27, 16, ?

Solution:
এখানে,
দুটি সিরিজ বিদ্যমান
১ম সিরিজ = 1, 4, 9, 16, ...... [১ থেকে শুরু করে স্বাভাবিক সংখ্যার বর্গ করে বাড়ছে]
২য় সিরিজ = 1, 8, 27, 64, ......[১ থেকে শুরু করে স্বাভাবিক সংখ্যার ঘন করে বাড়ছে ]

৭,৫৫৪.

A number when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing the same number by 31?

ক
5
খ
6
গ
7
ঘ
8

ব্যাখ্যা

Let p be the number
p ÷ 44 = 432, remainder = 0
⇒ p = 432 × 44 + 0 = 19008
p ÷ 31
= 19008 ÷ 31
= 613, remainder = 5.

৭,৫৫৫.

A man invests Tk. 8,100 partly in 14% stock at 294 and partly in 12% stock at 288. If his income from both is the same, find his investment in the 14% stock.

ক
3780 Tk
খ
3980 Tk
গ
3820 Tk
ঘ
4120 Tk
ঙ
3020 Tk

ব্যাখ্যা

Question: A man invests Tk. 8,100 partly in 14% stock at 294 and partly in 12% stock at 288. If his income from both is the same, find his investment in the 14% stock.

Solution:
Let he invests x at 14% stock.
x Investment at 12% stock = 8100 - x

As income is same.
x × (14/100) × (1/294) = (8100 - x) × (12/100) × (1/288)
⇒ x/2100 = (8100 - x)/2400
⇒ x = {(8100 - x)/2400} × 2100
⇒ 24x = 170100 - 21x
⇒ 45x = 170100
∴ x = 3780 Tk

৭,৫৫৬.

What value of x satisfies the equation x - 1 = 1 - x.

ক
2
খ
1
গ
0
ঘ
- 2
ঙ
None

ব্যাখ্যা

প্রশ্ন: What value of x satisfies the equation x - 1 = 1 - x.

সমাধান:
দেওয়া আছে,
x - 1 = 1 - x
⇒ x + x = 1 + 1
⇒ 2x = 2
⇒ x = 2/2
∴ x = 1

৭,৫৫৭.

Two numbers are in the ratio 5 : 2. If the difference of their squares is 84, then find the largest number-

ক
12
খ
10
গ
8
ঘ
4

ব্যাখ্যা

Question: Two numbers are in the ratio 5 : 2. If the difference of their squares is 84, then find the largest number-

Solution:
দুটি সংখ্যার অনুপাত ৫ : ২
সংখ্যা দুটি ৫x, ২x

প্রশ্নমতে,
(৫x)^২ - (২x)^২ = ৮৪
⇒ ২৫x^২ - ৪x^২ = ৮৪
⇒ ২১x^২ = ৮৪
⇒ x^২ = ৪
∴ x = ২

সংখ্যা দুটি ১০, ৪
বড় সংখ্যাটি ১০

৭,৫৫৮.

ক
ক) 13
খ
খ) 13.5
গ
গ) 12
ঘ
ঘ) None of these

ব্যাখ্যা

(27/4) × (40/3) + 4 × x = (520 × 30)/100
90 + 4x = 156
4x = 156 - 90
4x = 66
x = 66/4
x = 16.5

৭,৫৫৯.

If 2x - y = 10 and x/y = 3, then x = ?

ক
ক) - 10
খ
খ) 2
গ
গ) 4
ঘ
ঘ) 6

ব্যাখ্যা

দেয়া আছে
x/y = 3
x = 3y

এখানে
2x - y = 10
বা, 2(3y) - y = 10
বা, 6y - y = 10
বা, 5y = 10
y = 2

আবার
x = 3(2)
x = 6

৭,৫৬০.

4log√5 + 3log2 - (1/4)log10000 =?

ক
ক) log27.5
খ
খ) 0
গ
গ) log20
ঘ
ঘ) 1

ব্যাখ্যা

Question: 4log√5 + 3log2 - (1/4)log10000 =?

Solution:
4log√5 + 3log2 - (1/4)log10000
= log(√5)⁴ + 3log2 - (1/4)log10⁴
= log5² + 3log2 - (4/4) log10
= 2log5 + 3log2 - log10
= 2log5 + 3log2 - log (2 × 5)
= 2log5 + 3log2 - log2 - log5
= log5 + 2log2
= log5 + log2²
= log (5 × 4)
= log20

৭,৫৬১.

At what profit percent must an article be sold so that by selling it at two-thirds of that price, there will be a loss of 20%?

ক
25%
খ
16.66%
গ
20%
ঘ
30.2%

ব্যাখ্যা

Question: At what profit percent must an article be sold so that by selling it at two-thirds of that price, there will be a loss of 20%?

