Bank Math

PrepBank · পাতা ১৮ / ১৬১ · ১,৭০১–১,৮০০ / ১৬,১২৪

১,৭০১.

The average price of three items of furniture is Tk. 30000. If their prices are in the ratio 3 : 5 : 7, what is the price of the cheapest item?

ক
ক) 3000 tk
খ
খ) 6000 tk
গ
গ) 10000 tk
ঘ
ঘ) 18000 tk

সঠিক উত্তর: ঘ

ঘ) 18000 tk

উত্তর

সঠিক উত্তর: ঘ

ঘ) 18000 tk

ঘ

ব্যাখ্যা

Question: The average price of three items of furniture is Tk. 30000. If their prices are in the ratio 3 : 5 : 7, what is the price of the cheapest item?

Solution:
The average price of three items of furniture is Rs. 30000.
total price = (30000 × 3) = 90000
their prices are in the ratio 3 : 5 : 7

∴ the price of the cheapest item is = 90000 × 3/15
= 18000 tk

১,৭০২.

In how many ways can a group of 5 members be formed by selecting 3 boys out of 6 boys and 2 girls out of 5 girls?

ক
200
খ
350
গ
462
ঘ
30
ঙ
None of these

সঠিক উত্তর: ক

200

উত্তর

সঠিক উত্তর: ক

200

ক

ব্যাখ্যা

Question: In how many ways can a group of 5 members be formed by selecting 3 boys out of 6 boys and 2 girls out of 5 girls?

Solution:
Number of ways 3 boys can be selected out of 6 = ⁶C₃ = 6!/[(3!) × (3!)] = (6 × 5 × 4) / (3 × 2 × 1) = 20

Number of ways 2 girls can be selected out of 5 = ⁵C₂ = 5!/[(2 !) × (3 !)] = (5 × 4)/(2 × 1) = 10

Therefore, total number of ways of forming the group = 20 × 10 = 200

১,৭০৩.

If 7^{(x + 2)} = 49^{(3x - 4)} then the value of x = ?

ক
0
খ
2
গ
5
ঘ
7

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: If 7^{(x + 2)} = 49^{(3x - 4)} then the value of x = ?

Solution:
7^{(x + 2)} = 49^{(3x - 4)}
⇒ 7^{(x + 2)} = (7²)^{(3x - 4)}
⇒ 7^{(x + 2)} = 7^{(6x - 8)}
⇒ x + 2 = 6x - 8
⇒ 5x = 10
∴ x = 2

১,৭০৪.

Out of 80 children, 35% can play only cricket, 45% can play only table tennis and remaining children can play both the games. In all, how many children can play cricket?

ক
ক) 28
খ
খ) 36
গ
গ) 44
ঘ
ঘ) 55

সঠিক উত্তর: গ

গ) 44

উত্তর

সঠিক উত্তর: গ

গ) 44

গ

ব্যাখ্যা

Both game is played by = 100 - (35 + 45) = 20% children
So, in all cricket can be played by = 55% of 80 children
= 55/100 × 80 = 44 children

১,৭০৫.

If the side of a square is increased by 10%, by what percent will the area be increased?

ক
16%
খ
21%
গ
32%
ঘ
100%

সঠিক উত্তর: খ

21%

উত্তর

সঠিক উত্তর: খ

21%

খ

ব্যাখ্যা

Question: If the side of a square is increased by 10%, by what percent will the area be increased?

Solution:
Let the original side length = 10 units.

∴ Area = 10 × 10 = 100 square units

Again,
After a 10% increase, the new side length = 10 + 10% of 10
= 10 + 1 = 11 units

∴ New area = 11 × 11 = 121 square units

∴ Increase in area = 121 - 100 square units
= 21 square units

∴ Percentage increase in area = (21/100) × 100%
= 21%

So the area will increase by 21%

১,৭০৬.

A and B together can complete a piece of work in 12 days, B and C can do it in 20 days and C and A can do it in 15 days. A, B and C together can complete it in-

ক
ক) 12 days
খ
খ) 6 days
গ
গ) 8 days
ঘ
ঘ) 10 days

সঠিক উত্তর: ঘ

ঘ) 10 days

উত্তর

সঠিক উত্তর: ঘ

ঘ) 10 days

ঘ

ব্যাখ্যা

A + B can do the work in 12 days.
In a single day A + B will do 1/12^th portion of the work.
B+C can do the work in 15 days.
In a single day B+C will do 1/15^th portion of the work.
A + C can do the work in 20 days.
In a single day A+C will do 1/20^th portion of the work.

In a day (A+B) + (A+C) + (C+A) will do = (1/12) + (1/15) + (1/20) portion of the work.
⇒ 2(A+B+C) = (1/12)+(1/15)+(1/20) = (5+4+3)/60 = 1/5 portion of the work.
Then, (A+B+C) will do = 1/10 portion of the work in a day
∴ A+B+C will complete the work in 10 days.

১,৭০৭.

If 70% of the students in a school are boys and the number of girls is 504, what is the number of boys?

ক
1281
খ
1280
গ
1311
ঘ
1176

সঠিক উত্তর: ঘ

1176

উত্তর

সঠিক উত্তর: ঘ

1176

ঘ

ব্যাখ্যা

Question: If 70% of the students in a school are boys and the number of girls is 504, what is the number of boys?

Solution:
Given,
percentage of boys = 70%
The percentage of girls is = (100 - 70)% = 30%

if 30% of students = 504
∴ 1% of students= 504/30
∴ 100% of students = (504 × 100) / 30 = 1680

Total number of Student = 1680

so the boys are = 1680 - 504 = 1176

১,৭০৮.

ⁿC₁ + ⁿC₂ + ⁿC₃ + .. .. ⁿC_n = ?

ক
ক) 2ⁿ
খ
খ) 2^n-1
গ
গ) {n(n-1)(n²+1)}/2
ঘ
ঘ) 2ⁿ - 1

সঠিক উত্তর: ঘ

ঘ) 2ⁿ - 1

উত্তর

সঠিক উত্তর: ঘ

ঘ) 2ⁿ - 1

ঘ

ব্যাখ্যা

We know that, (1+x)ⁿ= ⁿC₀+ ⁿC₁x + ⁿC₂x² + ⁿC₃x³ + ..... + ⁿC_nxⁿ
Let us consider, x=1

Then,
(1+1)ⁿ= ⁿC₀+ ⁿC₁×1 + ⁿC₂×1² + ⁿC₃×1³..... + ⁿC_n×1ⁿ2ⁿ= 1 + ⁿC₁ + ⁿC₂ + ⁿC₃+.... + ⁿC_nⁿC₁ + ⁿC₂ + ⁿC₃+.... + ⁿC_n= 2ⁿ− 1

১,৭০৯.

The mean of the first 10 even natural number numbers is-

ক
ক) 10
খ
খ) 11
গ
গ) 12
ঘ
ঘ) 13

সঠিক উত্তর: খ

খ) 11

উত্তর

সঠিক উত্তর: খ

খ) 11

খ

ব্যাখ্যা

First 10 even natural number = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20

Mean = (2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20)/10
= 110/10
= 11

১,৭১০.

Mr. Karim deposited a certain amount of money for a fixed period of time. On maturity, he received a total of Tk. 50,000 when the ratio of interest and investment became 1: 4. If the simple interest rate was 5%, calculate the time period for which the money was invested.

ক
3 years
খ
4 years
গ
5 years
ঘ
8 years
ঙ
10 years

সঠিক উত্তর: গ

5 years

উত্তর

সঠিক উত্তর: গ

5 years

গ

ব্যাখ্যা

Question: Mr. Karim deposited a certain amount of money for a fixed period of time. On maturity, he received a total of Tk. 50,000 when the ratio of interest and investment became 1: 4. If the simple interest rate was 5%, calculate the time period for which the money was invested.

Solution:
প্রদত্ত তথ্য অনুযায়ী, আসল এবং সুদের অনুপাত = 4 : 1
মোট প্রাপ্ত টাকা = 50,000 টাকা
মোট অনুপাত = 4 + 1 = 5
সুতরাং, আসল = 50,000 টাকার (4/5) অংশ = 40,000 টাকা
এবং, সুদ = 50,000 টাকার (1/5) অংশ = 10,000 টাকা

এখানে,
I = সুদ = 10,000 টাকা
P = আসল = 40,000 টাকা
R = সুদের হার = 5%
T = সময়কাল = ?

আমরা জানি, সরল সুদের ক্ষেত্রে,
I = (P × R × T)/100
⇒ 10,000 = (40,000 × 5 × T)/100
⇒ 10,000 = 400 × 5 × T
⇒ 10,000 = 2,000 × T
⇒ T = 10,000/2,000
⇒ T = 5

সুতরাং, টাকাটি 5 বছরের জন্য বিনিয়োগ করা হয়েছিল।

১,৭১১.

As a salesperson, Poly can choose one of two methods of annual payment either an annual salary of Tk. 35,000 with no commission or an annual salary of Tk. 10,000 plus a 20 percent commission on her total annual sales. What must her total annual sales be to give her the same annual pay with either method?

ক
ক) Tk. 100,000
খ
খ) Tk. 120,000
গ
গ) Tk. 125,000
ঘ
ঘ) Tk. 130,000

সঠিক উত্তর: গ

গ) Tk. 125,000

উত্তর

সঠিক উত্তর: গ

গ) Tk. 125,000

গ

ব্যাখ্যা

Let, total annual sales Tk. x
Therefore,
20% of x + 10,000 = 35,000
or, 20x/100 = 35,000 - 10,000
or, x/5 = 25,000
or, x = 125,000

১,৭১২.

A train takes 10 seconds to cross a pole and 25 seconds to cross a platform of length 180m. What is the length of the train?

ক
100 meters
খ
96 meters
গ
150 meters
ঘ
120 meters

সঠিক উত্তর: ঘ

120 meters

উত্তর

সঠিক উত্তর: ঘ

120 meters

ঘ

ব্যাখ্যা

Question: A train takes 10 seconds to cross a pole and 25 seconds to cross a platform of length 180m. What is the length of the train?

