Bank Math

PrepBank · পাতা ৭৮ / ১৬১ · ৭,৭০১–৭,৮০০ / ১৬,১২৪

৭,৭০১.

A group of men can do a job in 25 days. But 10 men did not turn up for the job and the remaining men did the job in 30 days. The original number of men in group was

ক
ক) 40
খ
খ) 60
গ
গ) 50
ঘ
ঘ) 70

ব্যাখ্যা

The group of men can do a job = 25 Days

Formula used:

W = E × T Where, W = Work, E = Efficiency, and T = Time

Calculation:
Let the initially the number of men be X

According to the question
⇒ 25 × X = 30 × (X - 10)
⇒ 25X = 30X - 300
⇒ 30X - 25X = 300

⇒ 5X = 300
⇒ X = 300/5

⇒ X= 60

The initially the number of men = 60

∴ The required result will be 60.

৭,৭০২.

The greatest of the 21 positive integers in a certain list is 16. The median of the 21 integers is 10. What is the least possible average (arithmetic mean) of the 21 integers ?

ক
ক) 4
খ
খ) 5
গ
গ) 8
ঘ
ঘ) 6

ব্যাখ্যা

Question: The greatest of the 21 positive integers in a certain list is 16. The median of the 21 integers is 10. What is the least possible average (arithmetic mean) of the 21 integers?

Solution:

তালিকায় 21টি সংখ্যা রয়েছে এবং সংখ্যাগুলিকে ঊর্ধ্বক্রম সাজালে মধ্যমাটি হবে 11 তম সংখ্যা।

ধরি,

প্রথম ১০টি সংখ্যার প্রতিটির মানে হলো = 1,

শেষ ১০টি সংখ্যার প্রতিটির মানে হলো = 10,

এবং শেষ সংখ্যা হলো = 16.

অতএব, গড় হলো = (10 x 1 + 10 x 10 + 16)/21 = 126/21 = 6.

৭,৭০৩.

The number of students in a school leaves a remainder of 4 when divided by 5, 8, and 20. Find the total number of students.

ক
40
খ
44
গ
36
ঘ
60

ব্যাখ্যা

Question: The number of students in a school leaves a remainder of 4 when divided by 5, 8, and 20. Find the total number of students.

Solution:
Given,
When the number of students is divided by 5, 8, and 20, the remainder is always 4.
So, the number of students is 4 more than the LCM of 5, 8, and 20.

Now,
Prime factors of 5 = 5 × 1
Prime factors of 8 = 2 × 2 × 2
Prime factors of 20 = 2 × 2 × 5

LCM of 5, 8, and 20 = 2 × 2 × 2 × 5 = 40

Total number of students = (40 + 4) = 44

৭,৭০৪.

A man can row 30 km upstream in 6 hours. If the speed of the man in still water is 6 km/hr, find how much he can row downstream in 10 hours.

ক
ক) 70 km
খ
খ) 140 km
গ
গ) 95 km
ঘ
ঘ) 50 km

ব্যাখ্যা

Question: A man can row 30 km upstream in 6 hours. If the speed of the man in still water is 6 km/hr, find how much he can row downstream in 10 hours.

Solution:
Speed of upstream = 30/6 = 5 km/hr.
Speed of man in still water = 6 km/hr.

∴ Speed of current = 6 - 5 = 1 km / hr.
So speed of downstream = 6 + 1 = 7 km / hr.

∴ Distance traveled in 10 hrs = 10 × 7 = 70 km.

৭,৭০৫.

The sum of the square of three numbers is 532 and the ratio of the first and the second as also of the second and the third is 3:2. Then the first number is-

ক
18
খ
6
গ
12
ঘ
2x+3
ঙ
None of above

ব্যাখ্যা

The first number : The second Number = 3:2 = 3 × 3:2 × 3 = 9:6
The second Number : 3rd Number = 3:2 =3 × 2:2 × 2 = 6:4
1st:2nd:3rd = 9:6:4
Let,
The 1st, 2nd & 3rd are consecutively = 9x, 6x, 4x
Therefore,
(9x)² + (6x)² + (4x)² = 532
So, X = 2 and 1st number is 9 × 2 = 18

৭,৭০৬.

A train covered first 160 km at a speed of 20 km/h and then covered the remaining 240 km at a speed of 30 km/h. Find its average speed.

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

ব্যাখ্যা

Question: A train covered first 160 km at a speed of 20 km/h and then covered the remaining 240 km at a speed of 30 km/h. Find its average speed.

Solution:
Total distance = 160 + 240 = 400 km.

Time taken for the first 160 km = 160/20 = 8 hrs.
Time taken for the next 240 km = 240/30 = 8 hrs.
Total time taken = 8 + 8 = 16 hrs.

Average Speed =Total distance travelled/Total time taken
= 400/16
= 25 km/h

৭,৭০৭.

If a^x = b^y, then:

ক
log (a/b) = x/y
খ
(log a)/ (log b) = x/y
গ
(log a)/ (log b) = y/x
ঘ
None of these

ব্যাখ্যা

Question: If a^x = b^y, then:

Solution:
a^x= b^y
⇒ log a^x = log b^y
⇒ x log a = y log b
⇒ (log a)/ (log b) = y/x

৭,৭০৮.

The average of a family of 6 members is 25 years. After a 45 year old member leaves the family, what is the average age (in years) of the family?

ক
ক) 22
খ
খ) 21
গ
গ) 20
ঘ
ঘ) 19

ব্যাখ্যা

6 জন সদস্যের বয়সের গড় 25 বছর
6 জন সদস্যের বয়সের সমষ্টি = (25 × 6) বছর
= 150 বছর

5 জন সদস্যের বয়সের সমষ্টি = (150 - 45) বছর
= 105 বছর

5 জন সদস্যের বয়সের গড় = 105/5 বছর
= 21 বছর

৭,৭০৯.

The value of a machine depreciates at the rate of 10% every year. It was purchased 3 years ago. It its present value is tk. 8748 its purchases price was-

ক
ক) Tk. 12500
খ
খ) Tk. 10000
গ
গ) Tk. 12000
ঘ
ঘ) Tk. 14000

ব্যাখ্যা

Question: The value of a machine depreciates at the rate of 10% every year. It was purchased 3 years ago. It its present value is tk. 8748 its purchases price was-

Solution:
Let, purchased price = x

We know,
C = (1 - r)ⁿ
∴ Depreciated price = x(1 - 10%)³= x{(1 - 10/100)}³= x{1 - (1/10)}³ATQ,
x{1 - (1/10)}³ = 8748
⇒ x(9/10)³ = 8748
⇒ x = (8748 × 10 × 10 × 10)/(9 × 9 × 9)
∴ x = 12000

∴ Purchased price = Tk. 12000

৭,৭১০.

A man travelled a distance of 61km in 9 hours. He travelled partly on foot at 4 km/hr and partly on bicycle at 9 km/hr. What is the distance travelled on foot?

ক
18 km
খ
14 km
গ
12 km
ঘ
16 km
ঙ
20 km

ব্যাখ্যা

Let the time in which he travelled on foot = x hr
Then the time in which he travelled on bicycle = (9 − x ) hr
distance = speed × time
⇒ 4 x + 9 (9 − x) = 61
⇒ 4 x + 81 − 9 x = 61
⇒ 5 x = 20
⇒ x = 4
Distance travelled on foot = 4x
= 4 × 4
= 16 km

৭,৭১১.

In a 500 m race, A gives B a start of 50 m and still beats him by 25 m. What is the ratio of their speeds A : B ?

ক
21 : 20
খ
20 : 17
গ
18 : 16
ঘ
22 : 19
ঙ
None of the above

ব্যাখ্যা

Question: In a 500 m race, A gives B a start of 50 m and still beats him by 25 m. What is the ratio of their speeds A : B ?

Solution:
একটি ৫০০ মিটার রেসে B , A এর ৫০ মিটার আগে থেকে দৌড় শুরু করে।
তাহলে A কে দৌড়াত হবে ৫০০ মিটার কিন্তু B কে দৌড়াতে হবে ৪৫০ মিটার

আবার
রেসে A, B কে ২৫ মিটার দূরত্বে হারায়।
এখানে A যখন B কে অতিক্রম করে জিতে যায় তখন B অতিক্রম করে = ৪৫০ - ২৫ = ৪২৫ মিটার
এখন যেহেতু সময় একই তাই তাদের গতির অনুপাত হবে = A : B
= ৫০০ : ৪২৫
= ২০ : ১৭

৭,৭১২.

If the numerator of a fraction is increased by 200% and the denominator is increased by 300%, the resultant fraction is 15/26. What was the original fraction?

ক
10/13
খ
10/11
গ
8/11
ঘ
9/13

ব্যাখ্যা

Question: If the numerator of a fraction is increased by 200% and the denominator is increased by 300%, the resultant fraction is 15/26. What was the original fraction?

Solution:
Let the fraction be x/y

Then,
(x + 200% of x)/(y + 300% of y) = 15/26
⇒ (x + 2x)/(y + 3y) = 15/26
⇒ 3x/4y = 15/26
⇒ x/y = (15/26) × (4/3)
∴ x/y=10/13

৭,৭১৩.

P and Q together can do a job in 10 days. Q and R together can do it in 12 days. P and R together can do it in 15 days. If all of them work together, in how many days can they finish the work?