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%

৭,৫৬২.

The monthly incomes of two brothers are in the ratio 11 : 7 and their monthly expenditures are in the ratio 9 : 5. Each of them saves Tk. 4,800 per month. Find the monthly income of the first brother.

ক
Tk. 28800
খ
Tk. 25200
গ
Tk. 24000
ঘ
Tk. 27600
ঙ
Tk. 26400

ব্যাখ্যা

Question: The monthly incomes of two brothers are in the ratio 11 : 7 and their monthly expenditures are in the ratio 9 : 5. Each of them saves Tk. 4,800 per month. Find the monthly income of the first brother.

Solution:
Let the monthly income of the two brothers are 11x and 7x
Let the monthly expenses of the two brothers are 9y and 5y
Since each saves Tk. 4800 per month.

Then we get,
11x - 9y = 7x - 5y
⇒ 4x = 4y
∴ x = y

Now,
11x - 9y = 4800
⇒ 11x - 9x = 4800
⇒ 2x = 4800
⇒ x = 4800/2
∴ x = 2400
∴ y = 2400

Therefore,
Monthly income of the first brother = 11x = 11 × 2400 = Tk. 26400

So the monthly incomes are Tk. 26400.

৭,৫৬৩.

In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?

ক
ক) 6/7
খ
খ) 19/21
গ
গ) 7/31
ঘ
ঘ) 5/21
ঙ
ঙ) None of the above

ব্যাখ্যা

Number of ways of (selecting at least two couples among five people selected) = (⁵C₂ × ⁶C₁)
As remaining person can be any one among three couples left.
Required probability = (⁵C₂ × ⁶C₁)/¹⁰C₅
= (10 x 6)/252
= 5/21

৭,৫৬৪.

The least number of five digits which has 123 as a factor is-

ক
10086
খ
10077
গ
10081
ঘ
10065

ব্যাখ্যা

Question: The least number of five digits which has 123 as a factor is-

Solution:
Here,
The smallest number of 5 digits = 10000

Remainder on dividing 10000 by 123
= 37

∴ Required number = 10000 + (123 - 37)
= 10086

৭,৫৬৫.

A boat goes 30 km downstream and comes back in a total of 4 hours 30 minutes. Its speed is 15 km/hr in still water. What is the speed of the stream (in km/hr)?

ক
4 km/h
খ
5 km/h
গ
6 km/h
ঘ
18 km/h

ব্যাখ্যা

Let the speed of the stream be x km/hr
Then,
Speed downstream = (15 + x) km/hr
Speed upstream = (15 - x) km/hr
∴30/(15+x) + 30/(15−x) = 4.5
⇒ x²= 25
⇒ x = 5km/hr

৭,৫৬৬.

What percentage of odd prime numbers lying between 1 and 30 divide 7,700 completely?

ক
20.33%
খ
25.5%
গ
30.67%
ঘ
33.33%
ঙ
40%

ব্যাখ্যা

Question: What percentage of odd prime numbers lying between 1 and 30 divide 7,700 completely?

Solution:
Odd prime numbers : 3, 5, 7, 11, 13, 17, 19, 23, 29 (Count: 9)
Factor of 7700 = 7 × 11 × 5² × 2²

Numbers divisible 7700 by: 5, 7, 11 (Count: 3)

∴ Required Percentage = (3/9) × 100 = 33.33%

৭,৫৬৭.

The present ages of A and B are in the ratio 6 : 4. Five years ago their ages were in the ratio 5 : 3. Find their present ages.

ক
ক) 42, 28
খ
খ) 36. 24
গ
গ) 30, 20
ঘ
ঘ) 25, 15
ঙ
ঙ) None of these

ব্যাখ্যা

Question: The present ages of A and B are in the ratio 6 : 4. Five years ago their ages were in the ratio 5: 3. Find their present ages.

Solution:
বর্তমানে A এর বয়স 6x বছর
বর্তমানে B এর বয়স 4x বছর

5 বছর আগে, A এর বয়স 6x - 5 বছর
5 বছর আগে, B এর বয়স 4x - 5 বছর

প্রশ্নমতে,
(6x - 5)/(4x - 5) = 5/3
⇒ 18x - 15 = 20x - 25
⇒ 20x - 18x = 25 - 15
⇒ 2x = 10
⇒ x = 5

বর্তমানে A এর বয়স = (6 × 5) = 30 বছর
বর্তমানে B এর বয়স = (4 × 5) বছর = 20 বছর

৭,৫৬৮.

What is the length of the diagonal of a square whose area is 4 times of another square with diagonal as 5√2 cm?