Solution:
মনে করি, ট্রেনটির দৈর্ঘ্য L মিটার।

আমরা জানি, একটি খুঁটি (pole) অতিক্রম করার সময় ট্রেনটি কেবল তার নিজের দৈর্ঘ্য অতিক্রম করে।
সুতরাং, ট্রেনের গতিবেগ = L/10 মি./সে. [গতিবেগ = দূরত্ব/সময়]

আবার, প্ল্যাটফর্ম অতিক্রম করার সময় ট্রেনটি (নিজের দৈর্ঘ্য + প্ল্যাটফর্মের দৈর্ঘ্য) অতিক্রম করে।
শর্তমতে, গতিবেগ = (L + 180)/25 মি./সে.

যেহেতু গতিবেগ একই, তাই,
L/10 = (L + 180)/25
⇒ 25L = 10(L + 180)
⇒ 25L = 10L + 1800
⇒ 25L - 10L = 1800
⇒ 15L = 1800
⇒ L = 1800/15
∴ L = 120

∴ ট্রেনটির দৈর্ঘ্য 120 মিটার।

১,৭১৩.

There are 8 black, 5 red and 7 green marbles in a jar. If a marble is picked at random, what is the probability of having either a black or a green marble?

ক
5/12
খ
3/4
গ
2/3
ঘ
7/12

সঠিক উত্তর: খ

3/4

উত্তর

সঠিক উত্তর: খ

3/4

খ

ব্যাখ্যা

Question: There are 8 black, 5 red and 7 green marbles in a jar. If a marble is picked at random, what is the probability of having either a black or a green marble?

Solution:
মোট মার্বেলের সংখ্যা = 8 + 5 + 7 = 20

কালো মার্বেল পাওয়ার সম্ভাবনা, P(Black) = 8/20

সবুজ মার্বেল পাওয়ার সম্ভাবনা P(Green) = 7/20

যেহেতু কালো এবং সবুজ মার্বেল পাওয়া দুটি বিচ্ছিন্ন (mutually exclusive) ঘটনা,
∴ কালো অথবা সবুজ মার্বেল পাওয়ার সম্ভাবনা (P(Black or Green) = P(Black) + P(Green)
= 8/20 + 7/20
= (8 + 7) / 20 = 15/20
= 3/4

অতএব, কালো অথবা সবুজ মার্বেল পাওয়ার সম্ভাবনা হলো 3/4।

• Shortcut:
মোট মার্বেলের সংখ্যা = 8 + 5 + 7 = 20
অনুকূল ঘটনা = কালো + সবুজ = 8 + 7 = 15টি
∴ সম্ভাবনা = অনুকূল ঘটনা/মোট ঘটনা = 15/20 = 3/4

১,৭১৪.

Three years ago, the average age of Anita, Priya, and Varsha was 27 years. If five years ago, the average age of Priya and Varsha was 20 years, find the present age of Anita.

ক
30
খ
40
গ
60
ঘ
25

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: Three years ago, the average age of Anita, Priya, and Varsha was 27 years. If five years ago, the average age of Priya and Varsha was 20 years, find the present age of Anita.

Solution:
Sum of the present ages of Anita, Priya and Varsha = (27 × 3 + 3 × 3) years = 90 years.
Sum of the present ages of Priya and Varsha = (20 × 2 + 5 × 2) years = 50 years.
Anita's present age = (90 - 50) years = 40 years.

১,৭১৫.

A chemist has two solutions, one containing 40% acid and the other containing 80% acid. How many liters of each solution should be mixed to get 12 liters of a solution containing 60% acid?

ক
4 liters of 40% and 8 liters of 80%
খ
5 liters of 40% and 7 liters of 80%
গ
6 liters of 40% and 6 liters of 80%
ঘ
3 liters of 40% and 9 liters of 80%

সঠিক উত্তর: গ

6 liters of 40% and 6 liters of 80%

উত্তর

সঠিক উত্তর: গ

6 liters of 40% and 6 liters of 80%

গ

ব্যাখ্যা

Question: A chemist has two solutions, one containing 40% acid and the other containing 80% acid. How many liters of each solution should be mixed to get 12 liters of a solution containing 60% acid?

Solution:
Let x liters of 40% solution be used. Then (12 - x) liters of 80% solution will be used.

According to the problem:

40% × x + 80% × (12 - x) = 60% × 12
⇒ 40x + 80(12 - x) = 720
⇒ 40x + 960 - 80x = 720
⇒ -40x + 960 = 720
⇒ -40x = -240
⇒ x = 6

∴ 6 liters of 40% solution and 6 liters of 80% solution are needed.

১,৭১৬.

A boat travels upstream from Q to P and downstream from P to Q in 3 hours. If the distance between P to Q is 4km and the speed of the stream is 1kmph, then what is the velocity of the boat in still water?

ক
3 km/hr
খ
4 km/hr
গ
5 km/hr
ঘ
7.2 km/hr

সঠিক উত্তর: ক

3 km/hr

উত্তর

সঠিক উত্তর: ক

3 km/hr

ক

ব্যাখ্যা

Let the velocity or speed of the boat in still water is x km/hr.
And the Speed of the stream = 1km/hr

So, the speed of the boat along the stream = (x+1) km/hr.
The speed of the boat against the stream = (x-1) km/hr.

Note: time = Distance/Speed

So, [4/(x + 1)] + [4/(x - 1)] = 3 hrs.
⇒ [4 (x + 1 + x - 1)]/[(x + 1) (x - 1)] = 3
⇒ 8x = 3(x² - 1)
⇒ 8x = 3x² - 3
⇒ 3x² - 8x - 3=0
⇒ 3x² - 9x + x - 3 = 0
⇒ (x - 3) (3x + 1) = 0
Therefore x = 3 or, x = -1/3 (speed can't be -ve)

∴ Hence, the speed or velocity of the boat in still water is 3 km/hr.

১,৭১৭.

In how many ways can 5 letters be posted in 4 letter boxes?

ক
ক) 512
খ
খ) 1024
গ
গ) 625
ঘ
ঘ) 20
ঙ
ঙ) None of these

সঠিক উত্তর: খ

খ) 1024

উত্তর

সঠিক উত্তর: খ

খ) 1024

খ

ব্যাখ্যা

First letter can be posted in 4 letter boxes in 4 ways.
Similarly the second letter can be posted in 4 letter boxes in 4 ways and so on.
Hence all the 5 letters can be posted in = 4 x 4 x 4 x 4 x 4 = 1024

১,৭১৮.

If x - 1/x = - √3, then x⁴ + 1/x⁴ =?

ক
23
খ
27
গ
3
ঘ
9

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: If x - 1/x = - √3, then x⁴ + 1/x⁴ =?

Solution:
Given that,
x - 1/x = - √3
⇒ (x - 1/x)² = (- √3)²
⇒ x² + 1/x² - 2.x.(1/x) = 3
⇒ x² + 1/x² = 3 + 2
⇒ (x² + 1/x²)² = 5
⇒ (x²)² + (1/x²)² + 2.x².(1/x²) = 25
⇒ x⁴ + 1/x⁴ = 25 - 2
∴ x⁴ + 1/x⁴ = 23

১,৭১৯.

The ratio of a man's age to his son's age is 5 : 2, and the product of their ages is 490. What will the son's age be after 5 years?

ক
7 years
খ
12 years
গ
14 years
ঘ
19 years

সঠিক উত্তর: ঘ

19 years

উত্তর

সঠিক উত্তর: ঘ

19 years

ঘ

ব্যাখ্যা

Question: The ratio of a man's age to his son's age is 5 : 2, and the product of their ages is 490. What will the son's age be after 5 years?

Solution:
Let the man's age = 5x years
And, son's age = 2x years

∴ 5x × 2x = 490
⇒ 10x²= 490
⇒ x² = 49
⇒ x = 7

Son's age = 2 × 7 = 14 years
∴ Son's age after 5 years = 14 + 5 = 19 years

১,৭২০.

The side of an equilateral triangle is 4m. What is the height of the triangle?

ক
√3 m
খ
4√3 m
গ
3√3 m
ঘ
2√3 m

সঠিক উত্তর: ঘ

2√3 m

উত্তর

সঠিক উত্তর: ঘ

2√3 m

ঘ

ব্যাখ্যা

Question: The side of an equilateral triangle is 4m. What is the height of the triangle?

Solution:
Given,
The side of an equilateral triangle = 4m

We know,
Area of an equilateral triangle = (√3/4) × 4²
= (√3/4) × 16
= 4√3

Let,
the height of the triangle = h

We also know,
(1/2) × base × height = area
⇒ (1/2) × 4 × h = 4√3
⇒ h = (4√3 × 2)/4
∴ h = 2√3

So, the height of the triangle = 2√3 m

১,৭২১.

A tank is filled in 8 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?

ক
56 hours
খ
28 hours
গ
36 hours
ঘ
45 hours
ঙ
42 hours

সঠিক উত্তর: ক

56 hours

উত্তর

সঠিক উত্তর: ক

56 hours

ক

ব্যাখ্যা

Quesation: A tank is filled in 8 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?

Solution:
Suppose,
pipe A alone takes x hours to fill the tank. Then, pipes B and C will take (x/2) and (x/4) hours respectively to fill the tank.

Now,
⇒ (1/x) + (2/x) + (4/x) = 1/8
⇒ 7/x = 1/8
⇒ x = 56
∴ Pipe A alone takes 56 hours to fill the tank.

১,৭২২.

ধানে চাল ও তুষের অনুপাত 7 : 3 হলে, এতে শতকরা কী পরিমাণ চাল আছে?

ক
70%
খ
30%
গ
7%
ঘ
3%

সঠিক উত্তর: ক

70%

উত্তর

সঠিক উত্তর: ক

70%

ক

ব্যাখ্যা

প্রশ্ন: ধানে চাল ও তুষের অনুপাত 7 : 3 হলে, এতে শতকরা কী পরিমাণ চাল আছে?

