Bank Math

PrepBank · পাতা ১৬ / ১৬১ · ১,৫০১–১,৬০০ / ১৬,১২৪

১,৫০১.

Asad went to the market to buy 12 oranges. But he found that he had the money to buy only 10 oranges. He calculated that if the price per piece of orange was TK. 3 less, he could have bought 12 oranges. How much money did Asad have?

ক
150
খ
160
গ
175
ঘ
180

সঠিক উত্তর: ঘ

180

উত্তর

সঠিক উত্তর: ঘ

180

ঘ

ব্যাখ্যা

Question: Asad went to the market to buy 12 oranges. But he found that he had the money to buy only 10 oranges. He calculated that if the price per piece of orange was Tk. 3 less, he could have bought 12 oranges. How much money did Asad have ?

Solution:
মনেকরি,
আসাদের ছিল = x টাকা

10টি কমলা কিনলে প্রতিটি কমলার দাম = x/10 টাকা

প্রশ্নমতে,
(x/10) - (x/12) = 3
(6x - 5x)/60 = 3
x/60 = 3
x = 180

আসাদের ছিল = 180 টাকা

১,৫০২.

The price of the sugar rise by 25%. If a family wants to keep their expenses on sugar the same as earlier, the family will have to decrease its consumption of sugar by-

ক
10%
খ
12%
গ
20%
ঘ
25%

সঠিক উত্তর: গ

20%

উত্তর

সঠিক উত্তর: গ

20%

গ

ব্যাখ্যা

Question: The price of the sugar rise by 25%. If a family wants to keep their expenses on sugar the same as earlier, the family will have to decrease its consumption of sugar by-

Solution:

২৫% বৃদ্ধিতে দাম = (১০০ + ২৫) = ১২৫টাকা।

১২৫ টাকায় চিনি খাওয়া কমে = ১২৫ - ১০০ = ২৫ টাকা

১ টাকায় চিনি খাওয়া কমে = ২৫/১২৫ টাকা

১০০ টাকায় চিনি খাওয়া কমে = (২৫ × ১০০)/১২৫
= ২০ টাকা

অর্থাৎ, শতকরা ২০% কমিয়েছিল

১,৫০৩.

A cricket team has a ratio of win to loss 4 : 3. After losing 5 games in a row, the team's ratio of win to loss became 9 : 8. How many games had the team loss before it played the last five games?

ক
24
খ
27
গ
30
ঘ
33
ঙ
35

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: A cricket team has a ratio of win to loss 4 : 3. After losing 5 games in a row, the team's ratio of win to loss became 9 : 8. How many games had the team loss before it played the last five games?

Solution:
মনে করি,
দলটির জেতা খেলার সংখ্যা ছিল 4p
দলটির হারা খেলার সংখ্যা ছিল 3p
পরপর 5 টি খেলা হারার পর,
জেতা খেলার সংখ্যা 4p
হারা খেলার নতুন সংখ্যা (3p + 5)

প্রশ্নমতে,
4p : (3p + 5) = 9 : 8
⇒ 4p/(3p + 5) = 9/8
⇒ 32p = 27p + 45
⇒ 32p - 27p = 45
⇒ 5p = 45
⇒ p = 45/5
⇒ p = 9
∴ p = 9

∴ ১ম অবস্থায় হারা খেলার সংখ্যা ছিল = 3 × 9 = 27
অতএব, শেষ 5 টি খেলা খেলার আগে দলটি 27 খেলায় হেরেছিল।

১,৫০৪.

An old man is walking on a foggy road at a speed of x km/hr. Due to low visibility, the old man see only up to 600 meters. If a car overtakes the man from behind with the speed of 15 km/hr then the man can see the car for 216 seconds. Find the speed of the man?

ক
4 km/hr
খ
5 km/hr
গ
8 km/hr
ঘ
10 km/hr

সঠিক উত্তর: খ

5 km/hr

উত্তর

সঠিক উত্তর: খ

5 km/hr

খ

ব্যাখ্যা

Question: An old man is walking on a foggy road at a speed of x km/hr. Due to low visibility, the old man see only up to 600 meters. If a car overtakes the man from behind with the speed of 15 km/hr then the man can see the car for 216 seconds. Find the speed of the man?