ক
ক) 10 cm
খ
খ) 10√2 cm
গ
গ) 20√2 cm
ঘ
ঘ) 20 cm

ব্যাখ্যা

Question: What is the length of the diagonal of a square whose area is 4 times of another square with diagonal as 5√2 cm?

Solution:
Area of square = (1/2) × (length of diagonal)²
Area of square₂ =(1/2) × (5√2)² =
Area of square₁= 4 × 25 = 100

Length of diagonal of square₁ = √(2 × area)
= √(2 × 100)
= 10√2 cm

৭,৫৬৯.

If 555/0.01 = x/0.001, then what is the value of x?

ক
ক) 55.5
খ
খ) 5.55
গ
গ) 0.555
ঘ
ঘ) 5550

ব্যাখ্যা

Question: If 555/0.01 = x/0.001, then what is the value of x?

Solution:
555/0.01 = x/0.001
⇒ 0.01x = 0.001 × 555
⇒ 0.01x = 0.555
⇒ x = 0.555 / 0.01
⇒ x = 55.5

৭,৫৭০.

If b = 9d - c and d = (a/6), what is the average (arithmetic mean) of a, b, c and d?

ক
2d
খ
3d
গ
4d
ঘ
none

ব্যাখ্যা

Question: If b = 9d - c and d = (a/6), what is the average (arithmetic mean) of a, b, c and d?

Solution:
d = a/6
∴ 6d = a

b = 9d - c
⇒ b + c = 9d

Average of the four values = (a + b + c + d)/4
Substitute to get: average = (6d + 9d + d)/4 = 16d/4 = 4d

৭,৫৭১.

A man completes a certain journey by a car. If he covered 30% of the distance at the speed of 20kmph. 60% of the distance at 40km/h and the remaining of the distance at 10 kmph, his average speed is:

ক
25 km/h
খ
45 km/h
গ
35 km/h
ঘ
27 km/h

ব্যাখ্যা

Suppose, total distance = 100 km

He covered 30% of the distance at the speed of 20kmph
His time taken = 30/20 hours

He covered 60% of the distance at 40km/h
His time taken = 60/40 hours

He covered the remaining of the distance at 10 kmph
The remaining of the distance = 100% - (30 + 60)% = 10%
His time taken = 10/10 hour

Average speed = total distance/time
= 100/(30/20 + 60/40 + 10/10)
= 25 km/h

৭,৫৭২.

University A charges Tk. 9,000 annually for tuition and Tk. 3,000 annually for room and board. University A charges 10% less than University B does for tuition and 20% more than University B does for room and board. The total annual cost of tuition, room and board is how much more or less at University A than it is at University B?

ক
Tk. 1,200 less
খ
Tk. 500 less
গ
Tk. 300 less
ঘ
Tk. 300 more
ঙ
The costs are equal.

ব্যাখ্যা

Question: University A charges Tk. 9,000 annually for tuition and Tk. 3,000 annually for room and board. University A charges 10% less than University B does for tuition and 20% more than University B does for room and board. The total annual cost of tuition, room and board is how much more or less at University A than it is at University B?

Solution:
University A
tuition fees annually = Tk. 9000
Room and Boarding price annually Tk. 3000
Total fee for University A = Tk. 12000

University B
Tuition fees annually x
Room and Boarding price annually y

Tuition fee of A is 10% less than that of B
x - (10% of x) = 9000
⇒ 0.9x = 9000
∴ x = 10000

Boarding price of A is 20% more than B
y + (20% of y) = 3000
⇒ 1.2y = 3000
∴ y = 2500

Total fee for University B = 10000 + 2500 =12500

Total fee of A is less than that of B by = 12500 - 12000 = 500 annually

৭,৫৭৩.

A bag contains 5 red and 3 blue balls. Two balls are drawn at random. Find the probability that they are of same color.

ক
ক) 7/15
খ
খ) 9/11
গ
গ) 11/16
ঘ
ঘ) 13/28

ব্যাখ্যা

Question: A bag contains 5 red and 3 blue balls. Two balls are drawn at random. Find the probability that they are of same color.

Solution:
Total number of balls = 5 + 3 = 8
where red balls = 5
blue balls = 3

If we want to draw two balls at random out of 5 red balls the ways = ⁵C₂/⁸C₂
If we want to draw two balls at random out of 3 blue balls the ways = ³C₂/⁸C₂

∴ Probability of both being same color
= (Both are red) + ( Both are blue)
= (⁵C₂/⁸C₂ ) + ( ³C₂/⁸C₂)
= (10/28) + (3/28)
= 13/28

৭,৫৭৪.

A dog starts chasing to a cat 2 hours later. It takes 2 hours to dog to catch the cat. If the speed of the dog is 30 km/h, what is the speed of cat?