সমাধান:
ধানের চাল ও তুষের অনুপাত 7 : 3
অনুপাতের যোগফল = 7 + 3 = 10

এতে শতকরা চালের পরিমাণ = (7/10) × 100%
= 70%

১,৭২৩.

If P = {x ∈ N : 2 < x ≤ 6} and Q = {x ∈ N : x even number and x ≤ 8} then what is the value of (P ∩ Q)?

ক
ক) {4, 8}
খ
খ) {4, 6}
গ
গ) {5, 6}
ঘ
ঘ) {2, 5}

সঠিক উত্তর: খ

খ) {4, 6}

উত্তর

সঠিক উত্তর: খ

খ) {4, 6}

খ

ব্যাখ্যা

Question: If P = {x ∈ N : 2 < x ≤ 6} and Q = {x ∈ N : x even number and x ≤ 8} then what is the value of (P ∩ Q)?

Solution:
দেওয়া আছে,
P = {x ∈ N : 2 < x ≤ 6}
∴ P = {3, 4, 5, 6}

Q = {x ∈ N : x জোড় সংখ্যা এবং x ≤ 8}
∴ Q = {2, 4, 6, 8}

এখন,
(P ∩ Q) = {3, 4, 5, 6} ∩ {2, 4, 6, 8}
= {4, 6}

১,৭২৪.

If (2^p + 1) is a prime number, which one of the following digits could be the value of p?

ক
3
খ
6
গ
5
ঘ
4

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

ব্যাখ্যা

Question: If (2^p + 1) is a prime number, which one of the following digits could be the value of p?

Solution:
In such questions, each alternative should be tried.

So, if P = 3, we will get; 8 + 1= 9

If P = 4, we will get; 16 + 1 = 17

If P = 5, we will get; 32 + 1 = 33

If P= 6, we will get; 64 + 1= 65

Out of the four results, only 17 is the prime number. So, the required value of the P is 4.

১,৭২৫.

What will be the difference between simple and compound interest at 5% on a sum of Tk. 8000 after 2 years?

ক
Tk. 20
খ
Tk. 25
গ
Tk. 32
ঘ
Tk. 50

সঠিক উত্তর: ক

Tk. 20

উত্তর

সঠিক উত্তর: ক

Tk. 20

ক

ব্যাখ্যা

Question: What will be the difference between simple and compound interest at 5% on a sum of Tk. 8000 after 2 years?

Solution:

দেওয়া আছে,
Principal, P = 8000 টাকা
Rate of interest, r = 5%
Time, n = 2 বছর

Simple Interest (SI):
SI = (P × r × n) / 100 = (8000 × 5 × 2) / 100 = 800 টাকা

Compound Interest (CI):
CI = P × (1 + r/100)ⁿ - P
= 8000 × (1 + 5/100)² - 8000
= 8000 × (1.05)² - 8000
= 8000 × 1.1025 - 8000
= 8820 - 8000 = 820 টাকা

∴ Difference between CI and SI:
= 820 - 800 = 20 টাকা

১,৭২৬.

If x + 1/x = 99, find the value of 100x/(2x² + 2 + 102x) is?

ক
1/6
খ
1/3
গ
1
ঘ
1/2

সঠিক উত্তর: খ

1/3

উত্তর

সঠিক উত্তর: খ

1/3

খ

ব্যাখ্যা

Question: If x + 1/x = 99, find the value of 100x/(2x² + 2 + 102x) is?

Solution:
x + 1/x = 99
(x² + 1)/x = 99
x² + 1 = 99x
2(x² + 1) = 99x × 2
2x² + 2 = 198x

100x/(2x²+ 2 + 102x) = 100x/(198x + 102x)
= 100x/300x
= 1/3

১,৭২৭.

The Average age of 20 students and a teacher is 15 years. When the teacher's age is excluded, the average decreases by 1. What is the age of the teacher?

ক
ক) 30 years
খ
খ) 35 years
গ
গ) 40 years
ঘ
ঘ) 50 years

সঠিক উত্তর: খ

খ) 35 years

উত্তর

সঠিক উত্তর: খ

খ) 35 years

খ

ব্যাখ্যা

Question: The Average age of 20 students and a teacher is 15 years. When the teacher's age is excluded, the average decreases by 1. What is the age of the teacher?

Solution:
20 boys + 1 teacher's total age is = 21 × 15 = 315 years
Without the teacher, 20 boys total age = 20 × (15 - 1) = 280 years

So, the teacher's age is = (315 - 280) years = 35 years

১,৭২৮.

In a class of 92 students, 40 are taking English, 24 are taking Arabic, and 10 are taking both courses. How many students are not enrolled in either course?

ক
26
খ
32
গ
38
ঘ
45

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: In a class of 92 students, 40 are taking English, 24 are taking Arabic, and 10 are taking both courses. How many students are not enrolled in either course?

Solution:
Total students = 92
Students taking English n(E) = 40
Students taking Arabic n(A) = 24
Students taking both English and Arabic = 10

We know,
n(E ∪ A) = n(E) + n(A) - n(E ∩ A)
n(E ∪ A) = 40 + 24 - 10 = 54

∴ Not enrolled = Total students - n(E ∪ A) = 92 - 54 = 38

১,৭২৯.

What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?

ক
ক) 814
খ
খ) 820
গ
গ) 840
ঘ
ঘ) 844

সঠিক উত্তর: ক

ক) 814

উত্তর

সঠিক উত্তর: ক

ক) 814

ক

ব্যাখ্যা

Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm.
Area of each tile = (41 x 41) cm².
Required number of tiles
= (1517 x 902) / (41 x 41)= 814.

১,৭৩০.

If tan3A = √3, then what is the value of A?

ক
ক) 60°
খ
খ) 40°
গ
গ) 30°
ঘ
ঘ) 20°

সঠিক উত্তর: ঘ

ঘ) 20°

উত্তর

সঠিক উত্তর: ঘ

ঘ) 20°

ঘ

ব্যাখ্যা

Question: If tan3A = √3, then what is the value of A?

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

১,৭৩১.

What is the probability that an integer selected at random from those between 10 and 100 inclusive is a multiple of 5 or 9?

ক
ক) 27/89
খ
খ) 90/91
গ
গ) 27/91
ঘ
ঘ) 23/89

সঠিক উত্তর: গ

গ) 27/91

উত্তর

সঠিক উত্তর: গ

গ) 27/91

গ

ব্যাখ্যা

প্রশ্ন: What is the probability that an integer selected at random from those between 10 and 100 inclusive is a multiple of 5 or 9?

সমাধান:
10 থেকে 100 এর মধ্যে 5 এর গুণিতক সংখ্যা গুলো হলো: 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100 = ১৯টি

10 থেকে 100 এর মধ্যে 9 এর গুণিতক সংখ্যা গুলো হলো: 18, 27, 36, 45, 54, 63, 72, 81, 90, 99 = 10টি
মোট গুণিতক = (19 + 10)টি = 29

45 ও 90 উভয়ের গুণিতক।
মোট অনুকূল ফলাফল = 29 - 2 = 27

10 থেকে 100 এর মধ্যে মোট সংখ্যা = 91টি

নির্ণেয় সম্ভাবনা = 27/91

১,৭৩২.

Three years ago the average age of a family of 5 members was 17 years. With the birth of a new baby, the average remains the same three even today. Find out the age of the baby.

ক
1 year
খ
2 years
গ
3 years
ঘ
4 years

সঠিক উত্তর: খ

2 years

উত্তর

সঠিক উত্তর: খ

2 years

খ

ব্যাখ্যা

Question: Three years ago the average age of a family of 5 members was 17 years. With the birth of a new baby, the average remains the same three even today. Find out the age of the baby.

Solution:
Three years ago the average age of a family of 5 members was 17 years.
∴ Total age of a family of 5 members was = 17 × 5 years
= 85 years

∴ Present age of 5 members = (85 + 3 × 5) years
= 100 years.

Present age of 5 members and a baby = 17 × 6 = 102 years.

∴ Age of the baby = (102 - 100) years = 2 years.

১,৭৩৩.

Two numbers are in ratio 4:5 and their LCM is 180. The smaller number is-

ক
ক) 9
খ
খ) 15
গ
গ) 36
ঘ
ঘ) 45

সঠিক উত্তর: গ

গ) 36

উত্তর

সঠিক উত্তর: গ

গ) 36

গ

ব্যাখ্যা

Numbers are in the ratio 4:5
Let the numbers be 4x and 5x
Hence, LCM = 20x
Hence, 20x = 180
Hence, x = 180/20 = 9
Hence the numbers are 36 and 45

১,৭৩৪.

How many 3-digit numbers can be formed from the digits 4, 6, 5, 9 and 2, which are divisible by 5 and none of the digits is repeated?

ক
12 ways
খ
8 ways
গ
20 ways
ঘ
36 ways

সঠিক উত্তর: ক

12 ways

উত্তর

সঠিক উত্তর: ক

12 ways

ক

ব্যাখ্যা

Question: How many 3-digit numbers can be formed from the digits 4, 6, 5, 9 and 2, which are divisible by 5 and none of the digits is repeated?

Solution:
We know,
the number will be divisible by 5 if the last number is 5.
So, first number can be chosen in = ⁴C₁ ways
= 4 ways

As the digit is not repeated
the second number can be chosen in = ³C₁
= 3 ways

∴ Total ways = 4 × 3 ways
= 12 ways

১,৭৩৫.

If the selling price is doubled, the profit triples, Find the profit percent.

ক
ক) 65.5%
খ
খ) 90.5%
গ
গ) 100%
ঘ
ঘ) 115%

সঠিক উত্তর: গ

গ) 100%

উত্তর

সঠিক উত্তর: গ

গ) 100%

গ

ব্যাখ্যা

Let cost price = x selling price = y
Then, profit = y − x
If selling price is doubled, selling price = 2y
profit = 2y − x

2y − x = 3 (y − x)
⇒ 2y − x = 3y − 3 x
⇒ y = 2x
profit = (y − x) = (2x − x) = x
∴ profit percent = (x × 100)/x = 100%

১,৭৩৬.