ক
3 days
খ
5 days
গ
9 days
ঘ
6 days
ঙ
None of these

ব্যাখ্যা

Question: P and Q together can do a job in 10 days. Q and R together can do it in 12 days. P and R together can do it in 15 days. If all of them work together, in how many days can they finish the work?

Solution:
(P + Q) 1 দিনে করে কাজটির 1/10 অংশ
(Q + R ) 1 দিনে করে কাজটির 1/12 অংশ
(P + R) 1 দিনে করে কাজটির 1/15 অংশ

∴ (P + Q + Q + R + P + R) 1 দিনে করে কাজটির = (1/10) + (1/12) + (1/15) অংশ
(2P + 2Q + 2R) 1 দিনে করে কাজটির = (6 + 5 + 4)/60 অংশ
2(P + Q + R) 1 দিনে করে কাজটির = 1/4 অংশ
(P + Q + R) 1 দিনে করে কাজটির = 1/8 অংশ

(P + Q + R) 1/8 অংশ কাজ করে 1 দিনে
∴ (A + B + C) 1 বা সম্পূর্ণ অংশ কাজ করে = (8 × 1)/1 = 8 দিনে

৭,৭১৪.

A train started with 540 passengers. At the first stop 1/9 of them got down and 24 got up. On its second stop 1/8 of the existing passengers got down and 9 got up. With how many passengers did it reach the third stop?

ক
ক) 420
খ
খ) 450
গ
গ) 480
ঘ
ঘ) 500

ব্যাখ্যা

Question: A train started with 540 passengers. At the first stop 1/9 of them got down and 24 got up. On its second stop 1/8 of the existing passengers got down and 9 got up. With how many passengers did it reach the third stop?

Solution:
Number of passengers after first stop = {540 - (1/9 of 540) + 24} = 504
Number of passengers after second stop = {504 - (1/8 of 504) + 9} = 450

৭,৭১৫.

The least prime number is

ক
ক) 0
খ
খ) 1
গ
গ) 3
ঘ
ঘ) 2

ব্যাখ্যা

১ এর চেয়ে বড় যে সকল সংখ্যাকে শুধু ১ এবং ঐ সংখ্যা ছাড়া আর কোনো সংখ্যা দ্বারা ভাগ করা যায় না, তাদেরকে মৌলিক সংখ্যা বলে।
অর্থাৎ মৌলিক সংখ্যার উৎপাদক হবে দুইটি: ১ এবং শুধুমাত্র সেই সংখ্যাটি।
যেমন : ২, ৩, ৫, ৭, ১১, ১৩... ইত্যাদি মৌলিক সংখ্যা।

অর্থাৎ সবচেয়ে ক্ষুদ্র মৌলিক সংখ্যা ২.

৭,৭১৬.

Two pipes X and Y together can fill a tank in 72 minutes. If the size of the pipe X is thrice as Y then Y alone can fill the tank in -

ক
ক) 4 hours and 48 minutes
খ
খ) 3 hours and 48 minutes
গ
গ) 4 hours and 36 minutes
ঘ
ঘ) 3 hours and 15 minutes

ব্যাখ্যা

Let,
The time taken by Y alone to fill the tank be A minutes.
Given that, the size of the pipe X is thrice as Y.
Then, X fills the tank in A/3 minutes.
Part filled by X in 1 minute = 1/(A/3)
= 3/A
Part filled by Y in 1 minute = 1/A
Since, X and Y together take 72 minutes.
Part filled by (X + Y) in 1 minute = 1/72
i.e.,
(1/A + 3/A) = 1/72
⇒ 4/A = 1/72
A = 288 minutes
= (288/60) hours
= 4(48/60)
= 4(4/5) hours
= 4 hours and (4/5 x 60) minutes
= 4 hours and 48 minutes.
Hence, the pipe Y alone takes 4 hours and 48 minutes to fill the tank.

৭,৭১৭.

Iqbal sold an article at 6% loss. Had he sold it for Tk. 64 more, he would have made a profit of 10%. Then the cost of the article is =?

ক
Tk. 400
খ
Tk. 420
গ
Tk. 450
ঘ
Tk. 475

ব্যাখ্যা

Question: Iqbal sold an article at 6% loss. Had he sold it for Tk. 64 more, he would have made a profit of 10%. Then the cost of the article is =?

Solution:
Let, the cost of the article is x taka

Selling price = 0.94x

ATQ,
0.94x + 64 = 1.1x
⇒ 1.1x - 0.94x = 64
⇒ 0.16x = 64
⇒ x = 64/0.16
∴ x = 400 taka

৭,৭১৮.

By selling 90 ball pens for Tk. 160 a person loses 20%. How many ball pens should be sold for Tk. 96 so as to have a profit of 20%?

ক
30
খ
36
গ
42
ঘ
44

ব্যাখ্যা

Question: By selling 90 ball pens for Tk. 160 a person loses 20%. How many ball pens should be sold for Tk. 96 so as to have a profit of 20%?

Solution:

S.P. of 90 ball pens = Tk. 160

Loss % = 20%

∴ C.P. of 90 ball pens = [100/(100 - Loss%)] × Selling Price = [100/(100 - 20)] × 160

= (100 × 160)/80 = 200

C.P. of 1 ball pen = 20/9

Now we find how many pens should be sold for 96 to have a profit of 20%

Let us say, ‘x’ number of pens be sold for 96

Then, S.P. of x pens = 96

C.P of x pens = (20/9)x

Profit = S.P - C.P. = 96 - 20x/9
Profit% = (Profit/ C.P.) × 100
{96 - (20x/9)}/(20x/9) × 100 = 20
⇒ {96 - (20x/9)} × 5 = 20x/9
⇒ 96 - (20x/9) = 4x/9
⇒ 96 × 9 - 20x = 4x
⇒ 24x = 96 × 9

⇒ x = (96 × 9)/24 = 36

Therefore, 36 pens should be sold

৭,৭১৯.

With a uniform speed, a car covers a distance in 8 hours. Had the speed been increased by 4 km/hr, the same distance could have been covered in 7 hr and 30 min. What is the distance covered?

ক
ক) 480 km.
খ
খ) 520 km.
গ
গ) 620 km.
ঘ
ঘ) 420 km.

ব্যাখ্যা

Question: With a uniform speed, a car covers a distance in 8 hours. Had the speed been increased by 4 km/hr, the same distance could have been covered in 7 hr and 30 min. What is the distance covered?

Solution:
Let the speed of car be x km/hr
Distance = Speed × Time
Distance = 8x km

According to the question,
(x + 4) × 7.5 = 8x
⇒ 7.5x + 30 = 8x
⇒ 8x - 7.5x = 30
⇒ 0.5x = 30
⇒ x = 30/0.5
∴ x = 60 km/hr

Required distance = 8 × 60
= 480 km.

৭,৭২০.

The time taken by a man to travel 36 miles downstream is 90 min less than to go the same distance upstream. The speed of the man in still water is 10 mph. Find the speed of the stream?

ক
ক) 2 mph
খ
খ) 2.5 mph
গ
গ) 3.5 mph
ঘ
ঘ) 5 mph

ব্যাখ্যা

ধরি,
স্রোতের বেগ x mph

স্রোতের অনুকূলে লোকটির বেগ =(10 + x) mph
স্রোতের প্রতিকূলে লোকটির বেগ = (10 - x) mph

প্রশ্নমতে,
36/(10 - x) - 36 /(10 + x) = 90/60
⇒ (360 + 36x - 360 + 36x)/ (10 - x) (10 + x) = 90/60
⇒ 72x/ (100 -x²) = 3/2
⇒ 24x/(100 - x² )= 1/2
⇒ 48x = 100 - x²
⇒ x² + 48x -100 = 0
⇒ x²+50x - 2x - 100=0
⇒ x(x +50) - 2(x +50)=0
∴ (x +50) (x - 2) = 0
এখানে,
x - 2 = 0 x +50 = 0
x =2 x ≠ - 50

স্রোতের বেগ 2 mph

৭,৭২১.

The speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hr. The distance traveled downstream in 12 minutes is

ক
ক) 1.2 km
খ
খ) 3.6 km
গ
গ) 1.8 km
ঘ
ঘ) 2.4 km

ব্যাখ্যা

এখানে, 12 মিনিট = 12/60 = 1/5 ঘন্টা
স্রোতের অনুকূলে নৌকার বেগ = 15 + 3 = 18 kmph
অর্থাৎ নৌকাটি 1 ঘন্টা বা 60 মিনিটে যায় = 18 km
নৌকাটি 12 মিনিটে যায় = (18 × 12)/60
= 3.6 km

৭,৭২২.

For the function f(x) = x² - 4x + 3 find x when f(x) = 8

ক
- 1, 5
খ
- 2, 3
গ
- 1, - 4
ঘ
2, 5

ব্যাখ্যা

Question: For the function f(x) = x² - 4x + 3 find x when f(x) = 8

Solution:
f(x) = x² - 4x + 3
f(x) = 8

Now,
⇒ x² - 4x + 3 = 8
⇒ x² - 4x + 3 - 8 = 0
⇒ x² - 4x - 5 = 0
⇒ x² - 5x + x - 5 = 0
⇒ x(x - 5) + 1(x - 5) = 0
⇒ (x - 5)(x + 1) = 0
Now,
x - 5 = 0
∴ x = 5
Or,
⇒ x + 1 = 0
∴ x = - 1

∴ x = - 1, 5

৭,৭২৩.