ক
15 km/hr
খ
18 km/hr
গ
20 km/hr
ঘ
25 km/hr
ঙ
None of the above

ব্যাখ্যা

Question: A dog starts chasing to a cat 2 hours later. It takes 2 hours to dog to catch the cat. If the speed of the dog is 30 km/h, what is the speed of cat?

Solution:
Let the speed of the cat be = x km/hr
The speed of the dog be = 30 km/hr

Distance covered by cat in 2 hrs = (x × 2) = 2x km

Relative speed = (30 - x) km/hr

t = s/v
⇒ 2 = 2x/(30 - x) [It takes 2 hours to dog to catch the cat, so t = 2]
⇒ x = 30 - x
⇒ 2x = 30
∴ x = 15 km/hr

৭,৫৭৫.

If the fractions 7/13, 2/3, 4/11, 5/9 are arranged in ascending order, then the correct sequence is ?

ক
2/3, 7/13, 4/11, 5/9
খ
7/13, 4/11, 5/9, 2/3
গ
4/11, 7/13, 5/9, 2/3
ঘ
5/9, 4/11, 7/13, 2/3
ঙ
None of these

ব্যাখ্যা

Question: If the fractions 7/13, 2/3, 4/11, 5/9 are arranged in ascending order, then the correct sequence is ?

Solution:
Given that,
(7/13) = 0.538
(2/3) = 0.666
(4/11) = 0.3636
(5/9) = 0.5555

Out of 2/3, 7/13, 4/11, 5/9

2/3 is the largest number followed by 5/9 then 7/13 and the smallest is 4/11.

∴ The ascending order will be 4/11, 7/13, 5/9, 2/3.

৭,৫৭৬.

If the angle of depression at a point on the ground 20 meters from the top of the house is 30°, then find the height of the house.

ক
8 m
খ
10 m
গ
12 m
ঘ
14 m

ব্যাখ্যা

Question: If the angle of depression at a point on the ground 20 meters from the top of the house is 30°, then find the height of the house.

Solution:

height of the house, = AB

sin30° = AB/20
⇒ 1/2 = AB/20
⇒ AB = 10 m

৭,৫৭৭.

The ratio of Sara’s age 4 years ago and Vaishali’s age after 4 years is 1 : 1. Presently, the ratio of their ages is 5 : 3. Find the ratio between Sara’s age 4 years hence and Vaishali’s age 4 years ago.

ক
1 : 3
খ
3 : 1
গ
4 : 3
ঘ
3 : 4
ঙ
None of these

ব্যাখ্যা

Question: The ratio of Sara’s age 4 years ago and Vaishali’s age after 4 years is 1 : 1. Presently, the ratio of their ages is 5 : 3. Find the ratio between Sara’s age 4 years hence and Vaishali’s age 4 years ago.

Solution:

Currently, the ratio of their ages is 5 : 3. Suppose, their ages are: 5x and 3x.

Sara’s age 4 years ago = 5x - 4

Vaishali’s age after 4 years = 3x + 4

Ratio of Sara’s age 4 years ago and Vaishali's age after 4 years is 1 : 1

Therefore,

(5x - 4)/(3x + 4) = 1/1
⇒ 5x - 4 = 3x + 4

⇒ 2x = 8
∴ x = 4

We are required to find the ratio between Sara’s age 4 years hence and Vaishali’s age 4 years ago.

Sara's age: (5x + 4)

Vaishali's age: (3x - 4)

Putting the value of x, we get:

(5x + 4)/(3x - 4) = 24/8 = 3/1 = 3 : 1

৭,৫৭৮.

A man walk at a speed of 10 km/h. After every 3 kilometers, he takes a rest of 5 minutes. How much time will he take to cover a distance of 15 km?

ক
1 hour
খ
1 hour 30 minutes
গ
40 minutes
ঘ
1 hour 50 minutes

ব্যাখ্যা

Question: A man walk at a speed of 10 km/h. After every 3 kilometers, he takes a rest of 5 minutes. How much time will he take to cover a distance of 15 km?

সমাধান:
দূরত্ব = 15 কিমি
গতিবেগ = 10 কিমি/ঘন্টা

∴ সময় = দূরত্ব/গতিবেগ
= 15 কিমি/10 কিমি/ঘন্টা
= 1.5 ঘন্টা
= 90 মিনিট

সে প্রতি 3 কিলোমিটারের পরে 5 মিনিট বিশ্রাম নেয়।
15 কিমি দূরত্বে সে (15/3) - 1 = 4 বার বিশ্রাম নেবে (3 কিমি, 6 কিমি, 9 কিমি এবং 12 কিমি অতিক্রম করার পর)।
শেষ কিলোমিটারের পরে তার আর বিশ্রাম নেওয়ার প্রয়োজন নেই।

মোট বিশ্রামের সময় = 4 × 5 মিনিট = 20 মিনিট।

∴ মোট সময় = হাঁটার সময় + বিশ্রামের সময়
= 90 মিনিট + 20 মিনিট
= 110 মিনিট
= 1 ঘন্টা 50 মিনিট

সুতরাং, লোকটি 15 কিমি দূরত্ব অতিক্রম করতে মোট 110 মিনিট বা 1 ঘন্টা 50 মিনিট সময় নেবে।

৭,৫৭৯.