By selling a bicycle for Tk,3680 a shopkeeper gains 15%. If the profit is reduced to 8%, then the selling price will be:

ক
Tk. 2180
খ
Tk. 2700
গ
Tk. 3456
ঘ
Tk. 4000

সঠিক উত্তর: গ

Tk. 3456

উত্তর

সঠিক উত্তর: গ

Tk. 3456

গ

ব্যাখ্যা

Question: By selling a bicycle for Tk,3680 a shopkeeper gains 15%. If the profit is reduced to 8%, then the selling price will be:

Solution:
Let, cost price is = a
a + 15% of a = 3680
⇒ (100a + 15)/100 = 3680
⇒ 115a/100 = 3680
⇒ 1.5a = 3680
∴ a = 3200
So, Cost Price = 3200 Tk.

Now, Selling Price When profit remains at 8%,
= 3200 + 8% of 3200
= Tk. 3456

১,৭৩৭.

The ratio of milk and water in a solution is 20 : 7 and after adding 5 liters of water in it the ratio of milk and water becomes 5 : 3, then find the final amount of water in the final solution.

ক
ক) 7 liters
খ
খ) 10 liters
গ
গ) 11 liters
ঘ
ঘ) 12 liters

সঠিক উত্তর: ঘ

ঘ) 12 liters

উত্তর

সঠিক উত্তর: ঘ

ঘ) 12 liters

ঘ

ব্যাখ্যা

প্রশ্ন: The ratio of milk and water in a solution is 20 : 7 and after adding 5 liters of water in it the ratio of milk and water becomes 5 : 3, then find the final amount of water in the final solution.

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

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

∴ Final amount of water in solution = 7x + 5 = 7 + 5 = 12 liters.

১,৭৩৮.

Last year, Company Y earned p dollars in total profit. One-third of the profit was kept for reinvestment, and the remaining amount was divided equally among the company's 6 shareholders. In terms of p, how much did each shareholder receive?

ক
p/8
খ
2p/5
গ
p/6
ঘ
p/9

সঠিক উত্তর: ঘ

p/9

উত্তর

সঠিক উত্তর: ঘ

p/9

ঘ

ব্যাখ্যা

Question: Last year, Company Y earned p dollars in total profit. One-third of the profit was kept for reinvestment, and the remaining amount was divided equally among the company's 6 shareholders. In terms of p, how much did each shareholder receive?

Solution:
Here,
Company Y's profit is p dollars.

Amount kept for reinvestment = (1/3 of p)
= p/3

∴ Remaining Profit = p - p/3
= (3p - p)/3 = 2p/3

The remaining amount was divided among 6 shareholders.
∴ Each shareholder receives = (2p/3) ÷ 6
= (2p/3) × (1/6)
= p/9

১,৭৩৯.

The sum of 10 numbers is 462. If the average of their first 4 numbers is 52 and that of the last five is 38, then what is the 5th number?

ক
64
খ
58
গ
62
ঘ
56

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

প্রশ্ন: The sum of 10 numbers is 462. If the average of their first 4 numbers is 52 and that of the last five is 38, then what is the 5th number?

সমাধান:

The total of the first 4 numbers = 4 × 52 = 208

The total of the last 5 numbers = 5 × 38 = 190

The total of the (4 + 5 = 9) numbers = 208 + 190 = 398

∴ The 5th number = 462 - 398 = 64

১,৭৪০.

The salaries of A and B together amount to Tk. 2000. A spends 95% of his salary and B 85% of his. If now, their savings are the same, what is A’s salary?

ক
ক) Tk. 750
খ
খ) Tk. 1250
গ
গ) Tk. 1500
ঘ
ঘ) Tk. 1600

সঠিক উত্তর: গ

গ) Tk. 1500

উত্তর

সঠিক উত্তর: গ

গ) Tk. 1500

গ

ব্যাখ্যা

Let,
A's salary = Tk. x.
Then, B's salary = Tk. (2000 - x)
According to the question,
(100 - 95)% of A = (100 - 85)% of B
⇒ (5x/100) = (15/100) × (2000 - x)
⇒ x = 1500.

১,৭৪১.

If f(x) = x² - 5x + 6 and f(x) = 0 then, x = ?

ক
2, 3
খ
3, 5
গ
1, 3
ঘ
2, 5

সঠিক উত্তর: ক

2, 3

উত্তর

সঠিক উত্তর: ক

2, 3

ক

ব্যাখ্যা

Question: If f(x) = x² - 5x + 6 and f(x) = 0 then, x = ?

Solution:
Given,
f(x) = x² - 5x + 6
and f(x) = 0

∴ x² - 5x + 6 = 0
⇒ x² - 2x - 3x + 6 = 0
⇒ x(x - 2) - 3(x - 2) = 0
⇒ (x - 2)(x - 3) = 0

Here,
x - 2 = 0
⇒ x = 2

or,
x - 3 = 0
⇒ x = 3

১,৭৪২.

A tank is filled in 8 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?

ক
ক) 36 hours
খ
খ) 56 hours
গ
গ) 46 hours
ঘ
ঘ) 52 hours

সঠিক উত্তর: খ

খ) 56 hours

উত্তর

সঠিক উত্তর: খ

খ) 56 hours

খ

ব্যাখ্যা

Let
Pipe A can fill the tank in x hours. Then,
Pipe B can fill the tank in x/2 hours,
Pipe C can fill the tank in x/4 hours.

Part filled by pipe A in 1 hour = 1/x
Part filled by pipe B in 1 hour = 2/x
Part filled by pipe C in 1 hour = 4/x

Now
1/x + 2/x + 4/x = 1/8
(1 + 2 + 4)/x = 1/8
7/x = 1/8
x = 56 hours

১,৭৪৩.

Which amount to be received after 4 years at the rate of 6% p.a of simple interest on a sum of Tk. 5700?

ক
Tk. 7068
খ
Tk. 6068
গ
Tk. 8250
ঘ
Tk. 7360
ঙ
None of these

সঠিক উত্তর: ক

Tk. 7068

উত্তর

সঠিক উত্তর: ক

Tk. 7068

ক

ব্যাখ্যা

Question: Which amount to be received after 4 years at the rate of 6% p.a of simple interest on a sum of Tk. 5700?

Solution:
Given that,
Rate of interest, r = 6%
Principal, P = 5700
time, n = 4 years

∴ Simple interest, I = prn/100
= (5700 × 6 × 4)/100
= 1368

So Total Amount = Principal + Simple interest = 5700 + 1368 = 7068 Tk

১,৭৪৪.

1 + 0.1 + 0.01 + 0.001 +......... =?

ক
9/10
খ
15/7
গ
10/9
ঘ
11/9

সঠিক উত্তর: গ

10/9

উত্তর

সঠিক উত্তর: গ

10/9

গ

ব্যাখ্যা

Question: 1 + 0.1 + 0.01 + 0.001 +......... =?

Solution:
1 + 0.1 + 0.01 + 0.001 +.........
= 1 + (1/10) + (1/100) + (1/1000) +....

প্রথম পদ a = 1
সাধারণ অনুপাত r = 1/10

সমষ্টি = a/(1 - r)
= 1/{1 - (1/10)}
= 1/9/10
= 10/9

১,৭৪৫.

In how many different ways can the letter of the word JUDGE be arranged in such a ways that the vowels always come together?

ক
ক) 48
খ
খ) 96
গ
গ) 120
ঘ
ঘ) 140

সঠিক উত্তর: ক

ক) 48

উত্তর

সঠিক উত্তর: ক

ক) 48

ক

ব্যাখ্যা

The word 'JUDGE' has 5 letters in which 'JDG' are consonants and 'UE' are vowels.
On keeping vowels together, we get JDG(UE)
∴ Number of arrangements = 4! × 2 !
=24 × 2
= 48

১,৭৪৬.

What is the largest four-digit number that is exactly divisible by 15, 20, 25, and 30?

ক
9900
খ
9936
গ
9945
ঘ
9972

সঠিক উত্তর: ক

9900

উত্তর

সঠিক উত্তর: ক

9900

ক

ব্যাখ্যা

Question: What is the largest four-digit number that is exactly divisible by 15, 20, 25, and 30?

Solution:
Greatest 4-digit number is 9999.
L.C.M. of 15, 20, 25 and 30 = 300.

On dividing 9999 by 300 the remainder is 99
(because 300 × 33 = 9900 and 9999 - 9900 = 99).

∴ Required number = 9999 - 99 = 9900.

১,৭৪৭.

The value of 0.1 x 0.1 is-

ক
ক) 0.1
খ
খ) 1
গ
গ) 0.01
ঘ
ঘ) 0.001

সঠিক উত্তর: গ

গ) 0.01

উত্তর

সঠিক উত্তর: গ

গ) 0.01

গ

ব্যাখ্যা

0.1 x 0.1= 0.01

১,৭৪৮.

SUNDAY, MONDAY, WEDNESDAY, SATURDAY, WEDNESDAY
Which day comes next?

ক
SUNDAY
খ
MONDAY
গ
WEDNESDAY
ঘ
SATURDAY

সঠিক উত্তর: খ

MONDAY

উত্তর

সঠিক উত্তর: খ

MONDAY

খ

ব্যাখ্যা

Question: SUNDAY, MONDAY, WEDNESDAY, SATURDAY, WEDNESDAY
Which day comes next?

Solution:
SUNDAY
SUNDAY + 1 = MONDAY
MONDAY + 2 = WEDNESDAY
WEDNESDAY + 3 = SATURDAY
SATURDAY + 4 = WEDNESDAY
WEDNESDAY + 5 = MONDAY

১,৭৪৯.

If the radius of a circle is increased by 100%, by what % is the area of the circle increased?