If x = 3t, y = 1/2 × (t + 1), then the value of t for which x = 2y is?

ক
1/3
খ
1/2
গ
1/4
ঘ
1/5

ব্যাখ্যা

Question: If x = 3t, y = 1/2 × (t + 1), then the value of t for which x = 2y is?

Solution:
Here given,
x = 3t -------(1)
and, y = 1/2 × (t + 1) ----(2)

Now, when:
x = 2y
⇒ x = 2 × 1/2 × (t + 1) [from equation 2]
⇒ x = t + 1 -------(3)
∴ 3t = t + 1 [From equation (1)]
⇒ 2t = 1
⇒ t = 1/2

৭,৭২৪.

If 2 (P's capital) = 5 (Q's capital) = 6 (R's capital), then out of the total profit of TK 6500, Q will receive-

ক
TK 1520
খ
TK 1500
গ
TK 1800
ঘ
TK 2000

ব্যাখ্যা

Question: If 2 (P's capital) = 5 (Q's capital) = 6 (R's capital), then out of the total profit of TK 6500, Q will receive-

solution:
Let,
P's capital = p
Q's capital = q
R's capital = r

Then,
2p = 5q = 6r

⇒ q = 2p/5

⇒ r = 2p/6 = p/3

P : Q : R = p : 2p/5 : p/3
= 15p : 6p : 5p [multiply by 15]
= 15 : 6 : 5

∴ sum of ratio = (15 + 6 + 5) = 26

so, Q's share = 6500 × 6/26 = 250 × 6 = 1500 TK

৭,৭২৫.

If Z = 52 and BAT = 46, then BALL will be equal to-

ক
50
খ
52
গ
54
ঘ
56

ব্যাখ্যা

Question: If Z = 52 and BAT = 46, then BALL will be equal to-

Solution:

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

Similarly,
BALL = (2 × 2) + (1 × 2) + (12 × 2) + (12 × 2)
= 4 + 2 + 24 + 24
= 54

৭,৭২৬.

A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother, what is the present age of the person?

ক
40 years
খ
25 years
গ
16 years
ঘ
8 years

ব্যাখ্যা

Question: A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother, what is the present age of the person?

Solution:
Let,
The present age of the person’s mother be x years
∴ Age of the person is = (2x)/5 years

After 8 years,
Age of the person’s mother will be = x + 8 years
Age of the person will be = (2x)/5 + 8 years

ATQ,
(2x)/5 + 8 = (x + 8)/2
⇒ (2x)/5 + 8 = (x/2) + 4
⇒ (x/2) - (2x)/5 = 8 - 4
⇒ (5x - 4x)/10 = 4
⇒ x/10 = 4
∴ x = 40

So, the present age of the person is (2 × 40)/5 = 80/5 = 16 years

৭,৭২৭.

A man starts from a point and travels 12 km in the north direction. Again he went east for 6 km and changed direction and again went north for 8 km. Finally went west for 6 km. What is the direct distance between his destination and journey?

ক
18 km
খ
20 km
গ
24 km
ঘ
32 km

ব্যাখ্যা

Question: A man starts from a point and travels 12 km in the north direction. Again he went east for 6 km and changed direction and again went north for 8 km. Finally went west for 6 km. What is the direct distance between his destination and journey?

Solution:

ঐ ব্যক্তির যাত্রাস্থান A এবং গন্তব্য স্থান E
∴ তার গন্তব্য স্থান ও যাত্রা স্থানের সরাসরি দূরত্ব, AE = (12 + 8) কি.মি.
= 20 কি.মি.

৭,৭২৮.

The population of a village grew from 18,000 to 22,500 over a decade. What is the average annual percentage increase in population?

ক
2%
খ
2.5%
গ
1.57%
ঘ
None of the above

ব্যাখ্যা

Question: The population of a village grew from 18,000 to 22,500 over a decade. What is the average annual percentage increase in population?

Solution:
The population rose in 10 years = (22500 - 18000) = 4500

Increase% of ten year = (4500/18000) × 100% = 25%

∴ Required average = (25/10)% = 2.5%

৭,৭২৯.

If A + B = 2C and C + D = 2A, then-

ক
ক) A + C = 2D
খ
খ) A + D = C + B
গ
গ) A + C = 2B
ঘ
ঘ) B + D = C + A

ব্যাখ্যা

Question: If A + B = 2C and C + D = 2A, then-

Solution:
Let
A + B = 2C.............(1)
C + D = 2A.............(2)

(1) + (2)⇒
A + B + C + D = 2C + 2A
A + B + C + D - A - C = 2C + 2A - A - C
B + D = C + A

৭,৭৩০.

The population of a town is decreasing at a rate of 10% per annum. If the population two years ago was 20000, what is the present population?

ক
15000
খ
15200
গ
16000
ঘ
16200

ব্যাখ্যা

Question: The population of a town is decreasing at a rate of 10% per annum. If the population two years ago was 20000, what is the present population?

Solution:
The present population = 20000(1 - 10/100)²
= 20000 × 0.9 × 0.9
= 16200

৭,৭৩১.

Rajeev buys goods worth Tk. 6650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax at 10%. Find the amount he will have to pay for the goods.

ক
ক) Tk. 6786.1
খ
খ) Tk. 6876.1
গ
গ) Tk. 8676.1
ঘ
ঘ) Tk. 7668.1

ব্যাখ্যা

Question: Rajeev buys goods worth Tk. 6650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax at 10%. Find the amount he will have to pay for the goods.

Solution:
Rebate = 6% of Tk.6650
= (6 × 6650)/100
= 399 Tk.
Tax = 10% of (6650 - 399)
= 10% of 6251
= (10 × 6251)/100
= 625.10
Total amount will have to pay =Tk. (6251 + 625.10)
= Tk. 6876.1

৭,৭৩২.

(3.25 × 3.20 - 3.20 × 3.05)/0.064 is equal to-

ক
ক) 1
খ
খ) 1/10
গ
গ) 10
ঘ
ঘ) 100

ব্যাখ্যা

(3.25 × 3.20 - 3.20 × 3.05)/0.064
= {3.20(3.25 - 3.05)}/0.064
= (3.20 × 0.2)/0.064
=0.64/0.064
=10

৭,৭৩৩.

The average of runs of a cricket player of 10 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4?

ক
2
খ
4
গ
70
ঘ
76

ব্যাখ্যা

Question: The average of runs of a cricket player of 10 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4?

Solution:
Total runs =32 × 10 = 320
Now increase in average is 4 runs
so,
New average = 32 + 4 = 36 runs
Total runs = 36 × 11 = 396
Runs made in the 11th inning = 396 - 320 = 76

৭,৭৩৪.

The speed of a boat is 15km/h and the rate of current is 3km/h. How much distance downstream can be travelled in 15 minutes?

ক
ক) 2.5km
খ
খ) 3km
গ
গ) 4km
ঘ
ঘ) 4.5km

ব্যাখ্যা

Question: The speed of a boat is 15km/h and the rate of current is 3km/h. How much distance downstream can be travelled in 15 minutes?

Solution:
here,
the speed of the boat is = 15km/h
rate of current is = 3km/h

in downstream total speed, S = 15 + 3 = 18km/h
time, T = 15 minutes = 15/60 = 1/4 hours

the distance, D = S × T
= 18 × 1/4
= 4.5 km

৭,৭৩৫.

A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is-

ক
1/55
খ
1/22
গ
2/73
ঘ
2/91

ব্যাখ্যা

Question: A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is-

Solution:
Let, S be the sample space

Then,
n(S) = number of ways of drawing 3 balls out of 15
= ¹⁵C₃
= (15 × 14 × 13)/(3 × 2 × 1)
= 455

Let, E = event of getting all the 3 red balls
∴ n(E) = ⁵C₃
= ⁵C₂
= (5 × 4)/(2 × 1)
= 10

∴ P(E) = n(E)/n(S)
= 10/455
= 2/91

৭,৭৩৬.

A man covers a total distance of 100 km on bicycle. For the first 2 hours, the speed was 20 km/hr and for the rest of the journey, it came down to 10 km/hr. The average speed will be -

ক
ক) 12.5 km/hr
খ
খ) 13 km/hr
গ
গ) 14.5 Km/hr
ঘ
ঘ) 20 Km/hr

ব্যাখ্যা

Distance covered by man in first 2 hrs = 2 × 20 = 40 km
Remaining distance = (100 - 40) = 60 km
Time to cover the remaining distance = (60 /10) kmh = 6 hrs
∴ Required average speed = 100 / (2 + 6) = 12.5 kmh

৭,৭৩৭.

For the inequality |x - 1| < 5, where x ∈ N. What is the solution set?

ক
{Ø}
খ
{4, 5, 6}
গ
{1, 2, 3, 4, 5}
ঘ
{- 4, - 3, ... ..., 5, 6}

ব্যাখ্যা

Question: For the inequality |x - 1| < 5, where x ∈ N. What is the solution set?