The average weight of the women in a group is 55 kg and that of the men is 70 kg. If the average weight of the group is 65 kg, what is the ratio of women to men in the group?

ক
2 : 3
খ
1 : 3
গ
1 : 2
ঘ
2 : 5

ব্যাখ্যা

Question: The average weight of the women in a group is 55 kg and that of the men is 70 kg. If the average weight of the group is 65 kg, what is the ratio of women to men in the group?

Solution:
Average weight of women = 55 kg
Average weight of men = 70 kg
Average weight of the entire group = 65 kg

Let,
the number of men = M.
and, the number of women = W.
Then, the total number of people in the group is (M + W)

ATQ,
55W + 70M = 65(M + W)
Or, 55W + 70M = 65M + 65W
Or, 70M - 65M = 65W - 55W
Or, 5M = 10W
Or, W : M = 1 : 2

∴ The ratio of women to men in the group is 1 : 2.

৭,৫৮০.

512 small sphere balls are formed from a big ball with a radius of 16cm. What will be the radius of a small ball?

ক
1cm
খ
2cm
গ
3cm
ঘ
4cm

ব্যাখ্যা

Question: 512 small sphere balls are formed from a big ball with a radius of 16cm. What will be the radius of a small ball?

Solution:
converting a big sphere ball to 512 small balls,
the volume will be the same for both cases.
let,
small ball radius = r
given, big ball radius, R = 16cm

∴ (4/3)πR³ = 512 × (4/3)πr³
or, R³ = 512 × r³
or, R = 8 × r
or, r = 16/8
r = 2cm

৭,৫৮১.

The price of rice falls by 20%. How much rice can be bought now with the money that was sufficient to buy 20 kg of rice previously?

ক
15kg
খ
28kg
গ
25kg
ঘ
35kg

ব্যাখ্যা

Question: The price of rice falls by 20%. How much rice can be bought now with the money that was sufficient to buy 20 kg of rice previously?

Solution:
Let
Tk. 100 be spend on rice initially for 20 kg.
As the price falls by 20%, new price for 20 kg rice,
= (100 - 20% of 100)
= 100 - 20
= 80

New price of rice = 80/20 = 4

Rice can be bought now = 100/4 = 25kg

৭,৫৮২.

The H. C. F of 9/10, 12/25, 18/35 and 21/40 is-

ক
ক) 7/1400
খ
খ) 3/1400
গ
গ) 9/1400
ঘ
ঘ) 1/140

ব্যাখ্যা

The H. C. F of 9/10, 12/25, 18/35 and 21/40 is-

H. C. F of 9, 12, 18 and 21 = 3
L. C. M of 10, 25, 35 and 40 = 1400

The H. C. F of 9/10, 12/25, 18/35 and 21/40 is = 3/1400

৭,৫৮৩.

The sum of the three consecutive even numbers is 60 more than the average of these numbers. Which of the following is the largest of these numbers?

ক
28
খ
32
গ
44
ঘ
46

ব্যাখ্যা

Question: The sum of three consecutive even numbers is 60 more than the average of these numbers. Which of the following is the largest of these numbers?

Solution:
Let,
the numbers be x, x + 2 and x + 4.

Then,
(x + x + 2 + x + 4) - (x + x + 2 + x + 4)/3 = 60
⇒ (3x + 6) - (3x + 6)/3 = 60
⇒ {3(3x + 6) - (3x + 6)}/3 = 60
⇒ (9x + 18 - 3x - 6) = 180
⇒ (6x + 12) = 180
⇒ x = 168/6
∴ x = 28

∴ Largest number = x + 4
= 28 + 4 = 32.

৭,৫৮৪.

A sum of money at simple interest amounts to Tk. 815 in 3 years and to Tk. 854 in 4 years. The sum is-

ক
Tk. 600
খ
Tk. 628
গ
Tk. 650
ঘ
Tk. 698

ব্যাখ্যা

Question: A sum of money at simple interest amounts to Tk. 815 in 3 years and to Tk. 854 in 4 years. The sum is-

Solution:
Simple interest for 1 year = Tk. (854 - 815)
= Tk. 39

∴ Simple interest for 3 years = Tk.(39 × 3)
= Tk. 117

∴ Sum = (815 - 117)
= Tk. 698

৭,৫৮৫.