ক
100%
খ
200%
গ
300%
ঘ
400%

সঠিক উত্তর: গ

300%

উত্তর

সঠিক উত্তর: গ

300%

গ

ব্যাখ্যা

Question: If the radius of a circle is increased by 100%, by what % is the area of the circle increased?

Solution:
ধরি,
বৃত্তের ব্যাসার্ধ, r = 10
∴ বৃত্তের ক্ষেত্রফল = πr²
= π (10)²
= 100π

আবার,
বৃত্তের ব্যাসার্ধ 100% বৃদ্ধিতে,
বৃত্তের নতুন ব্যাসার্ধ = 10 + 10 এর 100%
= 10 + 10 এর 100/100
= 20
∴ বৃত্তের নতুন ক্ষেত্রফল = πr²
= π (20)²
= 400π

∴ ক্ষেত্রফল বৃদ্ধি পায় = 400π - 100π
= 300π

100π থেকে ক্ষেত্রফল বৃদ্ধি পায় = 300π
1 থেকে ক্ষেত্রফল বৃদ্ধি পায় = 300π/100π
∴ 100 থেকে ক্ষেত্রফল বৃদ্ধি পায় = (300π × 100)/100π
= 300%

∴ বৃত্তের ক্ষেত্রফল শতকরা 100% বৃদ্ধি পায়

১,৭৫০.

405 sweets were distributed equally among children in such a way that the number of sweets received by each child is 20% of the total number of children. How many sweets did each child receive?

ক
9
খ
3
গ
10
ঘ
5
ঙ
8

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Let Children = X

A/Q,

405/X = 20% of X

Or, X2 = 2025

Or, x = 45

So each children receive = 405/45

= 9

১,৭৫১.

Find the number that should be placed in the gap of the series : 80, 96, _______, 128

ক
88
খ
120
গ
112
ঘ
64

সঠিক উত্তর: গ

112

উত্তর

সঠিক উত্তর: গ

112

গ

ব্যাখ্যা

Question: Find the number that should be placed in the gap of the series : 80, 96, _______, 128

Solution:
80 + 16 = 96
96 + 16 = 112
112 + 16 = 128

১,৭৫২.

A corporation declares an annual dividend of 5%. Mugdho owns 500 shares (par value Tk. 80). How much dividend will he receive?

ক
Tk. 1500
খ
Tk. 1600
গ
Tk. 2000
ঘ
None of these

সঠিক উত্তর: গ

Tk. 2000

উত্তর

সঠিক উত্তর: গ

Tk. 2000

গ

ব্যাখ্যা

Question: A corporation declares an annual dividend of 5%. Mugdho owns 500 shares (par value Tk. 80). How much dividend will he receive?

Solution:
Amount of total shares = 500 × 80 = Tk. 40000

From Tk. 100 Mugdho gets dividends Tk. 5
From Tk. 1 Mugdho gets dividends Tk. 5/100
From Tk. 40000 Mugdho gets dividends Tk. (5 × 40000)/100
= Tk. 2000

১,৭৫৩.

The sum of the two numbers is 22. Five times one number is equal to 6 times the other. The bigger of the two numbers is:

ক
10
খ
12
গ
15
ঘ
16

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: The sum of the two numbers is 22. Five times one number is equal to 6 times the other. The bigger of the two numbers is:

Solution:
Let,
The required number are x and y

Now
x + y = 22...........(1)

Five times one number is equal to 6 times the other,
5x = 6y
x = 6y/5..............(2)

(1)⇒
6y/5 + y = 22
(6y + 5y)/5 = 22
11y/5 = 22
y/5 = 2
y = 10

(2)⇒
x = (6 × 10)/5
x = 12

১,৭৫৪.

One year ago, the ratio of Hemal and Pavel ages was 2 : 3 respectively. After five years from now, this ratio becomes 4 : 5. How old is Pavel now?

ক
5 years
খ
25 years
গ
10 years
ঘ
15 years
ঙ
None of these

সঠিক উত্তর: গ

10 years

উত্তর

সঠিক উত্তর: গ

10 years

গ

ব্যাখ্যা

Question: One year ago, the ratio of Hemal and Pavel ages was 2 : 3 respectively. After five years from now, this ratio becomes 4 : 5. How old is Pavel now?

Solution:

We are given that age ratio of Hemal : Pavel = 2: 3

Hemal’s age = 2x and Pavel’s age = 3x

One year ago, their age was 2x and 3x.

Hence at present,
Hemal's age = 2x +1 and
Pavel's age = 3x +1

After 5 years,
Hemal’s age = (2x +1) + 5 = (2x + 6)

Pavel's age = (3x +1) + 5 = (3x + 6)

After 5 years, this ratio becomes 4 : 5.
Therefore,

(2x + 6)/(3x + 6) = 4/5

⇒ 10x + 30 = 12x + 24
⇒ 2x = 6
∴ x = 3

Pavel's present age = (3x + 1) = (3 × 3 + 1) = 10 years

১,৭৫৫.

A certain club has 237 local branches, one national office, and one social service office. If each local branch has 2 officers, and each of the two other offices has 4 officers, how many officers does the club have altogether?

ক
482
খ
476
গ
474
ঘ
239
ঙ
235

সঠিক উত্তর: ক

482

উত্তর

সঠিক উত্তর: ক

482

ক

ব্যাখ্যা

Question: A certain club has 237 local branches, one national office, and one social service office. If each local branch has 2 officers, and each of the two other offices has 4 officers, how many officers does the club have altogether?

Solution:
237 × 2 + 1 × 4 + 1 × 4
= 474 + 4 + 4
= 482

১,৭৫৬.

ক
1.2
খ
2.2
গ
3.2
ঘ
None of the avobe

সঠিক উত্তর: ক

1.2

উত্তর

সঠিক উত্তর: ক

1.2

ক

ব্যাখ্যা

Question:

Solution:

১,৭৫৭.

The LCM and ratio of four numbers are 630 and 2 : 3 : 5 : 7 respectively. The difference between the greatest and least numbers is = ?

ক
ক) 15
খ
খ) 18
গ
গ) 21
ঘ
ঘ) 24

সঠিক উত্তর: ক

ক) 15

উত্তর

সঠিক উত্তর: ক

ক) 15

ক

ব্যাখ্যা

Let the numbers be 2x, 3x, 5x and 7x respectively
Then their L.C.M. = (2 × 3 × 5 × 7)x = 210x.[∴ 2, 3, 5, 7 are prime numbers]
So, 210x = 630 or x = 3
∴ The numbers are 6, 9, 15 and 21
Required difference = 21 - 6 = 15
======================
মনে করি, সংখ্যাগুলো ২ক, ৩ক, ৫ক ও ৭ক
তাদের লসাগু = (২ × ৩ × ৫ × ৭)ক = ২১০ক
∴ ২১০ক = ৬৩০
⇒ ক = ৩
অতএব, সংখ্যাগুলো ৬, ৯, ১৫ ও ২১
নির্ণেয় পার্থক্য = ২১ - ৬ = ১৫

১,৭৫৮.

The present age of three persons are in the proportion of 4 : 7 : 9. Eight years ago, the sum of their ages was 56 years. The present age of the youngest person is -

ক
16
খ
28
গ
36
ঘ
12

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: The present age of three persons are in the proportion of 4 : 7 : 9. Eight years ago, the sum of their ages was 56 years. The present age of the youngest person is -

Solution:
Let, present ages of three persons 4x, 7x, 9x

Eight years ago, the sum of their ages was 56 years
At present, the sum of their ages is = 56 + 8 + 8 + 8
= 56 + 24 years
= 80 years

Here,
4x + 7x + 9x = 80
⇒ 20x = 80
⇒ x = 4

The present age of the youngest person is = 4 × 4 = 16 years

১,৭৫৯.

Two boys start from the same place walking at the rate of 5 kmph and 5.5 kmph respectively in the same direction. What time will they take to be 8.5 km apart?

ক
17 hr
খ
12 hr
গ
19 hr
ঘ
14 hr

সঠিক উত্তর: ক

17 hr

উত্তর

সঠিক উত্তর: ক

17 hr

ক

ব্যাখ্যা

Relative speed = 5.5 - 5
= 0.5 kmph (because they walk in the same direction)
Distance = 8.5 km
Time = Distance/Speed
= 8.5/0.5
= 17 hr.

১,৭৬০.

Two trains 180 m and 170 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:

ক
ক) 10.8 sec
খ
খ) 12.6 sec
গ
গ) 11.8 sec
ঘ
ঘ) 13.4 sec

সঠিক উত্তর: খ

খ) 12.6 sec

উত্তর

সঠিক উত্তর: খ

খ) 12.6 sec

খ

ব্যাখ্যা

Relative speed = (60 + 40) km/hr
= 100 km/hr
= 100 × (5/18) m/sec
= 250/9 m/sec

Distance covered in crossing each other = (180 + 170) m = 350 m

Required time = 350 × (9/250)
= 12.6 sec

১,৭৬১.

Alam sold two vehicles for Tk 46000 each. If he gained 10% on the first and lost 10% on another, then what is his percentage profit or loss in this transaction?

ক
ক) 2% loss
খ
খ) 1% profit
গ
গ) 1% loss
ঘ
ঘ) None of these

সঠিক উত্তর: গ

গ) 1% loss

উত্তর

সঠিক উত্তর: গ

গ) 1% loss

গ

ব্যাখ্যা

Let the profit be X% and loss be Y% . So,
Net profit or loss% = X + (-Y) + X×(-Y)/100
(Negative sign denotes that their is a loss)
Their is 10% loss and 10% profit then
∴ Net profit or loss% = 10 + (-10) + 10×(-10)/100
= 10 - 10 -100/100
= -1
∴ the net loss is 1%

১,৭৬২.

A sells an article which cost him TK.400 to B at a profit of 20%. B then sells it to C, making a profit 10% on the price he paid to A. How much does C pay B?