Solution:
Distance up to old man see = 600/1000 = 0.6 km
Time for which the man can see the car = 216/ (60 × 60) = 0.06 hour

ATQ,
0.6/(15 - x) = 0.06
⇒ 15 - x = 10
⇒ x = 5

Hence, the correct answer is 5 km/hr.

১,৫০৫.

If the average of m numbers is n² and the average of n numbers is m², find the average of all (m + n) numbers.

ক
mn
খ
m + n
গ
(m + n)/2
ঘ
m² + n²

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: If the average of m numbers is n² and the average of n numbers is m², find the average of all (m + n) numbers.

Solution:
Given that,
The average of m numbers is n²
Sum of m numbers = m⋅n²

And
The average of n numbers is m²
Sum of n numbers = n⋅m²

∴ Total sum = mn² + nm² = mn(m + n)

∴ Average = mn(m + n)/(m + n) = mn

১,৫০৬.

Which ratio will come next in the following series?
1 : 2, 3 : 6, 4 : 8, ?

ক
ক) 7: 21
খ
খ) 8 : 32
গ
গ) 6 : 8
ঘ
ঘ) 5 : 10

সঠিক উত্তর: ঘ

ঘ) 5 : 10

উত্তর

সঠিক উত্তর: ঘ

ঘ) 5 : 10

ঘ

ব্যাখ্যা

The given series is: 1 : 2, 3 : 6, 4 : 8, ?

The logic followed is:
All the quantities in the above series maintain the ratio of 1 : 2 with each other.

⇒ 1 : 2
⇒ 3 : 6 = 1 : 2
⇒ 4 : 8 = 1 : 2

Now, check from the options which option maintain the ratio of 1: 2 with each other.

1) 7 : 21 ⇒ 1 : 3

2) 8 : 32 ⇒ 1 : 4

3) 6 : 8 ⇒ 2 : 3

4) 5 : 10 ⇒ 1 : 2

Only option 4) maintains the ratio of 1 : 2 with each other.

Hence, the correct answer is "5 : 10".

১,৫০৭.

A, B, and C completed a work costing Tk 2250. A worked for 6 days, B for 4 days, and C for 9 days. If their daily wages are in the ratio of 5 : 6 : 4, how much will A receive?

ক
ক) 600 Tk
খ
খ) 620 Tk
গ
গ) 750 Tk
ঘ
ঘ) 800 Tk

সঠিক উত্তর: গ

গ) 750 Tk

উত্তর

সঠিক উত্তর: গ

গ) 750 Tk

গ

ব্যাখ্যা

Question: A, B, and C completed a work costing Tk 2250. A worked for 6 days, B for 4 days, and C for 9 days. If their daily wages are in the ratio of 5 : 6 : 4, how much will A receive?

Solution:
Let the daily wages of A, B, and C be Tk 5x, 6x, and 4x respectively.

Then, ratio of their amounts
=(5x × 6) : (6x × 4) : (4x × 9)
= 30 : 24 : 36
= 5 : 4 : 6

∴A's amount = 2250 × (5/15) = 750 Tk

১,৫০৮.

A barrel contains a mixture of wine and water in the ratio 3:1. How much fraction of the mixture must be drawn off and substituted by water so that the ratio of wine and water in the resultant mixture becomes 1:1 = ?

ক
ক) 1/4
খ
খ) 1/3
গ
গ) 3/4
ঘ
ঘ) 2/3

সঠিক উত্তর: খ

খ) 1/3

উত্তর

সঠিক উত্তর: খ

খ) 1/3

খ

ব্যাখ্যা

Original ratio of the mixture 3:1
Taking out the mixture actually means just taking out the wine because the water anyways is going to be added back.
If we remove 1 part of wine, it makes the ratio 2:2 (1 part water is added to keep the volume constant )
so, what we have actually done is remove 1 part wine from 3 part Wine. i.e. 1/3.
So, 1/3 mixture drawn.

১,৫০৯.

The present age of a father is four times the age of his daughter. After 5 years, the ratio of their ages will be 3 : 1. What is the present age of the father?

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

সঠিক উত্তর: খ

40 years

উত্তর

সঠিক উত্তর: খ

40 years

খ

ব্যাখ্যা

Question: The present age of a father is four times the age of his daughter. After 5 years, the ratio of their ages will be 3 : 1. What is the present age of the father?