Which of the following is irrational?

ক
4/3
খ
√169
গ
0.40
ঘ
√15

ব্যাখ্যা

Question: Which of the following is irrational?

Solution:
√15 একটি অমূলদ সংখ্যা (irrational number)।
অমূলদ সংখ্যা (irrational number):
- যে সংখ্যাকে p/q আকারে প্রকাশ করা যায় না, যেখানে p ও q পূর্ণসংখ্যা এবং q ≠ 0, সে সংখ্যাকে অমূলদ সংখ্যা বলা হয়।
- পূর্ণবর্গ নয় এরূপ যে কোনো স্বাভাবিক সংখ্যার বর্গমূল কিংবা তার ভগ্নাংশ একটি অমূলদ সংখ্যা। যেমন, √2 = 1.414213..., √6 = 2.229489... ইত্যাদি অমূলদ সংখ্যা।
- কোনো অমূলদ সংখ্যাকে দুইটিপূর্ণ সংখ্যার অনুপাত হিসেবে প্রকাশ করা যায় না।
-অমূলদ সংখ্যাকে একটি মূলদ সংখ্যা দ্বারা গুণ করলে অমূলদ সংখ্যা পাওয়া যায়।
অর্থাৎ, non zero rational number × irrational number = irrational number.

৭,৫৮৬.

Two dice are thrown simultaneously. Find the probability of getting a multiple of 2 on one dice and multiple of 3 on the other dice.

ক
13/36
খ
5/36
গ
11/36
ঘ
5/12

ব্যাখ্যা

Question: Two dice are thrown simultaneously. Find the probability of getting a multiple of 2 on one dice and multiple of 3 on the other dice.

Solution:
Let x be required events and S be the sample space
Total outcomes when two dice are thrown,
6 × 6 = 36
n(S) = 36
And then x = {(2, 3), (2, 6), (4, 3), (4, 6), (6, 3), (6, 6), (3, 2), (6, 2), (3, 4), (6, 4), (3, 6)}
n(x) = 11

Hence, required probability
= n(x)/n(S) = 11/36

৭,৫৮৭.

What will come in place of "?"?

ক
20
খ
25
গ
7
ঘ
10
ঙ
17

ব্যাখ্যা

Question: What will come in place of "?"?

Solution:
The inner value is half of sum of squares of outer numbers.
First figure = 6² + 2² + 4² + 2² ⇒ 60/2 = 30
2nd figure= 3² + 4² + 3² + 2² ⇒ 38/2 = 19
3rd figure = 3² + 1² + 2² + 6² ⇒ 50/2 = 25

৭,৫৮৮.

The simple interest on Tk. 36000 for the period from 5th January to 31st May 2013 at 9.5% per annum is =?

ক
Tk. 1388.25
খ
Tk. 1368.00
গ
Tk. 1568.50
ঘ
Tk. 1377.36

ব্যাখ্যা

Question: The simple interest on Tk. 36000 for the period from 5^th January to 31^st May 2013 at 9.5% per annum is =?

Solution:
Number of days = 27 + 28 + 31 + 30 + 31
= 147 days

We know,
I = Pnr
Or, I = (36000 × 147 × 9.5)/(100 × 365)
∴ I = Tk. 1,377.36

৭,৫৮৯.

Find the number of triangles that can be formed by joining the angular points of a polygon of 10 sides as vertices.

ক
28
খ
56
গ
84
ঘ
120

ব্যাখ্যা

Question: Find the number of triangles that can be formed by joining the angular points of a polygon of 10 sides as vertices.

Solution:
A triangle needs 3 points.
A polygon of 10 sides has 10 angular points.

Hence, the number of triangles formed = ¹⁰C₃
= (10 × 9 × 8)/(3 × 2 × 1)
= 3 × 5 × 8
= 120

৭,৫৯০.

8% of the people eligible to vote are between 18 and 21 years of age. In an election, 85% of those eligible to vote, who were between 18 and 21, actually voted. In that election, the number of persons between 18 and 21, who actually voted, was what percent of those eligible to vote?

ক
7.2%
খ
6.8%
গ
5.9%
ঘ
7.6%
ঙ
8.2%

ব্যাখ্যা

Question: 8% of the people eligible to vote are between 18 and 21 years of age. In an election, 85% of those eligible to vote, who were between 18 and 21, actually voted. In that election, the number of persons between 18 and 21, who actually voted, was what percent of those eligible to vote?

Solution:
Let x be the number of persons eligible to vote,
Hence the nuber eligible persons between 18 and 21 = 8 of x.
Number of persons between 18 and 21, who voted = 85 of (8 of x)

Implies that,
(85/100) × (8/100) × x = 6x/1000
Hence the required percentage,
(68x/100) × (1/x) × 100% = 6.8%

৭,৫৯১.