ক
ক) TK. 472
খ
খ) Tk. 476
গ
গ) Tk. 528
ঘ
ঘ) Tk. 532

সঠিক উত্তর: গ

গ) Tk. 528

উত্তর

সঠিক উত্তর: গ

গ) Tk. 528

গ

ব্যাখ্যা

'A' sells an article, which costs him Tk 400, to B at a profit of 20%.
profit of A = 400 × 20/100 = Tk 80
Cost Price for B = 400 + 80 = Tk 480
B then sells it to C, making a profit of 10% on the price he paid to A
Profit for B = 480 × 10/100 = Tk 48
Cost Price for C = 480 + 48 = Tk 528
Thus C pays Tk 528 to B.

১,৭৬৩.

ΔABC is a triangle where AB is perpendicular to BC. Which equation is true?

ক
ক) AB² = AC² + BC²
খ
খ) BC² = AB² + AC²
গ
গ) AC² = AB² - BC²
ঘ
ঘ) AC² = AB² + BC²

সঠিক উত্তর: ঘ

ঘ) AC² = AB² + BC²

উত্তর

সঠিক উত্তর: ঘ

ঘ) AC² = AB² + BC²

ঘ

ব্যাখ্যা

Question: ΔABC is a triangle where AB is perpendicular to BC. Which equation is true?

Solution:

so,
AC² = AB² + BC²

১,৭৬৪.

In an examination, a student's average marks was 63. If he had obtained 20 more marks for Geography and 2 more marks for History, his average would have been 65. How many subjects were there in the examination?

ক
14
খ
12
গ
11
ঘ
13

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Let the number of subjects = x
Total marks = 63x
If he had obtained 20 more marks for Geography and 2 more marks for history, his average would have been 65. That is, in this case, the total marks would have been 65x
Now we have,
65x - 63x = 20 + 2
⇒ 2x = 22
⇒ x = 11.

১,৭৬৫.

The ratio of milk and water in a solution is 20 : 7 and after adding 5 liters of water in it the ratio of milk and water becomes 5 : 3, then find the final amount of water in the final solution.

ক
9 litres
খ
10 litres
গ
11 litres
ঘ
12 litres

সঠিক উত্তর: ঘ

12 litres

উত্তর

সঠিক উত্তর: ঘ

12 litres

ঘ

ব্যাখ্যা

Question: The ratio of milk and water in a solution is 20 : 7 and after adding 5 liters of water in it the ratio of milk and water becomes 5 : 3, then find the final amount of water in the final solution.

Solution:
Let the initial amount of milk be 20x and of water 7x.
Ratio of milk and water after adding 5 litres,
20x/ (7x + 5) = 5/3
⇒ 60x = 35x + 25
⇒ 25x = 25
⇒ x = 1.

∴ Final amount of water in solution = 7x + 5 = 7 + 5 = 12 litres.

১,৭৬৬.

In how many ways can the letters of the word 'ENGINEERING' be arranged such that the first letter is always 'R'?

ক
22,700
খ
25,200
গ
27000
ঘ
30,240

সঠিক উত্তর: খ

25,200

উত্তর

সঠিক উত্তর: খ

25,200

খ

ব্যাখ্যা

Question: In how many ways can the letters of the word 'ENGINEERING' be arranged such that the first letter is always 'R'?

Solution:
'ENGINEERING' শব্দটিতে মোট 11টি বর্ণ রয়েছে।

শর্ত: প্রথম স্থানে 'R' স্থির।
এখন বাকি 11 - 1 = 10টি স্থানে বাকি বর্ণগুলোকে সাজাতে হবে।
বাকি 10টি বর্ণের মধ্যে পুনরাবৃত্ত অক্ষর:
E (3 বার), N (3 বার), G (2 বার), I (2 বার)।

∴ বাকি ১০টি বর্ণের বিন্যাস সংখ্যা = 10!/(3! × 3! × 2! × 2!)
= 3,628,800/(6 × 6 × 2 × 2)
= 3,628,800/144
= 25,200

∴ প্রথম অক্ষর 'R' রেখে 'ENGINEERING' শব্দটির বিন্যাস সংখ্যা হলো 25,200.

১,৭৬৭.

A man purchased a cow for Tk. 3000 and sold it the same day for Tk. 3600, allowing the buyer a credit of 2 years. If the rate of interest be 10% per annum, then the man has a gain of :

ক
ক) 0%
খ
খ) 5%
গ
গ) 7.5%
ঘ
ঘ) 10%

সঠিক উত্তর: ক

ক) 0%

উত্তর

সঠিক উত্তর: ক

ক) 0%

ক

ব্যাখ্যা

Cost price = Tk 3000
Selling price = [{3600 × 100}/{100 + (10 × 2)}]
= Tk. 3000
Gain = 0%.

১,৭৬৮.

Two pipes A and B can fill a tank in 25 and 50 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?

ক
50/3 minutes
খ
47/3 minutes
গ
53/3 minutes
ঘ
44/3 minutes

সঠিক উত্তর: ক

50/3 minutes

উত্তর

সঠিক উত্তর: ক

50/3 minutes

ক

ব্যাখ্যা

Question: Two pipes A and B can fill a tank in 25 and 50 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?

Solution:
pipe A fill a tank in 25 minutes
so, it fills in one minute (1/25) part

pipe B fill a tank in 50 minutes
so, it fills in one minute (1/50) part

both pipes fill in one minute = (1/25) + (1/50) part
= 3/50 part

So, it will take to fullfill the tank = 1/(3/50) minutes
= 50/3 minutes

১,৭৬৯.

A batsman made 100 runs including 10 boundaries and 5 sixes. What percentage of his runs were made by running between the wickets?

ক
15%
খ
20%
গ
30%
ঘ
35%

সঠিক উত্তর: গ

30%

উত্তর

সঠিক উত্তর: গ

30%

গ

ব্যাখ্যা

Question: A batsman made 100 runs including 10 boundaries and 5 sixes. What percentage of his runs were made by running between the wickets?

Solution:
Given,
Runs from 4s = 10 × 4 = 40
Runs from 6s = 5 × 6 = 30
Total from boundaries = 40 + 30 = 70

Runs by running between the wickets = 100 - 70 = 30

∴ Percent = 30/100 × 100
= 30%

১,৭৭০.

9³ × (81)² ÷ (27)³ = (3)^?

ক
ক) 3
খ
খ) 5
গ
গ) 4
ঘ
ঘ) 6

সঠিক উত্তর: খ

খ) 5

উত্তর

সঠিক উত্তর: খ

খ) 5

খ

ব্যাখ্যা

Question: 9³ × (81)² ÷ (27)³ = (3)^?

Solution:
ধরি,
9³ × (81)² ÷ (27)³ = (3)^x
⇒ (3²)³ × (3⁴)² ÷ (3³)³ = 3^x
⇒ (3⁶× 3⁸) ÷ 3⁹ = 3^x
⇒ 3^{6 + 8} ÷ 3⁹ = 3^x
⇒ 3¹⁴ ÷ 3⁹ = 3^x
⇒ 3^{14 - 9} = 3^x
⇒ 3^x = 3⁵
∴ x = 5

১,৭৭১.

ক
ক) 7/16
খ
খ) 2/7
গ
গ) 2/11
ঘ
ঘ) 2/16

সঠিক উত্তর: ক

ক) 7/16

উত্তর

সঠিক উত্তর: ক

ক) 7/16

ক

ব্যাখ্যা

দেওয়া আছে,
1/y = 7/2
=> y = 2/7

1/ (y + 2)
= 1/ (2/7 + 2)
= 1/(16/7)
= 7/16

১,৭৭২.

If 5x - (5/x) = 15, then what is the value of x³ - (1/x)³?

ক
27
খ
36
গ
52
ঘ
49

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

প্রশ্ন: If 5x - (5/x) = 15, then what is the value of x³ - (1/x)³?

সমাধান:
দেওয়া আছে,
5x - 5/x = 15
⇒ (5x - 5/x)/5 = 15/5
∴ x - 1/x = 3

এখন,
x³ - (1/x)³
= (x - 1/x)³ + 3 . x . (1/x)(x - 1/x)
= (x - 1/x)³ + 3(x - 1/x)
= 3³ + 3 × 3
= 27 + 9
= 36

১,৭৭৩.

One-fourth of the boys and three-eight of the girls in a school participated in the annual ports. What proportional part of the total student population of the school participated in the annual sports?

ক
ক) 4/12
খ
খ) 5/8
গ
গ) 8/12
ঘ
ঘ) None of these

সঠিক উত্তর: ক

ক) 4/12

উত্তর

সঠিক উত্তর: ক

ক) 4/12

ক

ব্যাখ্যা

মনেকরি
ছাত্রসংখ্যা 4জন এবং প্রতিযোগিতায় অংশ গ্রহণ করেছে 1 জন
ছাত্রী সংখ্যা 8 জন এবং প্রতিযোগিতায় অংশ গ্রহণ করেছে 3 জন
মোট ছাত্রছাত্রী = 4 + 8
=12 জন
মোট প্রতিযোগিতায় অংশ গ্রহণ করেছে= 1 + 3
= 4

প্রতিযোগিতায় ছাত্রছাত্রীদের 4/12 অংশ গ্রহণ করেছে।

১,৭৭৪.

If 8 workers can complete a task in 24 days, how many days will it take for 12 workers to complete the same task assuming they all work at the same rate?

ক
10 days
খ
16 days
গ
22 days
ঘ
8 days

সঠিক উত্তর: খ

16 days

উত্তর

সঠিক উত্তর: খ

16 days

খ

ব্যাখ্যা

Question: If 8 workers can complete a task in 24 days, how many days will it take for 12 workers to complete the same task assuming they all work at the same rate?

Solution:
8 workers can complete work in 24 days
∴ 1 worker can complete work in = 8 × 24 days
∴ 12 workers can complete work in = (8 × 24)/12 days
= 16 days

It will take 12 workers 16 days to complete the same task.

১,৭৭৫.