Solution:
দেওয়া আছে,
|x - 1| < 5 এবং x ∈ N
⇒ - 5 < x - 1 < 5
⇒ - 5 + 1 < x - 1 + 1 < 5 + 1
∴ - 4 < x < 6

এখন,
x ∈ N এর অর্থ হলো x স্বাভাবিক সংখ্যা।
সুতরাং, - 4 < x < 6 সীমার মধ্যে স্বাভাবিক সংখ্যা গুলো হলো 1, 2, 3, 4, 5

সুতরাং, সমাধান সেট = {1, 2, 3, 4, 5}

৭,৭৩৮.

Jony got married 8 years ago. Today his age is 9/7 times his age at the time of his marriage. At present his daughter's age is one-sixth of his age. What was his daughter's age 3 years ago?

ক
3 years
খ
4 years
গ
6 years
ঘ
9 years

ব্যাখ্যা

Question: Jony got married 8 years ago. Today his age is 9/7 times his age at the time of his marriage. At present his daughter's age is one-sixth of his age. What was his daughter's age 3 years ago?

Solution:
Let, Jony's age 8 years ago be x years.
Then, his present age (x + 8) years.

ATQ,
x + 8 = 9x/7
⇒ 9x = 7x + 56
⇒ 9x - 7x = 56
⇒ 2x = 56
∴ x = 28

Jony's age now = x + 8 = 28 + 8 = 36 years.
His daughter's age now = 36/6 = 6 years.
His daughter's age 3 years ago = (6 - 3) = 3 years.

৭,৭৩৯.

A number when divided by 315 leaves a remainder of 47. If the same number is divided by 21, what will be the remainder?

ক
5
খ
7
গ
16
ঘ
26
ঙ
30

ব্যাখ্যা

Question: A number when divided by 315 leaves a remainder of 47. If the same number is divided by 21, what will be the remainder?

Solution:
Let the number be x, and the quotient is q.

Then,
x = 315q + 47
= (21 × 15q) + (21 × 2) + 5
= 21(15q + 2) + 5

So, the given number when divided by 21 gives 5 as a remainder.

৭,৭৪০.

In recent survey of the students of a public university, it is found that 65% students are good in Mathematics and 45% students are good in Statistics. How many students are good in both Mathematics and Statistics of the public university?

ক
20%
খ
5%
গ
15%
ঘ
10%

ব্যাখ্যা

Question: In recent survey of the students of a public university, it is found that 65% students are good in Mathematics and 45% students are good in Statistics. How many students are good in both Mathematics and Statistics of the public university?

Solution:
Good at Mathematics n(M) = 65
Good at Statistics n(S) = 45
good in both Mathematics and Statistics n(M ∩ S)

We know that
n(M ∪ S) = n(M) + n(S) - n(M ∩ S)
⇒ n(M ∩ S) = n(M) + n(S) - n(M ∪ S) = 65 + 45 - 100 = 110 - 100 = 10

৭,৭৪১.

৩০ × ১৬ ফুটের একটি মেঝে মেরামত করতে ২৪৯৬ টাকা ব্যয় হল। প্রতি বর্গফুটে ব্যয় কত টাকা?

ক
ক) ৪.২০ টাকা
খ
খ) ৬.২০ টাকা
গ
গ) ৫.২০ টাকা
ঘ
ঘ) ৫.৫০ টাকা

ব্যাখ্যা

প্রশ্ন: ৩০ × ১৬ ফুটের একটি মেঝে মেরামত করতে ২৪৯৬ টাকা ব্যয় হল। প্রতি বর্গফুটে ব্যয় কত টাকা?

সমাধান:
মেঝের ক্ষেত্রফল = ৩০ × ১৬ বর্গফুট
= ৪৮০ বর্গফুট

প্রতি বর্গফুটে ব্যয় (২৪৯৬/৪৮০) টাকা
= ৫.২০ টাকা

৭,৭৪২.

A woman says, ''If you reverse my own age, the figures represent my husband's age. He is, of course, senior to me and the difference between our ages is one-eleventh of their sum.'' The woman's age is

ক
ক) 23 years
খ
খ) 34 years
গ
গ) 45 years
ঘ
ঘ) 54 years

ব্যাখ্যা

Let x and y be the ten's and unit's digits respectively of the numeral denoting the woman's age.

Then, woman's age = (10X + y) years;
husband's age = (10y + x) years.
Therefore (10y + x) - (10X + y) = (1/11) (10y + x + 10x + y)
⇒ (9y - 9x) = (1/11)(11y + 11x) = (x + y)
⇒ 10x = 8y
⇒ x = (4/5)y

Clearly, y should be a single-digit multiple of 5, which is 5.
So, x = 4, y = 5.
Hence, woman's age = 10x + y = 45 years.

৭,৭৪৩.

Which of the following numbers can be removed from the set S = {0, 2, 4, 5, 9} without changing the average of set S?

ক
4
খ
5
গ
0
ঘ
9

ব্যাখ্যা

Question: Which of the following numbers can be removed from the set S = {0, 2, 4, 5, 9} without changing the average of set S?

Solution:
The average of the elements in the original set S is (0 + 2 + 4 + 5 + 9)/5
= 20/5
= 4

If we remove an element that equals the average, then the average of the new set will remain unchanged.
The new set after removing 4 is {0, 2, 5, 9}.

∴ The average of the elements is (0 + 2 + 5 + 9)/4
= 16/4
= 4

৭,৭৪৪.

The present age of a father is five times that of his son. Eight years from now, the son's age will equal one-third of the father's age at that time. How old will the father be in 2 years?

ক
40 years
খ
42 years
গ
50 years
ঘ
48 years

ব্যাখ্যা

Question: The present age of a father is five times that of his son. Eight years from now, the son's age will equal one-third of the father's age at that time. How old will the father be in 2 years?

Solution:
ধরি,
পুত্রের বর্তমান বয়স = x বছর
পিতার বর্তমান বয়স = 5x বছর

8 বছর পর,
পুত্রের বয়স হবে = (x + 8) বছর
পিতার বয়স হবে = (5x + 8) বছর

প্রশ্নমতে,
(x + 8) = (1/3) × (5x + 8)
3(x + 8) = 5x + 8
3x + 24 = 5x + 8
5x - 3x = 24 - 8
2x = 16
x = 16/2
x = 8

∴ পুত্রের বর্তমান বয়স = 8 বছর
এবং পিতার বর্তমান বয়স = (5 × 8) বছর = 40 বছর

∴ 2 বছর পর পিতার বয়স হবে = (40 + 2) বছর = 42 বছর

৭,৭৪৫.

There are a total of 40 dishes of rice and meat. If the ratio of the number of rice dishes to the number of meat dishes is 3 to 2, how many meat dishes are there?

ক
ক) 16
খ
খ) 24
গ
গ) 8
ঘ
ঘ) 32

ব্যাখ্যা

Let,
Rice dishes 3x, meat dishes 2x
ATQ,
3x + 2x = 40
Or, 5x = 40
Or, x = 8
∴ Meat dishes = 2x = 2 × 8 = 16

৭,৭৪৬.

A man sells two horses for tk 4000 each, neither losing nor gaining in the deal. If he sold 1 horse at a gain of 25%, the other horse is sold at a loss of:

ক
ক) 16.67
খ
খ) 18.33
গ
গ) 25%
ঘ
ঘ) 20%
ঙ
ঙ) 12.5%

ব্যাখ্যা

ধরি প্রথম ঘোড়ার ক্রয়মূল্য = x টাকা
তাহলে, x + x এর 25/100 = 4000
বা, x = 3200 টাকা

তাহলে প্রথম ঘোড়ার ক্ষেত্রে মোট লাভ করেছে ৮০০ টাকা তাহলে দ্বিতীয় ঘোড়াতে ক্ষতি হয়েছে = ৮০০ টাকা

তাহলে দ্বিতীয় ঘোড়ার ক্রয়মূল্য = ৪০০০ + ৮০০ = ৪৮০০ টাকা।

তাহলে ক্ষতির শতকরা হার = (৮০০ × ১০০) / ৪৮০০ = ১৬.৬৭%

৭,৭৪৭.

The ratio of the ages of father and son now is 6 : 1. After 5 years the ratio will become 7 : 2. What is the sum of their ages now?

ক
ক) 35 years
খ
খ) 30 years
গ
গ) 40 years
ঘ
ঘ) 45 years

ব্যাখ্যা

Question: The ratio of the ages of father and son now is 6 : 1. After 5 years the ratio will become 7 : 2. What is the sum of their ages now?

Solution:
Let, the ages of the father = 6x
and the ages of the son = x

ATQ,
(6x + 5) / (x +5) = 7/2
⇒ 12x + 10 = 7x + 35
⇒ 5x = 25
⇒ x = 5

So, the ages of the son = 5 years
and the ages of the father = 6 × 5 = 30 years

∴ the sum of their ages now = 30 + 5 = 35 years

৭,৭৪৮.

A circular garden with diameter of 20 meters is surrounded by a walkway of width 1 meter. What is the area of the walkway?

ক
ক) 41π m
খ
খ) 41π m
গ
গ) 21πm²
ঘ
ঘ) 21m²

ব্যাখ্যা

ব্যাসার্ধ r = 20/2 = 10 m
∴ বৃত্তের ক্ষেত্রফল = πr² = π(10)² = 100π বর্গমিটার
রাস্তাসহ বৃত্তের ক্ষেত্রফল = π(10+1)² = 121π বর্গমিটার
∴ রাস্তার ক্ষেত্রফল = (121π - 100π) = 21π বর্গমিটার

৭,৭৪৯.