Solution:
Let the daughter’s present age be x years.
Then father’s present age = 4x years.

After 5 years,
∴ (4x + 5)/(x + 5) = 3/1
⇒ 1(4x + 5) = 3(x + 5)
⇒ 4x + 5 = 3x + 15
⇒ 4x - 3x = 15 - 5
⇒ x = 10

∴ Present age of the father = 4x years
= 4 × 10
= 40 years

১,৫১০.

The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:

ক
286
খ
300
গ
322
ঘ
346

সঠিক উত্তর: গ

322

উত্তর

সঠিক উত্তর: গ

322

গ

ব্যাখ্যা

Question: The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:

Solution:
Let, the two numbers be 23 x and 23 y.
Since the other two factors of LCM are 13 and 14, the values of x and y are 13 and 14, respectively.
So, the largest number is 23y,
23y = 23 × 14 = 322

১,৫১১.

If P : 6 = Q : 8 = R : 10, then (P + Q + R)/P =?

ক
2
খ
3
গ
4
ঘ
5
ঙ
8

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: If P : 6 = Q : 8 = R : 10, then (P + Q + R)/P =?

Solution:
P : 6 = Q : 8
or, P/6 = Q/8
or, 6Q = 8P
or, Q = 8P/6
or, Q = 4P/3

P : 6 = R : 10
or, P/6 = R/10
or, 6R = 10P
or, R = 10P/6
or, R = 5P/3

∴ (P + Q + R)
= P + (4P/3) + (5P/3)
= (3P + 4P + 5P)/3
= 12P/3
= 4P

∴ (P + Q + R)/P
= 4P/P
= 4

১,৫১২.

Three workers can do a job in 12 days. Two of the workers work twice as fast as the third. How long would it take one of the faster workers to do the job alone?

ক
30
খ
35
গ
40
ঘ
42
ঙ
None of these

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Let, the first and 2nd worker need X days.
Third worker needs 2X days
ATQ, 1/X + 1/X + 1/2x = 1/12
or, (2 + 2 + 1)/2x = 1/12
or, x = 30

১,৫১৩.

Find the largest number -

ক
ক) 13/15
খ
খ) 16/17
গ
গ) 17/21
ঘ
ঘ) 21/25

সঠিক উত্তর: খ

খ) 16/17

উত্তর

সঠিক উত্তর: খ

খ) 16/17

খ

ব্যাখ্যা

• 13/15 = 0.87
• 16/17 = 0.94
• 17/21 = 0.81
• 21/25 = 0.84

১,৫১৪.

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
ঙ
None of these

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.

১,৫১৫.

In a bag, there are 5 red, 3 green, and 2 blue balls. If two balls are drawn one after the other without replacement, what is the probability that the first one is green and the second one is blue?

ক
1/15
খ
3/5
গ
2/3
ঘ
1/10

সঠিক উত্তর: ক

1/15

উত্তর

সঠিক উত্তর: ক

1/15

ক

ব্যাখ্যা

Question: In a bag, there are 5 red, 3 green, and 2 blue balls. If two balls are drawn one after the other without replacement, what is the probability that the first one is green and the second one is blue?

Solution:
মোট বলের সংখ্যা = 5 (লাল) + 3 (সবুজ) + 2 (নীল) = 10টি
প্রথম বলটি সবুজ হওয়ার সম্ভাবনা = 3/10
প্রথম বল তোলার পর বাক্সে বলের সংখ্যা = 10 - 1 = 9
দ্বিতীয় বলটি নীল হওয়ার সম্ভাবনা = 2/9

সুতরাং, প্রথমটি সবুজ ও দ্বিতীয়টি নীল হওয়ার সম্ভাবনা = (3/10) × (2/9)
= 6/90
= 1/15

১,৫১৬.

Joyanta started a business and he invested in 38000, After some month, Omar came to join with him and invest 28500. The end of the year the total profit was divided among them into ratio form 16 : 8. Find after how many months did Omar join.

ক
3
খ
4
গ
6
ঘ
8

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: Joyanta started a business and he invested in 38000, After some month, Omar came to join with him and invest 28500. The end of the year the total profit was divided among them into ratio form 16 : 8. Find after how many months did Omar join.