Two pipes A and B can fill the cistern in 10 hour and 12 hour respectively, while C can empty it in 20 hour. If all pipes are opened simultaneously, then the cistern will be filled in-

ক
19/2 hours
খ
17/2 hours
গ
15/2 hours
ঘ
13/2 hours
ঙ
11/2 hours

সঠিক উত্তর: গ

15/2 hours

উত্তর

সঠিক উত্তর: গ

15/2 hours

গ

ব্যাখ্যা

Question: Two pipes A and B can fill the cistern in 10 hour and 12 hour respectively, while C can empty it in 20 hour. If all pipes are opened simultaneously, then the cistern will be filled in-

Solution:
in one hour,
A can fill = 1/10
B can fill = 1/12
C can reduce = 1/20

So, in one-hour, total fill up = 1/10 + 1/12 - 1/20
= (6 + 5 - 3)/60
= 8/60
= 2/15

∴ 2/15 part fill up in 1 hour
∴ 1 part fill up in 15/2 hour

So, it will take 15/2 hours to fill the tank if all three pipes are opened together.

১,৭৭৬.

If both the length and the breadth of a rectangle are increased by 20%, what is the percentage increase in its area?

ক
40%
খ
36%
গ
42%
ঘ
None of these

সঠিক উত্তর: ঘ

None of these

উত্তর

সঠিক উত্তর: ঘ

None of these

ঘ

ব্যাখ্যা

Question: If both the length and the breadth of a rectangle are increased by 20%, what is the percentage increase in its area?

Solution:
Let the original length = x
and breadth = y
∴ Original area = x × y = xy

After 20% increase,
New length = x + 20% of x = x × (1 + 20/100)
= x × 1.2 = 1.2x
and new breadth = y × 1.2 = 1.2y

∴ New area = (1.2x) × (1.2y) = 1.44xy

∴ Increase in area = New area - Original area = 1.44xy - xy = 0.44xy

∴ Percentage increase in area = (Increase in area / Original area) × 100%
= (0.44xy/xy) × 100%
= 0.44 × 100%
= 44%

১,৭৭৭.

A father is three times as old as his son. After 12 years, he will be twice as old as his son. Find the father’s present age.

ক
36 years old
খ
42 years old
গ
38 years old
ঘ
26 years old

সঠিক উত্তর: ক

36 years old

উত্তর

সঠিক উত্তর: ক

36 years old

ক

ব্যাখ্যা

Question: A father is three times as old as his son. After 12 years, he will be twice as old as his son. Find the father’s present age.

Solution:
Let the son’s present age be x years.
Then, the father’s present age = 3x years.

After 12 years,
Son’s age = x + 12
Father’s age = 3x + 12

According to the question,
3x + 12 = 2(x + 12)
⇒ 3x + 12 = 2x + 24
⇒ 3x - 2x = 24 - 12
⇒ x = 12

∴ Father’s present age = 3 × 12 = 36 years.

১,৭৭৮.

The area of a triangle is 216 cm² and sides are in the ratio 3 : 4 : 5. The perimeter of the triangle is-

ক
12 cm
খ
36 cm
গ
72 cm
ঘ
144 cm

সঠিক উত্তর: গ

72 cm

উত্তর

সঠিক উত্তর: গ

72 cm

গ

ব্যাখ্যা

Question: The area of a triangle is 216 cm² and sides are in the ratio 3 : 4 : 5. The perimeter of the triangle is-

Solution:
3² + 4² = 5²

It is a right-angled triangle.
let, the sides 3x, 4x, 5x

(1/2) × 3x × 4x = 216
⇒ 12x2 = 432
⇒ x2 = 36
⇒ x = 6

perimeter = (3 × 6) + (4 × 6) + (4 × 6)
= 72 cm

১,৭৭৯.

How long will a boy take to run round a square field of side 35 meters, If he runs at the rate of 9 km/hr?

ক
ক) 56 sec
খ
খ) 45 sec
গ
গ) 39 sec
ঘ
ঘ) 25 sec

সঠিক উত্তর: ক

ক) 56 sec

উত্তর

সঠিক উত্তর: ক

ক) 56 sec

ক

ব্যাখ্যা

Speed = 9 km/hr = 9 x (5/18) m/sec = 5/2 m/sec
Distance = (35 x 4) m = 140 m
Time taken = 140 x (2/5) sec = 56 sec

১,৭৮০.

A train has a length of 150 metres. It is passing a man who is moving at 2 km/hr in the same direction of the train, in 3 seconds. Find out the speed of the train?

ক
ক) 169 km/hr
খ
খ) 182 km/hr
গ
গ) 152 km/hr
ঘ
ঘ) 180 km/hr
ঙ
ঙ) 108 km/hr

সঠিক উত্তর: খ

খ) 182 km/hr

উত্তর

সঠিক উত্তর: খ

খ) 182 km/hr

খ

ব্যাখ্যা

Length of the train = 150 m
Speed of the man = 2 km/hr
Relative speed = 150/3 = 50 m/s
= 50 × 18/5
= 180 km/hr
Relative speed = Speed of train - Speed of the man (as both are moving in the same direction).
Therefore,
Speed of the train = Relative speed + Speed of the man
= 180 + 2
= 182 km/hr

১,৭৮১.

An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:

ক
ক) 2%
খ
খ) 2.02%
গ
গ) 4%
ঘ
ঘ) 4.04%

সঠিক উত্তর: ঘ

ঘ) 4.04%

উত্তর

সঠিক উত্তর: ঘ

ঘ) 4.04%

ঘ

ব্যাখ্যা

100 cm is read as 102 cm.
A₁ = (100 x 100) cm² and A₂ (102 x 102) cm².
(A₂ - A₁) = [(102)² - (100)²]
= (102 + 100) x (102 - 100)
= 404 cm².
Percentage error =404/(100 x 100) x 100%= 4.04%

১,৭৮২.

If the area of the trapezium whose parallel sides are 6 cm and 10 cm is 32 sq. cm, then the distance between the parallel sides is:

ক
2 cm
খ
3 cm
গ
4 cm
ঘ
5 cm

সঠিক উত্তর: গ

4 cm

উত্তর

সঠিক উত্তর: গ

4 cm

গ

ব্যাখ্যা

Question: If the area of the trapezium whose parallel sides are 6 cm and 10 cm is 32 sq. cm, then the distance between the parallel sides is:

Solution:
Let the required distance be P cm
Then,
½ × (6 + 10) × P = 32
⇒ P = 4 cm

১,৭৮৩.

A man and a boy received Tk. 800 as wages for 5 days for the work they did together . The man's efficiency in the work was four times that of the boy. What are the daily wages of the boy?

ক
Tk. 50
খ
Tk. 44
গ
Tk. 32
ঘ
Tk. 28
ঙ
None

সঠিক উত্তর: গ

Tk. 32

উত্তর

সঠিক উত্তর: গ

Tk. 32

গ

ব্যাখ্যা

Question: A man and a boy received Tk. 800 as wages for 5 days for the work they did together . The man's efficiency in the work was four times that of the boy. What are the daily wages of the boy?

Solution:
Man's wage = 4 boy's wage
Daily wages for them = 800/5
= 160

(1 man + 1 boy) = (4 + 1) = 5 boys

5 boys wage = 160
∴ 1 boys wage = 160/5 = Tk. 32

the daily wages of the boy = Tk. 32

১,৭৮৪.

Nisha is 15 years elder to Romi. If 5 years ago, Nisha was 3 times as old as Romi, then find Nisha’s present age.

ক
32.5 years
খ
27.5 years
গ
25 years
ঘ
24.9 years

সঠিক উত্তর: খ

27.5 years

উত্তর

সঠিক উত্তর: খ

27.5 years

খ

ব্যাখ্যা

Question: Nisha is 15 years elder to Romi. If 5 years ago, Nisha was 3 times as old as Romi, then find Nisha’s present age.

Solution:

Let,
Age of Romi be y

Nisha is 15 years elder than Romi = (y + 15).
So Nisha's age 5 years ago = (y + 15 - 5).

Romi's age before 5 years = (y - 5)

5 years ago, Nisha is 3 times as old as Romi

(y + 15 - 5) = 3 (y - 5)

⇒ (y + 10) = (3y - 15)

⇒ 2y = 25
⇒ y = 12.5

Romi's age = 12.5 years

Nisha's age = (y + 15) = (12.5 + 15) = 27.5 years.

১,৭৮৫.

A rectangular block 6 cm by 12 cm by 15 cm is cut up into an exact number of equal cubes. Find the least possible number of cubes.

ক
ক) 30
খ
খ) 40
গ
গ) 50
ঘ
ঘ) 60

সঠিক উত্তর: খ

খ) 40

উত্তর

সঠিক উত্তর: খ

খ) 40

খ

ব্যাখ্যা

Volume of the block = (6 × 12 × 15) cm³
= 1080 cm³
Side of the largest cube
= H.C.F of 6 cm, 12 cm, 15 cm
= 3 cm.
Volume of this cube = (3 × 3 × 3) cm³
= 27 cm³
Number of cubes = 1080/27
= 40.

১,৭৮৬.

In a particular country, one person is born every 6 seconds while one person dies every 10 seconds. Based on these birth and death rates, the net increase in population is one person after how many seconds?

ক
20 seconds
খ
21 seconds
গ
15 seconds
ঘ
10 seconds
ঙ
5 seconds

সঠিক উত্তর: গ

15 seconds

উত্তর

সঠিক উত্তর: গ

15 seconds

গ

ব্যাখ্যা

Question: In a particular country, one person is born every 6 seconds while one person dies every 10 seconds. Based on these birth and death rates, the net increase in population is one person after how many seconds?

Solution:
Let,
x be the number of seconds for the population to increase by one person.

We know,
Population growth = Birth rate - Death rate

ATQ,
⇒ 1 person/6 seconds - 1 person/10 seconds = 1 person/x seconds
⇒ (5 - 3) person/30 seconds = 1 person/x seconds
⇒ 2 persons/30 seconds = 1 person/x seconds
⇒ 1 person/15 seconds = 1 person/x seconds

∴ x = 15 seconds

১,৭৮৭.