The current of a stream runs at the rate of 2 km per hr. A motor boat goes 10 km upstream and back again to the starting point in 55 min. Find the speed of the motor boat -

ক
16 km/hr
খ
20 km/hr
গ
12 km/hr
ঘ
22 km/hr

ব্যাখ্যা

Let the speed of the boat in still water=x km/hr
Speed of the current = 2 km/hr

Then, speed downstream = (x + 2) km/hr
speed upstream = (x - 2) km/hr
Total time taken to travel 10 km upstream and back = 55 minutes
= (55/60) hr
= 11/12 hr.

According to question,
10/(x - 2) + 10/(x + 2) = 11/12
⇒ 120(x + 2)+120(x - 2) = 11(x² - 4)
⇒ 240x = 11x² - 44
⇒ 11x² - 240x - 44 = 0
⇒ 11x(x -22) + 2(x - 22) = 0
⇒ (x -22) (11x + 2) = 0
Since x cannot be negative.
So, x = 22 km/hr.

Hence, the Speed of the motorboat is 22 km/hr.

৭,৫৯২.

The slope of the line 4x - 8y = 16 is not the same as the slope of which one of the following lines?

ক
x - 2y = 8
খ
3x - 6y = 12
গ
y = 3x + 5
ঘ
y = x/2 + 4

ব্যাখ্যা

Question: The slope of the line 4x - 8y = 16 is not the same as the slope of which one of the following lines?

Solution:
প্রথমে, প্রদত্ত রেখাটির ঢাল নির্ণয় করতে হবে। রেখাটির সমীকরণকে y = mx + c আকারে রূপান্তর করতে হবে। এখানে 'm' হলো ঢাল (Slope)।

প্রদত্ত রেখার সমীকরণ:
4x - 8y = 16
⇒ - 8y = - 4x + 16
⇒ y = (- 4/- 8)x + (16/- 8)
⇒ y = (1/2)x - 2
∴ এই রেখাটির ঢাল (m) হলো 1/2.

এবার, প্রদত্ত অপশনগুলোর প্রত্যেকটির ঢাল নির্ণয় করি:

ক) x - 2y = 8
⇒ - 2y = - x + 8
⇒ y = (- x/- 2) + (8/- 2)
⇒ y = (1/2)x - 4
∴ ঢাল, m = 1/2

খ) 3x - 6y = 12
⇒ - 6y = - 3x + 12
⇒ y = (- 3/- 6)x + (12/- 6)
⇒ y = (1/2)x - 2
∴ ঢাল, m = 1/2

গ) y = 3x + 5
∴ ঢাল, m = 3

ঘ) y = x/2 + 4
⇒ y = (1/2)x + 4
∴ ঢাল, m = 1/2

সুতরাং, দেখা যাচ্ছে যে শুধুমাত্র অপশন (গ) এর রেখার ঢাল মূল রেখার ঢাল থেকে ভিন্ন।
∴ সঠিক উত্তর: গ) y = 3x + 5

৭,৫৯৩.

The average marks of four subjects is 120. If in one subject 33 was misread as 13 during the calculation, what would be the correct average?

ক
ক) 125
খ
খ) 130
গ
গ) 135
ঘ
ঘ) 140

ব্যাখ্যা

Question: The average marks of four subjects is 120. If in one subject 33 was misread as 13 during the calculation, what would be the correct average?

Solution:
The average given is 120.
Difference of 33 and 13 is 20.
That means 20 must be added to the total.
Then the average of is and so must be added to average, i.e.
Correct average = 120 + 5 = 125

৭,৫৯৪.

Three machines, individually, can do a certain job in 4, 5, and 6 hours, respectively. What is the greatest part of the job that can be done in one hour by two of the machines working together at their respective rates?

ক
11/30
খ
9/20
গ
3/5
ঘ
11/15
ঙ
5/6

ব্যাখ্যা

Question: Three machines, individually, can do a certain job in 4, 5, and 6 hours, respectively. What is the greatest part of the job that can be done in one hour by two of the machines working together at their respective rates?

Solution:
Machine A in one hour can perform 1/4 of job
Machine B in one hour can perform 1/5 of job
Machine C in one hour can perform 1/6 of job

Machine A and B Together, their rate is 1/4 + 1/5 = 9/20.

Machine A and C Together, their rate is 1/4 + 1/6 = 5/12.

Machine B and C Together, their rate is 1/5 + 1/6 = 11/30.

The question asks for the greatest part of the job that can be done in one hour by two of the machines working together at their respective rates. So we want to find the maximum of the rates we just calculated.

The maximum is 9/20, which is achieved when machines A and B work together.

৭,৫৯৫.