Solution:
we can assume that Omar join into business after x months.
So Omar money was invested for (12 - x) months.

(38000 × 12)/{28500 × (12 - x)} = 2/1 (The given ratio of 16 : 8 is equivalent to 2 :1)
⇒ 456000 = 28500(12 - x)
⇒ 456000 = 57000(12 - x)
⇒ 57(12 - x) = 456
⇒ 12 - x = 8
∴ x = 4

After 4 months Omar join the business.

১,৫১৭.

Find the smallest number of five digits exactly divisible by 16, 24, 36, and 54.

ক
9632
খ
10362
গ
10638
ঘ
10368

সঠিক উত্তর: ঘ

10368

উত্তর

সঠিক উত্তর: ঘ

10368

ঘ

ব্যাখ্যা

Question: Find the smallest number of five digits exactly divisible by 16, 24, 36, and 54.

Solution:
The smallest number of five digits is = 10000
The number must be divisible by the LCM of 16, 24, 36, and 54 = 432
On dividing 10000 by 432, we get 64 as the remainder.

So, required number is = 10000 + (432 - 64)
= 10000 + 368
= 10368

১,৫১৮.

Silver is 12 times as heavy as water, and lead is 8 times as heavy as water. In what ratio should these be mixed to get an alloy 9 times as heavy as water?

ক
1 : 4
খ
1 : 3
গ
2 : 3
ঘ
3 : 1

সঠিক উত্তর: খ

1 : 3

উত্তর

সঠিক উত্তর: খ

1 : 3

খ

ব্যাখ্যা

Question: Silver is 12 times as heavy as water, and lead is 8 times as heavy as water. In what ratio should these be mixed to get an alloy 9 times as heavy as water?

Solution:
Let silver be 12x times as heavy and lead 8y times as heavy as water.

12x + 8y = 9(x + y)
⇒ 12x + 8y = 9x + 9y
⇒ 12x - 9x = 9y - 8y
⇒ 3x = y
∴ x/y = 1/3 = 1 : 3

১,৫১৯.

An accurate clock shows 3:20 PM. How many degrees will the hour hand rotate from 3:20 PM to 11:50 PM on the same day?

ক
240°
খ
260°
গ
255°
ঘ
270°

সঠিক উত্তর: গ

255°

উত্তর

সঠিক উত্তর: গ

255°

গ

ব্যাখ্যা

Question: An accurate clock shows 3:20 PM. How many degrees will the hour hand rotate from 3:20 PM to 11:50 PM on the same day?

Solution:
Given that,
From 3 : 20 PM to 11 : 20 PM = 8 hours
And from 11 : 20 PM to 11 : 50 PM = 30 minutes
∴ Total time = 8 hours 30 minutes

Now,
30 minutes = 30/60 = 0.5 hours
∴ Total time = 8 + 0.5 = 8.5 hours

We know,
The hour hand moves 360° in 12 hours.
∴ Speed of hour hand = 360°/12 = 30° per hour

∴ Degrees rotated by hour hand = 8.5 × 30° = 255°

So the hour hand will rotate 255°.

১,৫২০.

The next number in the sequence 1, 2, 3, 5, 8, 13, 21, ____ is-

ক
ক) 34
খ
খ) 36
গ
গ) 38
ঘ
ঘ) 40

সঠিক উত্তর: ক

ক) 34

উত্তর

সঠিক উত্তর: ক

ক) 34

ক

ব্যাখ্যা

আমরা জানি,
Fibonacci সংখ্যা = 0, 1, 1, 2, 3, 5, 8, 13, 21 ... পরপর দুটি সংখ্যার যােগফল পরবর্তী সংখ্যার সমান।
সুতরাং, এই ধারার পরবর্তী সংখ্যা হবে = 21 + 13 = 34

১,৫২১.

What will be the difference between simple and compound interest at 10% on a sum of TK. 5000 after 5 years?

ক
ক) 45
খ
খ) 152
গ
গ) 252
ঘ
ঘ) 552

সঠিক উত্তর: ঘ

ঘ) 552

উত্তর

সঠিক উত্তর: ঘ

ঘ) 552

ঘ

ব্যাখ্যা

Simple interest, I = pnr = 5000 × 5 × 10/100
= 2500 taka
Compound interest = Amount − Principal
Amount = 5000(1 + 10/100)⁵ = 8052.55
So, compound interest = 8052.55 - 5000 = 3052.55

∴ Difference = 3052.55 - 2500 = 552.55 ≅ 552 taka

১,৫২২.