How many seconds will a 500 metre long train take to cross a man walking with a speed fo 3 km/ hr in the direction of the moving train if the speed of the train is 63 km/hr?

ক
25
খ
30
গ
40
ঘ
45

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: How many seconds will a 500 metre long train take to cross a man walking with a speed fo 3 km/ hr in the direction of the moving train if the speed of the train is 63 km/hr?

Solution:
Speed of the train =(63 - 3)km/hr
= 60km/hr
= (60 × 1000)/3600 m/sec
= 50/3

Time taken to pass the man = 500/(50/3) sec
= 500 × (3/50) sec
= 30 sec

১,৭৮৮.

If Aman and Bijoy together can complete a piece of work in 15 days and Bijoy alone in 20 days, in how many days can Aman alone complete the work?

ক
ক) 40 days
খ
খ) 50 days
গ
গ) 60 days
ঘ
ঘ) 65 days

সঠিক উত্তর: গ

গ) 60 days

উত্তর

সঠিক উত্তর: গ

গ) 60 days

গ

ব্যাখ্যা

Question: If Aman and Bijoy together can complete a piece of work in 15 days and Bijoy alone in 20 days, in how many days can Aman alone complete the work?

Solution:
Aman and Bijoy together can complete a piece of work in 15 days
Aman and Bijoy together can complete in 1 day = 1/15

Bijoy alone in 20 days
Bijoy alone in one day = 1/20

Aman complete in one day = (1/15) - (1/20)
= (4 - 3)/60
= 1/60

Aman can complete the work in 60 days

১,৭৮৯.

, what is the value of

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question:

, what is the value of

?

Solution:
Given that,
x = 2

Now,

= 5 × (2)² ×

১,৭৯০.

The sum of three numbers is 132. If the first number be twice the second and third number be one third of the first, then the second number is:

ক
ক) 32
খ
খ) 36
গ
গ) 48
ঘ
ঘ) 60
ঙ
ঙ) None of the above

সঠিক উত্তর: খ

খ) 36

উত্তর

সঠিক উত্তর: খ

খ) 36

খ

ব্যাখ্যা

Let 2nd = 3x,
therefore, 3x + 6x + 2x = 132, x = 12
so, 3x = 36

১,৭৯১.

Asma's age is 1/6th of her father's age. Asma's father's age will be twice of Bahar's age after 10 years. If Bahar's 8th birthday was celebrated 2 years ago, then what is Asma's present age?

ক
5 years
খ
7 years
গ
10 years
ঘ
None of these

সঠিক উত্তর: ক

5 years

উত্তর

সঠিক উত্তর: ক

5 years

ক

ব্যাখ্যা

Question: Asma's age is 1/6th of her father's age. Asma's father's age will be twice of Bahar's age after 10 years. If Bahar's 8th birthday was celebrated 2 years ago, then what is Asma's present age?

Solution:
Bahar's age after 10 years = (8 + 2 + 10) years = 20 years.

Asma's father's age after 10 years = 40 years.

Asma's father's present age = 30 years.

∴ Asma's present age = 30/6 = 5 years.

১,৭৯২.

A cake is divided into 24 pieces. Rahim takes 1/4 of the cake. Karim takes 1/3 of the rest. How many pieces are left?

ক
6
খ
8
গ
12
ঘ
10

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: A cake is divided into 24 pieces. Rahim takes 1/4 of the cake. Karim takes 1/3 of the rest. How many pieces are left?

Solution:
Given that,
A cake is divided into 24 pieces.

Now,
Rahim takes 1/4 of the cake = 24 × (1/4) = 6 pieces
So Rahim takes 6 pieces.
∴ Remaining after Rahim = 24 - 6 = 18 pieces

And
Karim takes 1/3 of the rest = 18 × (1/3) = 6 pieces

∴ Pieces left after Karim = 18 - 6 = 12 pieces

So, 12 pieces are still left.

১,৭৯৩.

Ashik and Ruby run a race with their speed in the ratio of 5 : 3. They prefer to run on a circular track of circumference 2 km. What is the distance covered by Ashik when he passes Ruby for the sixth time?

ক
10.25 km
খ
15 km
গ
22 km
ঘ
26.5 km
ঙ
30 km

সঠিক উত্তর: ঙ

30 km

উত্তর

সঠিক উত্তর: ঙ

30 km

ঙ

ব্যাখ্যা

Question: Ashik and Ruby run a race with their speed in the ratio of 5 : 3. They prefer to run on a circular track of circumference 2 km. What is the distance covered by Ashik when he passes Ruby for the sixth time?

Solution:
Since the speeds of Ashik and Ruby are in the ratio 5 : 3 i.e., when Ashik covers 5 rounds, then Ruby covers 3 rounds
∴ Relative speed = 5 – 3 = 2 parts
Now, the first time Ashik and Ruby meet, when Ashik completes (5/2 = 2.5) rounds, and Ruby completes 1/2 round.

∴ Ashik to pass Ruby for the sixth time, Ashik would have completed = (6 × 2.5) rounds
= 15 rounds

Since each round is 2 km,
Hence, the distance covered by Ashik = (15 × 2) km
= 30 km

১,৭৯৪.

If 0.75 : x :: 5 : 8, then x is equal to:

ক
1.25
খ
1.12
গ
1.2
ঘ
1.30

সঠিক উত্তর: গ

1.2

উত্তর

সঠিক উত্তর: গ

1.2

গ

ব্যাখ্যা

Question: If 0.75 : x :: 5 : 8, then x is equal to:

Solution:
0.75 : x :: 5 : 8
⇒ 0.75/x = 5/8
⇒ 5x = 0.75 × 8
⇒ 5x = 6
⇒ x = 6/5
∴ x = 1.2

১,৭৯৫.

The ratio of cost price and selling price is 6 : 8. The profit percent is

ক
33.33%
খ
28.57%
গ
30.50%
ঘ
34.34%
ঙ
25%

সঠিক উত্তর: ক

33.33%

উত্তর

সঠিক উত্তর: ক

33.33%

ক

ব্যাখ্যা

Question: The ratio of cost price and selling price is 6 : 8. The profit percent is

Solution:
Given,
the ratio of cost price (C.P.) to selling price (S.P.) is 6 : 8
Let the cost price be 6x and the selling price be 8x.

Profit = S.P - .C.P. = 8x - 6x = 2x
Profit percent = (Profit/CP) × 100
= (2x/6x) × 100
= (1/3) × 100
= 33.33%

১,৭৯৬.

Consider that w + x = – 4, x + y = 25 and y + w = 15, Then the average of w, x, y is ____

ক
ক) 3
খ
খ) 4
গ
গ) 5
ঘ
ঘ) 6

সঠিক উত্তর: ঘ

ঘ) 6

উত্তর

সঠিক উত্তর: ঘ

ঘ) 6

ঘ

ব্যাখ্যা

w + x + x + y + y + w = -4 + 25 + 15
⇒ 2 (w + x + y) = 36
⇒ w + x + y = 18
So, average of w, x, y = 18/3 = 6

১,৭৯৭.

The present age of Sumon is half that of Akib. After 5 years, the ratio of Sumon's age to that of Akib's age will be 6:11. Then the present age of Sumon and Akib will be?

ক
20,40
খ
25,50
গ
30,60
ঘ
35,45

সঠিক উত্তর: খ

25,50

উত্তর

সঠিক উত্তর: খ

25,50

খ

ব্যাখ্যা

Let x be Sumon's age, then Akib's age will be 2x
After 5 years their ages will be (x + 5) and (2x + 5) respectively.
Given that the ratio(after 5 Years) is = 6:11
According to the question,
6/11 = (x + 5)/(2x + 5)
⇒ 6(2x + 5) = 11(x + 5)
⇒ 12x + 30 = 11x + 55
⇒ x = 55 - 30
= 25
And 2x = 50
Hence the ages of Sumon and Akib will be 25 and 50.

১,৭৯৮.

What is the smallest number divisible by 3, 5 and 9 with remainder 2?

ক
135
খ
17
গ
45
ঘ
47

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

ব্যাখ্যা

Question: What is the smallest number divisible by 3, 5 and 9 with remainder 2?

Solution:
প্রদত্ত সংখ্যাগুলো দ্বারা বিভাজ্য ক্ষুদ্রতম সংখ্যা হবে সংখ্যাগুলোর ল. সা. গু।
তাহলে, ৩, ৫, ৯ এর ল. সা. গু এর সাথে ২ যোগ করলে ক্ষুদ্রতম সংখ্যাটি পাওয়া যাবে।

এখন,
৩ = ৩ × ১
৫ = ৫ × ১
৯ = ৩ × ৩

∴ ৩, ৫, ৯ এর ল. সা. গু = ৩ × ৩ × ৫ = ৪৫

নির্ণেয় ক্ষুদ্রতম সংখ্যা = (৪৫ + ২) = ৪৭

১,৭৯৯.

If a = 4, b = 5, c = 3, what is the value of 4ab - 6ac + 2bc?

ক
38
খ
182
গ
183
ঘ
22

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: If a = 4, b = 5, c = 3, what is the value of 4ab - 6ac + 2bc?

Solution:
দেওয়া আছে
a = 4, b = 5, c = 3

প্রদত্ত রাশি = 4ab - 6ac + 2bc
= 4 × 4 × 5 - 6 × 4 × 3 + 2 × 5 × 3
= 80 - 72 + 30
= 38

১,৮০০.

L.C.M. of two numbers is 2079 and their H.C.F. is 27. If one of the numbers is 189, the other number is :

ক
297
খ
584
গ
189
ঘ
216

সঠিক উত্তর: ক

297

উত্তর

সঠিক উত্তর: ক

297

ক

ব্যাখ্যা

Given,
H.C.F. = 27
L.C.M. = 2079
one number = 189
Let another number be y

We know,
Product of numbers = L.C.M. × H.C.F.
∴ 189 x y = 27 × 2079
y = 297.