At a stationary shop, it costs Tk. 185 for 4 gel-pens, 8ball-point pens and 1 marker pen and Tk. 315 for 7 gel-pens, 15 ball-point pens and 1 marker pen. What would be the cost of 1 gel-pen, 1 ball-point pen and 1 marker pen?

ক
ক) Tk. 45
খ
খ) Tk. 60
গ
গ) Tk. 55
ঘ
ঘ) Tk. 70

ব্যাখ্যা

প্রশ্ন : At a stationary shop, it costs Tk. 185 for 4 gel-pens, 8ball-point pens and 1 marker pen and Tk. 315 for 7 gel-pens, 15 ball-point pens and 1 marker pen. What would be the cost of 1 gel-pen, 1 ball-point pen and 1 marker pen?

সমাধান :

মনে করি, ১টি জেল কলম, ১টি বল পয়েন্ট কলম ও ১টি মার্কার কলমের মূল্য যথাক্রমে x, y, z.

প্রশ্নমতে,

7x + 15y + z = 315 ----- (1)

4x + 8y +z = 185 ---- (2)

--------------------

3x + 7y = 130 ------ (3)

2 দ্বারা গুণ করে পাই,

6x + 14y = 260 ----- (4)

সমীকরণ (1) থেকে (4) বিয়োগ করে পাই,

x + y + z = 55

৭,৭৫০.

A 180 m long train takes 18 seconds to pass a pole. How long will it take to pass a 330 m long platform?

ক
55 seconds
খ
60 seconds
গ
50 seconds
ঘ
51 seconds

ব্যাখ্যা

Question: A 180 m long train takes 18 seconds to pass a pole. How long will it take to pass a 330 m long platform?

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

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

এখন,
180 মিটার অতিক্রম করে = 18 সেকেন্ডে
∴ 1 মিটার অতিক্রম করে = 18/180 সেকেন্ডে
∴ 510 মিটার অতিক্রম করে = (18 × 510)/180 = 51 সেকেন্ডে

৭,৭৫১.

The average salary of five employees is Tk. 23200. If one of them is excluded the average decreases by 200. The slary of the excluded employee is:

ক
Tk. 24000
খ
Tk. 25000
গ
Tk. 23500
ঘ
Tk. 24500

ব্যাখ্যা

Question: The average salary of five employees is Tk. 23200. If one of them is excluded the average decreases by 200. The slary of the excluded employee is:

Solution:
The average salary of five employees is Tk. 23200
Total salary = 23200 × 5 = 116000

After excluding one person,
The new average is become = 23200 - 200 = 23000

Total salary of remaining 4 employees = 23000 × 4 = 92000

Then,
The salary of excluded employee = 116000 - 92000
= 24000

৭,৭৫২.

The sum of five consecutive numbers is 55. What is the difference between the square of the largest number and the square of the smallest number?

ক
3
খ
13
গ
88
ঘ
63

ব্যাখ্যা

Question: The sum of five consecutive numbers is 55. What is the difference between the square of the largest number and the square of the smallest number?

Solution:
Let the smallest number be = x
Then the five consecutive numbers are: x, x + 1, x + 2, x + 3, x + 4

ATQ,
x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 55
⇒ 5x + 10 = 55
⇒ 5x = 45
⇒ x = 9

∴ Difference between the the square of the smallest number and the square of the largest number,
= (x + 4)² - x²
= (9 + 4)² - 9²
= 169 - 81
= 88

৭,৭৫৩.

The rate at which a sum becomes four times of itself in 25 years at simple interest, will be-

ক
30%
খ
25%
গ
12%
ঘ
49%

ব্যাখ্যা

Question: The rate at which a sum becomes four times of itself in 25 years at simple interest, will be-

Solution:
Let sum, P = x.
Then, simple interest, I = 3x
Time, n = 25 years
Rate = r

r = I/(Pn)
= 3x/(x × 25)
= (3 × 100)/25%
= 12%

৭,৭৫৪.

(x - 1/x) = 5 হলে, (x + 1/x)² এর মান কত?

ক
ক) 29
খ
খ) 27
গ
গ) 25
ঘ
ঘ) 32

ব্যাখ্যা

প্রশ্ন: (x - 1/x) = 5 হলে, (x + 1/x)² এর মান কত?

সমাধান:
দেওয়া আছে,
x - 1/x = 5

আমরা জানি,
(x + 1/x)² = (x - 1/x)² + 4x(1/x)
= 5² + 4
= 25 + 4
= 29

৭,৭৫৫.

What will be the total amount after 3 years if Tk. 1200 is invested at a simple interest rate of 5% annually?

ক
Tk. 1380
খ
Tk. 1320
গ
Tk. 1430
ঘ
Tk. 1560

ব্যাখ্যা

Question: What will be the total amount after 3 years if Tk. 1200 is invested at a simple interest rate of 5% annually?

Solution:
Here,
Principal, P = Tk. 1200
Rate of Interest, r = 5% = 5/100
Time, n = 3 years

We know,
Simple Interest, I = P × n × r
I = 1200 × 3 × (5/100)
I = 1200 × 3 × 5/100
I = 3600 × 5/100
I = 180 Tk.

Now, the Amount after 3 years, A = P + I
A = 1200 + 180
A = 1380 Tk.

∴ The amount after 3 years will be Tk. 1380.

৭,৭৫৬.

The volume of a right circular cylinder is 25π cubic units, and its height is 4 units. What is the circumference of its base?

ক
5π
খ
10π
গ
20π
ঘ
10√2π

ব্যাখ্যা

Question: The volume of a right circular cylinder is 25π cubic units, and its height is 4 units. What is the circumference of its base?

Solution:
আমরা জানি, একটি সিলিন্ডারের আয়তন = πr²h
যেখানে, r হলো ভূমির ব্যাসার্ধ এবং h হলো উচ্চতা।

প্রশ্নমতে,
πr² × 4 = 25π
⇒ 4r² = 25
⇒ r² = 25/4
⇒ r = √(25/4)
⇒ r = 5/2 = 2.5 একক

সিলিন্ডারের ভূমির পরিধি = 2πr
= 2π × 2.5
= 5π একক

∴ সিলিন্ডারটির ভূমির পরিধি হলো 5π একক।

৭,৭৫৭.

0.213 ÷ 0.00213 =?

ক
ক) 100
খ
খ) 10
গ
গ) 1
ঘ
ঘ) None of these

ব্যাখ্যা

Question: 0.213 ÷ 0.00213 =?

Solution:
0.213 ÷ 0.00213 = 100

৭,৭৫৮.

A motorboat, whose speed is 12 km/hr in still water goes 24 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/h) is :

ক
9 km/h
খ
7 km/h
গ
4 km/h
ঘ
10 km/h

ব্যাখ্যা

Question: A motorboat, whose speed is 12 km/hr in still water goes 24 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/h) is :

Solution:
Let the speed of the stream be x km/h
Then, Speed downstream = (12 + x) km/h
Speed upstream = (12 - x) km/h

ATQ,
24/(12 + x) + 24/(12 - x) = 4(1/2)
⇒ 576/(144 - x²) = 9/2
⇒ 9(144 - x²) = 1152
⇒ 1296 - 9x² = 1152
⇒ 1296 - 1152 = 9x²
⇒ 9x² = 144
⇒ x² = 16
∴ x = 4

৭,৭৫৯.

The three sides of a triangle are x + 1, 2x - 1 and 3x + 1 respectively and the perimeter is 25cm. The length of the biggest side is-

ক
5 cm
খ
11 cm
গ
7 cm
ঘ
13 cm

ব্যাখ্যা

Question: The three sides of a triangle are x + 1, 2x - 1 and 3x + 1 respectively and the perimeter is 25cm. The length of the biggest side is-

Solution:
Sides of the triangle are
x + 1, 2x - 1 and 3x + 1
Perimeter of the triangle = 25 cm

Now,
⇒ x + 1 + 2x - 1 + 3x + 1 = 25
⇒ 6x + 1 = 25
⇒ 6x = 25 - 1
⇒ 6x = 24
∴ x = 4

Find all sides
x + 1 = 4 + 1 = 5
2x - 1 = 2 × 4 - 1 = 7
3x + 1 = 3 × 4 + 1 = 13

So the biggest side is 13 cm.

৭,৭৬০.

A Zoo keeper counted the heads of the animals in a zoo and found it to be 80. When he counted the legs of the animals he found it to be 260. If the zoo had either pigeons or horses, how many horses were there in the zoo?

ক
60
খ
40
গ
30
ঘ
50

ব্যাখ্যা

Question: A Zoo keeper counted the heads of the animals in a zoo and found it to be 80. When he counted the legs of the animals he found it to be 260. If the zoo had either pigeons or horses, how many horses were there in the zoo?

Solution:
let, there are x horses and y pigeons.

x + y = 80
⇒ x = 80 - y ........(1)

ATQ,
4x + 2y = 260
⇒ 4 (80 - y) + 2y = 260
⇒ 320 - 4y + 2y = 260
⇒ 2y = 320 - 260
⇒ 2y = 60
∴ y = 30

x = 80 - 30
= 50
∴ there are 50 horses.