A box contains three pairs of blue gloves and two pairs of green gloves. Each pair consists of a left-hand glove and a right-hand glove. Each of the gloves is separate from its mate and thoroughly mixed together with the others in the box. If three gloves are randomly selected from the box, what is the probability that a matched set (i.e., a left- and right-hand glove of the same color) will be among the three gloves selected?

ক
3/10
খ
23/60
গ
7/12
ঘ
41/60
ঙ
5/6

সঠিক উত্তর: ঘ

41/60

উত্তর

সঠিক উত্তর: ঘ

41/60

ঘ

ব্যাখ্যা

Question: A box contains three pairs of blue gloves and two pairs of green gloves. Each pair consists of a left-hand glove and a right-hand glove. Each of the gloves is separate from its mate and thoroughly mixed together with the others in the box. If three gloves are randomly selected from the box, what is the probability that a matched set (i.e., a left- and right-hand glove of the same color) will be among the three gloves selected?

Solution:
Let's calculate the opposite probability of NOT getting a matched set and subtract this value from 1.

This could happen only if we pick all three same hand BLUE gloves; two same hand BLUE gloves and any green glove; or two same hand GREEN gloves and any BLUE glove

BBB: (6/10) × (2/9) × (1/8) =1/60 (after we pick a blue glove, 6/10, then there are 2 same hand gloves left out of the total 9 gloves : 2/9, and so on);

BBG: (6/10) × (2/9) × (4/8) × 3 = 12/60, [multiplying by 3 as this scenario can occur in 3 different ways: BBG, BGB, GBB;]

GGB: (4/10) × (1/9) × (6/8) × 3 = 6/60

P = 1 - (1/60 + 12/60 + 6/60) = 41/60

১,৫২৩.

64 persons can dig a trench 50m long, 2m wide, and 2m deep in 5 days, working 12 hours daily. In how many days, working 8 hours daily, will 80 persons dig another trench 75m long, 4m wide, and 3m deep?

ক
18 days
খ
45 days
গ
27 days
ঘ
36 days

সঠিক উত্তর: গ

27 days

উত্তর

সঠিক উত্তর: গ

27 days

গ

ব্যাখ্যা

Question: 64 persons can dig a trench 50m long, 2m wide, and 2m deep in 5 days, working 12 hours daily. In how many days, working 8 hours daily, will 80 persons dig another trench 75m long, 4m wide, and 3m deep?

Solution:
The volume of 50m long, 2m wide, and 2m deep is (50 × 2 × 2) m³ = 200 m³
The volume of 75m long, 4m wide, and 3m deep is (75 × 4 × 3) m³ = 900 m³

64 persons by working 12 hours daily can dig 200m³ in = 5 days.
∴ 1 person by working 1 hour daily can dig 1 m³ in = (5 × 64 × 12)/200 days.
∴ 80 persons by working 8 hour daily can dig 900 m³ in = (5 × 64 × 12 × 900)/(200 × 80 × 8) days.
= 27 days

১,৫২৪.

Karim can complete 2/5th of a certain work in 4 hours. Rahim works three times as fast as Karim and finishes the remaining work. How many hours did Rahim work?

ক
2 hours
খ
3 hours
গ
4 hours
ঘ
6.5 hours

সঠিক উত্তর: ক

2 hours

উত্তর

সঠিক উত্তর: ক

2 hours

ক

ব্যাখ্যা

Question: Karim can complete 2/5th of a certain work in 4 hours. Rahim works three times as fast as Karim and finishes the remaining work. How many hours did Rahim work?