The present ages of John and Mary are In the ratio of 6 : 4. Five years ago their ages were in the ratio of 5 : 3. How old is John now?

ক
ক) 42
খ
খ) 36
গ
গ) 30
ঘ
ঘ) 24

ব্যাখ্যা

ATQ,
6x - 5 : 4x - 5 = 5 : 3
Or, 20x - 25 = 18x - 15
Or, 2x = 10
Or, x = 5
So, John's age now is = 6×5 = 30 years

৭,৫৯৬.

A and B together can complete a work in 3 days. They start together but after 2 days, B left the work. If the work is completed after two more days, B alone could do the work in

ক
ক) 6 days
খ
খ) 7 days
গ
গ) 9 days
ঘ
ঘ) 5 days

ব্যাখ্যা

(A+B)'s one day's work = 1/3 part
(A+B) works 2 days together = 2/3 part
Remaining work = 1−2/3 = 1/3 part
1/3 part of work is completed by A in two days
Hence, one day's work of A = 1/6
Then, one day's work of B = 1/3−1/6 = 1/6
So, B alone can complete the whole work in 6 days.

৭,৫৯৭.

If the 11th number in a series of 11 consecutive integers has the value k + 15, what is the 1st number in the series expressed in terms of k?

ক
k + 4
খ
k + 5
গ
k + 10
ঘ
k - 25
ঙ
k + 7

ব্যাখ্যা

Question: If the 11th number in a series of 11 consecutive integers has the value k + 15, what is the 1st number in the series expressed in terms of k?

Solution:
Let the 1st number in the series be x.
Since there are 11 consecutive integers, the series is: x, (x + 1), (x + 2), ..., (x + 10).

According to the question, the 11th number is k + 15.
So,
x + 10 = k + 15
⇒ x = k + 15 - 10
⇒ x = k + 5

∴ The 1st number in the series is k + 5.

৭,৫৯৮.

A thief committed a crime and escaped from the spot at a speed of 12 m/s. A Security guard started chasing him 20 minutes after the thief started running and caught him in the next 20 minutes. What is the speed (in m/s) of the Security guard?

ক
32 m/s
খ
24 m/s
গ
18 m/s
ঘ
36 m/s

ব্যাখ্যা

Question: A thief committed a crime and escaped from the spot at a speed of 12 m/s. A Security guard started chasing him 20 minutes after the thief started running and caught him in the next 20 minutes. What is the speed (in m/s) of the Security guard?

Solution:
Given that,
Thief's speed = 12 m/s
Security guard starts 20 minutes or 1200 s later and catches thief in next 20 minutes or 1200 s

Now,
Distance covered by thief before guard starts,
d₁ = speed × time = 12 × 1200 = 14400 m ; [20 minutes = 1200 s]
So, thief has a 14400 m head start.

And
Guard catches thief in 20 minutes = 1200 s
d₂ = 12 × 1200 s = 14400 m
∴ Guard covers total distance = head start + distance thief runs during chase = 14400 + 14400 = 28800 m
and Time taken by guard = 1200 s

∴ Speed of guard = Distance/Time = 28800/1200 = 24 m

৭,৫৯৯.

A rectangular hall is 12.5 meters long and 6.4 meters wide. The cost of installing wooden flooring is Tk. 120 per square meter. What is the total cost of flooring the hall?

ক
Tk. 8500
খ
Tk. 9600
গ
Tk. 10000
ঘ
Tk. 9200

ব্যাখ্যা

Question: A rectangular hall is 12.5 meters long and 6.4 meters wide. The cost of installing wooden flooring is Tk. 120 per square meter. What is the total cost of flooring the hall?

Solution:
Given that,
Length of the hall = 12.5 meters
Width of the hall = 6.4 meters
Cost of wooden flooring = Tk. 120 per square meter

We know,
Area = Length × Width
= 12.5 m × 6.4 m
= 80 m²

∴ Total cost = Area × Cost per square meter
= 80 × 120
= Tk. 9600

Therefore, the total cost of installing wooden flooring in the hall is Tk. 9600.

৭,৬০০.

Three taps A, B and C fill a tank in 20 min, 15 min and 12 min, respectively. If all the taps are opened simultaneously, how long will they take to fill 40% of the tank?

ক
ক) 25 seconds
খ
খ) 40 seconds
গ
গ) 1 minutes
ঘ
ঘ) 2 minutes

ব্যাখ্যা

Part of the tank filled in 1 min by A, B and C.
1/20 + 1/15 + 1/12
= (3 + 4 + 5)/60
= 12/60
= 1/5

Therefore, Time taken by A, B and C to fill the tank = 5 min.
Therefore, Time taken by A, B and C to fill 40% of the tank
= 40% of 5 = 40/100 × 5 = 2 minutes