৭,৭৬১.

A retail fruit vendor buys pineapples at a score for Tk. 200, and retails them at a dozen for Tk. 156. What % was his gain or loss?

ক
loss 25%
খ
loss 30%
গ
gain 25%
ঘ
gain 30%

ব্যাখ্যা

Question: A retail fruit vendor buys pineapples at a score for Tk. 200, and retails them at a dozen for Tk. 156. What % was his gain or loss?

Solution:
C.P of 1 pineapple = 220/score = 200/20 = 10 [Note: 1 score = 20 nos.]
S.P of 1 pineapple = 156/dozen = 156/12 = 13.
∴ Profit = 13 - 10 = 3
∴ % Profit = 100 × (3/10) = 30%

৭,৭৬২.

In a race of 200 meters, B can give a start of 10 meters to A, and C can give a start of 20 meters to B. The starts that C can give to A, in the same race is:

ক
33 meters
খ
31 meters
গ
29 meters
ঘ
27 meters
ঙ
None of the above

ব্যাখ্যা

Question: In a race of 200 meters, B can give a start of 10 meters to A, and C can give a start of 20 meters to B. The starts that C can give to A, in the same race is:

Solution:
According to the question,
When B runs 200 m meters, A runs 190 meters;
Hence, when B runs 180 meters,

A runs = 190 × (180/200) meters
= 171 meters

When C runs 200m, B runs 180 meters.

Hence,
C will give a start to A by = (200 - 171) meters
= 29 meters

৭,৭৬৩.

Among three numbers, the first number is twice the second and half of the third. If the average of the three numbers is 56, find the difference between the first and third numbers.

ক
42
খ
36
গ
48
ঘ
52

ব্যাখ্যা

Question: Among three numbers, the first number is twice the second and half of the third. If the average of the three numbers is 56, find the difference between the first and third numbers.

Solution:
Let,
the second number be x.
Then first number = 2x, third number = 4x.

∴ 2x + x + 4x = 56 × 3
⇒ 7x = 168
⇒ x = 168/7
⇒ x = 24

Required difference:
= 4x - 2x
= 2x
= 2 × 24
= 48.

৭,৭৬৪.

At what angle the hands of a clock are inclined at 15 minutes past 5?

ক
60°
খ
55.5°
গ
67.5°
ঘ
80°

ব্যাখ্যা

Question: At what angle the hands of a clock are inclined at 15 minutes past 5?

Solution:
Hours hand moves in 15 past.
5 from 12 p.m = (5 + 15/60) hours = 21/4 hours
Angle of hours hand = (360/12) × (21/4)
= 157.5°

Minutes hands makes angle of = (360/60) × 15
= 90°

Angle between hours and minutes hands = (157.5° - 90°)
= 67.5°

৭,৭৬৫.

Find

ক
0.009
খ
1
গ
0.9
ঘ
0.09

ব্যাখ্যা

Question: Find

Solution:

৭,৭৬৬.

In how many ways, a committee of 5 members be selected from 7 men and 5 ladies, consisting of 3 men and 2 ladies?

ক
320 ways
খ
350 ways
গ
360 ways
ঘ
380 ways

ব্যাখ্যা

Question: In how many ways, a committee of 5 members be selected from 7 men and 5 ladies, consisting of 3 men and 2 ladies?

Solution:
there are total 7 men and 5 ladies

∴ number of ways a committee of 5 members can be slected = (⁷C₃) × (⁵C₂)
= 35 × 10
= 350 ways

৭,৭৬৭.

A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

ক
1/3 part
খ
1/4 part
গ
1/5 part
ঘ
1/7 part

ব্যাখ্যা

Question: A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

Solution:
The initial ratio of water : syrup is 3:5.
This means the total mixture has 3 parts water and 5 parts syrup → 8 parts in total.
We need to make the final ratio 1:1 (half water, half syrup).

Let x be the fraction of the mixture drawn off and replaced with water.
Water removed = 3x/8
Water left = (3/8) - 3x/8

Syrup removed = 5x/8
Syrup left = (5/8) - 5x/8

Since the removed mixture is replaced with water, the new amount of water is = (3/8) - 3x/8 + x

ATQ,
(3/8) - 3x/8 + x = (5/8) - 5x/8
3 - 3x + 8x = 5 - 5x
10x = 2
∴ x = 1/5

৭,৭৬৮.

The greatest 3-digit number that is divided by 15 and 25 is -

ক
ক) 950
খ
খ) 975
গ
গ) 980
ঘ
ঘ) 995

ব্যাখ্যা

Question: The greatest 3-digit number that is divided by 15 and 25 is -

Solution:
তিন অংকের বৃহত্তম সংখ্যা = ৯৯৯
১৫ = ৩ × ৫
২৫ = ৫ × ৫
ল.সা.গু = ৫ × ৫ × ৩ = ৭৫

৯৯৯ কে ৭৫ দিয়ে ভাগ করলে ভাগশেষ থাকে ২৪

∴ সংখ্যাটি = ৯৯৯ - ২৪ = ৯৭৫

৭,৭৬৯.

A distance is covered in 3 hrs 30 minutes at 5 km/hr. How much time will be taken to cover it at 21 km/hr?

ক
ক) 50 min
খ
খ) 60 min
গ
গ) 45 min
ঘ
ঘ) 55 min

ব্যাখ্যা

Question: A distance is covered in 3 hrs 30 minutes at 5 km/hr. How much time will be taken to cover it at 21 km/hr?

Solution:
Distance = [5 × 3 (1/2)]
= 5 × (7/2)
= 17.5 km.

Time taken to cover it at 21 km/hr = [(17.5/21) × 60] min
= 50 min.

৭,৭৭০.

If 2 tables and 3 chairs cost Tk. 3500 and 3 tables and 2 chairs cost Tk. 4000, then how much does a table cost?

ক
Tk. 500
খ
Tk. 750
গ
Tk. 1000
ঘ
Tk. 15000

ব্যাখ্যা

Question: If 2 tables and 3 chairs cost Tk. 3500 and 3 tables and 2 chairs cost Tk. 4000, then how much does a table cost?

Solution:
Let
The cost of a table and that of a chair be Tk. x and Tk. y respectively.

Then,
2x + 3y = 3500................(i)
and
3x + 2y = 4000................(ii)

(ii)× 3 - (i) × 2 ⇒
9x + 6y - 4x - 6y = 12000 - 7000
5x = 5000
x = 1000

The cost of a table Tk. 1000

৭,৭৭১.

The tops of two poles are connected by a wire. The heights of the poles are 10 m and 14 m respectively. If the wire makes a 30° angle with the horizontal, find the length of the wire?

ক
7 m
খ
7.5 m
গ
8 m
ঘ
8.5 m

ব্যাখ্যা

Question: The tops of two poles are connected by a wire. The heights of the poles are 10 m and 14 m respectively. If the wire makes a 30° angle with the horizontal, find the length of the wire?

Solution:

Let AD and BE, be the poles of height 10 m and 14 m respectively.
DE is the wire of length = L
DC is parallel to AB so AD = BC = 10 m
So, CE = BE - BC = 14 - 10 = 4 m

In ΔDCE,
sin30° = CE/DE
⇒ 1/2 = 4/L
⇒ L = 8

৭,৭৭২.

Two pipes P and Q can fill a reservoir in 15 and 20 hours respectively. Both pipes are opened together. After how many hours should pipe P be turned off so that the reservoir is filled in 12 hours?

ক
6 hours
খ
7.5 hours
গ
8 hours
ঘ
10 hours

ব্যাখ্যা

Question: Two pipes P and Q can fill a reservoir in 15 and 20 hours respectively. Both pipes are opened together. After how many hours should pipe P be turned off so that the reservoir is filled in 12 hours?

সমাধান:
ধরি, মোট সময় 12 ঘন্টা পর চৌবাচ্চাটি পূর্ণ হয়। এই সম্পূর্ণ সময়ে কেবল নল Q খোলা ছিল।

নল Q, 20 ঘন্টায় চৌবাচ্চাটি পূর্ণ করতে পারে।
1 ঘন্টায় Q পূর্ণ করে 1/20 অংশ।
12 ঘন্টায় Q পূর্ণ করে = 12/20 অংশ
= 3/5 অংশ।

অবশিষ্ট অংশ যা P পূর্ণ করেছিল = 1 - 3/5 অংশ
= 2/5 অংশ।

নল P, 15 ঘন্টায় পূর্ণ করে 1 অংশ।
1 অংশ পূর্ণ করে 15 ঘন্টায়।
∴ 2/5 অংশ পূর্ণ করে = (15 × 2/5) ঘন্টা
= 6 ঘন্টা।

অর্থাৎ, নল P, 6 ঘন্টা কাজ করার পর বন্ধ করা হয়েছিল।
∴ নল P কে 6 ঘন্টা পর বন্ধ করতে হবে।

৭,৭৭৩.

One side of a rhombus is 37 cm and its area is 840 cm². Find the sum of the lengths of its diagonals.

ক
ক) 94 cm
খ
খ) 95 cm
গ
গ) 96 cm
ঘ
ঘ) 98 cm

ব্যাখ্যা

Let X and Y be the lengths of diagonals of the rhombus,
Area of rhombus = Product of both diagonals/ 2,
⇒ 840 = (X × Y)/2,
⇒ X × Y = 1680,

Using Pythagorean Theorem we get,
⇒ (X/2)² + (Y/2)² = 37²
⇒ X² + Y² = 1369 × 4
⇒ X² + Y² = 5476

Now
(X + Y)² = X² + 2XY + Y²
⇒ (X + Y)² = 5476 + 2 × 1680
⇒ X + Y = 94

৭,৭৭৪.

What will be the least number that when doubled will be exactly divisible by 12, 18, 21 and 30?

ক
660
খ
620
গ
360
ঘ
630

ব্যাখ্যা

Question: What will be the least number that when doubled will be exactly divisible by 12, 18, 21 and 30?

Solution:
12 = 2 × 2 × 3
18 = 2 × 3 × 3
21 = 3 × 7
30 = 2 × 3 × 5

L.C.M. of 12, 18, 21 30 = 2 × 3 × 2 × 3 × 7 × 5 = 1260
Required number = 1260/2 = 630

৭,৭৭৫.

Rakib charges at 7% P.A. simple interest to Maruf and Sunny and lends a certain amount to Sunny and Tk. 2500 to Maruf. After 4 years, Rakib completely receives Tk. 1120 as interest from Maruf and Sunny. Find the amount lent to Sunny?

ক
ক) Tk. 3000
খ
খ) Tk. 1500
গ
গ) Tk. 900
ঘ
ঘ) Tk. 1600

ব্যাখ্যা

Question: Rakib charges at 7% P.A. simple interest to Maruf and Sunny and lends a certain amount to Sunny and Tk. 2500 to Maruf. After 4 years, Rakib completely receives Tk. 1120 as interest from Maruf and Sunny. Find the amount lent to Sunny?

Sulotion:
Let,
Rakib lent Sunny Tk. x,
∴ Rakib lent total Tk. (x + 2500)

We know that,
Interest, I = Pnr
∴ 1120 = (x + 2500) × 4 × (7/100)
⇒ 112000 = (x + 2500) × 28
⇒ x + 2500 = 112000/28
⇒ x + 2500 = 4000
⇒ x = 4000 - 2500
∴ x = 1500

∴ Rakib lent Sunny Tk. 1500

৭,৭৭৬.

In the given series which number comes next: 91, 86, 76, 61.....?

ক
ক) 31
খ
খ) 36
গ
গ) 41
ঘ
ঘ) 46

ব্যাখ্যা

91 - 5 =86
86 - 10 = 76
76 - 15 = 61
So, 61 - 20 = 41

৭,৭৭৭.

A can do a piece of work in 30 days. B is 20% more efficient than A. The number of days taken by B to do the same piece of work is:

ক
ক) 22 days
খ
খ) 25 days
গ
গ) 20 days
ঘ
ঘ) 26 days

ব্যাখ্যা

Question: A can do a piece of work in 30 days. B is 20% more efficient than A. The number of days taken by B to do the same piece of work is:

Solution:
A ও B কাজটি করার সময়ের অনুপাত
= 120 : 100
= 6 : 5

ধরি,
A কাজটি করতে x দিন সময় নেয়
6 : 5 :: 30 : x
⇒ 6/5 = 30/x
⇒ x = (5 × 30)/6
⇒ x = 25 দিন

B কাজটি করতে পারে 25 দিনে।

৭,৭৭৮.

Three numbers have an arithmetic mean of 3x + 2. If one of them is x, determine the average of the other two.

ক
4x + 3
খ
7x + 3
গ
5x + 7
ঘ
2x + 3

ব্যাখ্যা

Question: Three numbers have an arithmetic mean of 3x + 2. If one of them is x, determine the average of the other two.

Solution:
The average (arithmetic mean) of three numbers is 3x + 2
∴ The sum of three numbers is 3(3x + 2) = 9x + 6

If one of the numbers is x
∴ Sum of the other two numbers = 9x + 6 - x = 8x + 6

∴ The average of the other two numbers is = (8x + 6)/2 = 4x + 3

৭,৭৭৯.

ক
40
খ
38
গ
37
ঘ
More than one of the above
ঙ
None of the above

ব্যাখ্যা

Question:

Solution:

৭,৭৮০.

3 pumps, working 4 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work, to empty the tank in one day?

ক
ক) 4 hours
খ
খ) 5 hours
গ
গ) 6 hours
ঘ
ঘ) 6.5 hours

ব্যাখ্যা

Given that,
3 pumps, working 4 hours a day, can empty a tank in 2 days.
Therefore, it means that:
3 pumps take a total of 8 hours to empty the tank.
Hence, 1 pump will take 8 × 3 = 24 hours

As the number of pumps decreases, the time required increases.
So, if 4 pumps work, the time required decreases.
∴ 24/4 = 6 hours needed to empty the tank in 1 day.

৭,৭৮১.

A started a business with tk 21000 and is joined afterwards by B with tk 36000. After how many months did B join if the profits at the end of the year are divided equally?

ক
ক) 3
খ
খ) 4
গ
গ) 5
ঘ
ঘ) 6

ব্যাখ্যা

Suppose B joined after x months
then,
21000 × 12 = 36000 × (12 - x)
⇒ 36x = 180
⇒ x = 5

৭,৭৮২.

The cost of a watch is Tk. 900. To make the deal attractive to its customers, the shop sells it at a discount of 12% and still makes a profit of 10%. What is the advertised price?

ক
ক) Tk.. 812.5
খ
খ) Tk. 1050
গ
গ) Tk. 1125
ঘ
ঘ) Tk. 1225

ব্যাখ্যা

Since profit of 10% is there,
∴ S.P. = (100+10)% of C.P. = (110/100) × 900
= Tk. 990
Discount = 12%
So,
SP = (100-12)% of List Price
∴ 990 = (88/100) × L.P.
∴ L.P. = Tk. 1125 [List price = Advertised Price = Marked Price]

৭,৭৮৩.

Akash travels with his two friends to Australia. In his bag, he has 6 black, 4 red, 2 white and 3 blue shirts. On Christmas eve all three of them chose to wear shirts from Akash's collection. Find the probability of 2 red shirts and 1 blue shirt being chosen randomly.

ক
ক) 7/2730
খ
খ) 7/435
গ
গ) 18/455
ঘ
ঘ) 7/15

ব্যাখ্যা

We want 2 red and 1 blue shirt
There are 4 red shirts and 3 blue shirts
Total = 15 shirts
You can choose a blue shirt 1^st, then a red shirt and then a red shirt

Probability = 3/15 × 4/14 × 3/13 = 6/455

OR You can choose a red shirt 1^st, then redshirt and then a blue shirt
OR You can choose a red shirt 1^st, then a blue shirt and then red-shirt
For all 3 the probability remains the same = 6/455

We need to add these 3 probabilities to get the total probability
Total probability = 6/455 + 6/455 + 6/455 = 18/455.

৭,৭৮৪.

ক
11
খ
18
গ
25
ঘ
90

ব্যাখ্যা

Question:

Solution:

৭,৭৮৫.

√(4/3) - √(3/4) = ?

ক
ক) - 1/2√3
খ
খ) 1/3√2
গ
গ) - 1/3√2
ঘ
ঘ) 1/2√3

ব্যাখ্যা

Question: √(4/3) - √(3/4) = ?

Solution:
= (√4.√4 - √3.√3)/√3.√4
=(4 - 3)/2√3
=1/2√3

৭,৭৮৬.

Ten years ago, A was half of B in age. If the ratio of their present ages is 3 : 4, then what will be the total of their present ages?

ক
30 years
খ
35 years
গ
40 years
ঘ
45 years

ব্যাখ্যা

Let, present age of A = 3y
and present age of B = 4y
10 years ago, age of A = 3y - 10
10 years ago, age of B = 4y - 10
10 years ago, A = B/2
Therefore, 3y - 10 = (4y - 10)/2
or, y = 5
sum of age of A and B =3y + 4y = 7y = 35 years

৭,৭৮৭.

You have 4 favorite novels on your shelf. If you decide to arrange these 4 novels in every possible order and it takes 45 seconds to move one novel, how much time will it take to arrange all possible combinations?

ক
15 minutes
খ
20 minutes
গ
28 minutes
ঘ
72 minutes

ব্যাখ্যা

Question: You have 4 favorite novels on your shelf. If you decide to arrange these 4 novels in every possible order and it takes 45 seconds to move one novel, how much time will it take to arrange all possible combinations?

Solution:
4 novels can be arranged in = 4! ways
= 4 × 3 × 2 × 1 = 24 ways

Time required to move one novel = 45 seconds
time to arrange 4 novels = 45 × 4 = 180 seconds

So, total time required = 24 × 180 seconds
= 4320 seconds
= 4320/60
= 72 minutes

∴ It will take 72 minutes to arrange all possible combinations.

৭,৭৮৮.

If log(2a/b) + log(3b/a) = log(a + b), then -

ক
a + b = 1
খ
a + b = 6
গ
a + b = - 1
ঘ
a = - b

ব্যাখ্যা

Question: If log(2a/b) + log(3b/a) = log(a + b), then -

Solution:
log(2a/b) + log(3b/a) = log(a + b)
⇒ log{(2a/b) × (3b/a)} = log(a + b)
⇒ log6 = log(a + b)
∴ a + b = 6

৭,৭৮৯.

What is the arithmetic mean of the first 100 natural numbers?

ক
ক) 50
খ
খ) 50.5
গ
গ) 51
ঘ
ঘ) 51.5

ব্যাখ্যা

আমরা জানি,
n সংখ্যক স্বাভাবিক সংখ্যার যোগফল = {n(n + 1)/2}
∴ 100 টি স্বাভাবিক সংখ্যার যোগফল = {100(100 + 1)/2} = 5050
সুতরাং, এদের গড় = 5050/100 = 50.5

৭,৭৯০.

If x + 1/x = 3, then x³ + 1/x³ is equal to-

ক
0
খ
18
গ
27
ঘ
2

ব্যাখ্যা

Question: If x + 1/x = 3, then x³ + 1/x³ is equal to-

Solution:
x³ + 1/x³
= (x + 1/x)³ - 3.x.(1/x).(x + 1/x)
= 3³ - 3 × 3
= 27 - 9
= 18

৭,৭৯১.

If in a code language. COULD is written as BNTKC and MARGIN is written as LZQFHM, how will MOULDING be written in that code?

ক
NITKHCMF
খ
LNTKCHMF
গ
CHMFINTK
ঘ
LNKTCHMF

ব্যাখ্যা

Question: If in a code language. COULD is written as BNTKC and MARGIN is written as LZQFHM, how will MOULDING be written in that code?

Solution:
M এর আগের বর্ণ L
O এর আগের বর্ণ N
U এর আগের বর্ণ T
L এর আগের বর্ণ K
D এর আগের বর্ণ C
I এর আগের বর্ণ H
N এর আগের বর্ণ M
G এর আগের বর্ণ F

৭,৭৯২.

The width of a rectangular room is 2/3 of length. The perimeter of the room is 40m. Find the area of the room.

ক
ক) 72 m²
খ
খ) 64 m²
গ
গ) 96 m²
ঘ
ঘ) 60 m²

ব্যাখ্যা

Question: The width of a rectangular room is 2/3 of length. The perimeter of the room is 40m. Find the area of the room.

Solution:
ধরি,
ঘরটির দৈর্ঘ্য = x মি.
ঘরটির প্রস্থ = 2x/3 মি.

প্রশ্নমতে,
2{x + (2x/3)} = 40
বা, (3x + 2x)/3 = 40/2
বা, 5x/3 = 20
বা, 5x = 20 × 3
বা, 5x = 60
∴ x = 12

ঘরটির দৈর্ঘ্য = 12 মি.
ঘরটির প্রস্থ = (2 × 12)/3 মি.
= 8 মি.

আমরা জানি,
ঘরটির ক্ষেত্রফল = (দৈর্ঘ্য × প্রস্থ)
= (12 × 8) বর্গমি.
= 96 বর্গমি.

৭,৭৯৩.

If Machine A can produce 500 units in 3 hours and Machine B can produce 500 units in 6 hours, in how many hours can Machines A and B, working together at these constant rates, produce 500 units?

ক
2 hours
খ
3 hours
গ
4.5 hours
ঘ
5 hours

ব্যাখ্যা

Question: If Machine A can produce 500 units in 3 hours and Machine B can produce 500 units in 6 hours, in how many hours can Machines A and B, working together at these constant rates, produce 500 units?

Solution:
মেশিন A, 3 ঘণ্টায় তৈরি করে ৫০০টি ইউনিট।
∴ 1 ঘণ্টায় মেশিন A তৈরি করে = 500/3 ইউনিট

মেশিন B, 6 ঘণ্টায় তৈরি করে ৫০০টি ইউনিট।
∴ 1 ঘণ্টায় মেশিন B তৈরি করে = 500/6 ইউনিট

তারা একত্রে ১ ঘণ্টায় তৈরি করে = (500/3) + (500/6) ইউনিট
= (1000 + 500)/6
= 1500/6 = 250 ইউনিট

তারা একত্রে 250টি ইউনিট তৈরি করে 1 ঘণ্টায়।
∴ তারা একত্রে 500টি ইউনিট তৈরি করতে সময় নেবে = 500/250 = 2 ঘণ্টা

৭,৭৯৪.

If x = 10^1.4, y = 10^0.7 and x^z = y³, then what is the value of z?

ক
1/2
খ
1
গ
1/3
ঘ
2/5
ঙ
3/2

ব্যাখ্যা

Question: If x = 10^1.4, y = 10^0.7 and x^z = y³, then what is the value of z?

Solution:
Given,
x = 10^1.4, y = 10^0.7

Now,
x^z = y³
⇒ (10^1.4)^z = (10^0.7)³
⇒ 10^1.4z = 10^2.1
⇒ 1.4z = 2.1
⇒ z = 2.1/1.4
⇒ z = (2.1 × 10)/(1.4 × 10)
⇒ z = 21/14
∴ z = 3/2

৭,৭৯৫.

The ratio of milk to water in 60 liters of a mixture is 7 : 5. The milk to be added to it make the ratio 2 : 1 is-

ক
ক) 10 liters
খ
খ) 12 liters
গ
গ) 15 liters
ঘ
ঘ) 16 liters

ব্যাখ্যা

Question: The ratio of milk to water in 60 liters of a mixture is 7 : 5. The milk to be added to it make the ratio 2 : 1 is-

Solution:
Quantity of milk = 60 × (7/12) = 35 liters
Quantity of water = 60 - 35 = 25 liters

Let, x liters of milk be added to the mixture.

ATQ,
(35 + x)/25 = 2/1
⇒ 35 + x = 50
⇒ x = 50 - 35
⇒ x = 15

৭,৭৯৬.

A sum earns Tk. 1260 more interest in 8 years than in 5 years at 7.5% simple interest. Calculate the principal.

ক
Tk. 5000
খ
Tk. 6000
গ
Tk. 6250
ঘ
Tk. 5600

ব্যাখ্যা

Question: A sum earns Tk. 1260 more interest in 8 years than in 5 years at 7.5% simple interest. Calculate the principal.

Solution:
Given that,
Rate, r = 7.5% per annum
Extra interest earned in, n = (8 - 5) = 3 years
SI = Tk. 1260

We know,
Simple Interest,
SI = (P × r × n) / 100
⇒ 1260 = (P × 7.5 × 3) / 100
⇒ 1260 = (P × 22.5) / 100
⇒ 1260 × 100 = 22.5 × P
⇒ 126,000 = 22.5 × P
⇒ P = 126000/22.5
∴ P = 5600

So the principal is Tk. 5600

৭,৭৯৭.

At what angle the hands of a clock are inclined at 15 minutes past 5?

ক
57.5 degrees
খ
67.5 degrees
গ
77.5 degrees
ঘ
87.5 degrees
ঙ
None of the above

ব্যাখ্যা

Angle traced by hour hand in 21/4 hrs = (360/12) × (21/4)0 = 157(1/2 )
Angle traced by min. hand in 15 min = (360/60 × 15) = 90
Required Angle = (157(1/2) − 90 = 67(1/2)

৭,৭৯৮.

If log₇(2) = m, then log₄₉(28) is equal to-

ক
2m + 1
খ
m
গ
(2m + 1)/2
ঘ
(m + 1)/2

ব্যাখ্যা

Question: If log₇(2) = m, then log₄₉(28) is equal to-

Solution:
log₇(2) = m
7^m = 2
(7^m)² = 2²
49^m= 4

log₄₉(28)
= log₄₉(4 × 7)
= log₄₉4 + log₄₉7
= log₄₉49^m + log₄₉(49)^1/2
= m + 1/2
= (2m + 1)/2

৭,৭৯৯.

In a garden, a man worked 3 days, his wife 2 days, and daughter 4 days. The daily wage ratio between the man and the woman is 5 : 4, and between the man and daughter is 5 : 3. Their total income is Tk. 105. Find how much the daughter earns per day.

ক
Tk. 17
খ
Tk. 15
গ
Tk. 10
ঘ
Tk. 13
ঙ
Tk. 9

ব্যাখ্যা

Question: In a garden, a man worked 3 days, his wife 2 days, and daughter 4 days. The daily wage ratio between the man and the woman is 5:4, and between the man and daughter is 5:3. Their total income is Tk. 105. Find how much the daughter earns per day.

Solution:
Assume that the daily wages of man, women and daughter are Tk 5x, Tk 4x, Tk 3x respectively.
Multiply (no. of days) with (assumed daily wage) of each person to calculate the value of x.
[3 × (5x)] + [2 × (4x)] + [4 × (3x)] = 105
⇒ 15x + 8x + 12x = 105
⇒ 35x = 105
⇒ x = 3

Hence, man's daily wage = 5x = 5 × 3 = Tk. 15
Wife's daily wage = 4x = 4 × 3 = Tk. 12
Daughter's daily wage = 3x = 3 × 3 = Tk. 9

৭,৮০০.

If a^x = b^y, then

ক
ক) log(a/b) = x/y
খ
খ) loga/logb = x/y
গ
গ) loga/logb = y/x
ঘ
ঘ) None of these

ব্যাখ্যা

a^x = b^y
loga^x = logb^y
xloga = ylogb
loga/logb = y/x