Solution:
ধরি, সম্পূর্ণ কাজ = 1 অংশ

করিমের কাজের পরিমাণ = 2/5 অংশ
সময় = 4 ঘণ্টা

∴ পুরো কাজ (1 অংশ) করতে করিমের সময় লাগবে = 4 ÷ (2/5)
= 4 × 5/2
= 10 ঘণ্টা।

এখন, রহিম যেহেতু করিমের চেয়ে তিনগুণ দ্রুত কাজ করেন, তাই পুরো কাজটি সম্পন্ন করতে তার এক-তৃতীয়াংশ সময় লাগবে।

∴ পুরো কাজ করতে রহিমের সময় = 10 ÷ 3 = 10/3 ঘণ্টা।

বাকি কাজের পরিমাণ = 1 - (2/5) = 3/5 অংশ।

সুতরাং, রহিমের 3/5 অংশ কাজ করতে সময় লাগবে = (10/3) × (3/5) ঘণ্টা
= (10 × 3)/(3 × 5)
= 30/15
= 2 ঘণ্টা।

১,৫২৫.

Some solid metallic right circular cones, each with radius of the base 3 cm and height 4 cm are melted to from a solid sphere of radius 6 cm .The number of right circular cones is-

ক
ক) 22
খ
খ) 23
গ
গ) 24
ঘ
ঘ) 26

সঠিক উত্তর: গ

গ) 24

উত্তর

সঠিক উত্তর: গ

গ) 24

গ

ব্যাখ্যা

Volume of sphere :
= (4π/3)×6³cm³
= (288π)cm³

Volume of each cone :
=(1/3) × π × 3²× 4cm³
=(12π)cm³

∴ Number of cone : = 288π/12π =24

১,৫২৬.

The ratio of two numbers is 3 : 4 and their sum is 630. The smaller one of the numbers is -

ক
ক) 360
খ
খ) 270
গ
গ) 180
ঘ
ঘ) 120

সঠিক উত্তর: খ

খ) 270

উত্তর

সঠিক উত্তর: খ

খ) 270

খ

ব্যাখ্যা

ধরি,
ক্ষুদ্রতর সংখ্যাটি 3x এবং বৃহত্তর সংখ্যাটি 4x
প্রশ্নমতে,
3x + 4x = 630
⇒ 7x = 630
⇒ x = 630/7
⇒ x = 90
অতএব, ক্ষুদ্রতর সংখ্যাটি = 3 × 90
= 270.
Answer: 270.

১,৫২৭.

A car with a 12-gallon gas tank used 1/2 of a full tank of gas to make a 150-mile trip. How many miles per gallon did the car average on the trip?

ক
30
খ
25
গ
12.5
ঘ
8.33
ঙ
6

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: A car with a 12-gallon gas tank used 1/2 of a full tank of gas to make a 150-mile trip. How many miles per gallon did the car average on the trip?

Solution:
For 150 mile trip the car used (12/2) = 6 gallon gas

Using 6 gallon the car travels 150 mile
∴ Using 1 gallon the car travels (150/6) mile
= 25 mile

১,৫২৮.

An observer 1.6 m tall stands 20 meters away from a tree. The angle of elevation from his eye to the top of the tree is 45°. What is the height of the tree?

ক
18 m
খ
21.6 m
গ
24 m
ঘ
25.5 m

সঠিক উত্তর: খ

21.6 m

উত্তর

সঠিক উত্তর: খ

21.6 m

খ

ব্যাখ্যা

Question: An observer 1.6 m tall stands 20 meters away from a tree. The angle of elevation from his eye to the top of the tree is 45°. What is the height of the tree?

Solution:

মনে করি,
গাছটির উচ্চতা AB। পর্যবেক্ষকের চোখ C বিন্দুতে আছে এবং তার উচ্চতা CD = 1.6 m
পর্যবেক্ষক থেকে গাছটির দূরত্ব BD = 20 m
এখানে, A, C এবং E বিন্দু দ্বারা গঠিত ACE হলো একটি সমকোণী ত্রিভুজ, যার ∠C = 45°।

আমরা জানি,
tan θ = লম্ব/ভূমি
এখানে, লম্ব = AE এবং ভূমি = CE
∴ tan 45° = AE/20
∴ 1 = AE/20
∴ AE = 20 মিটার

গাছটির মোট উচ্চতা, AB = AE + EB
= 20 + 1.6
= 21.6 মিটার

সুতরাং, গাছটির উচ্চতা হলো 21.6 মিটার।

১,৫২৯.

If (3x + 2y) = 8 and (2x - 2y) = 2, then find the value of (4 - 3x).

ক
1.5
খ
3
গ
- 2.5
ঘ
- 2

সঠিক উত্তর: ঘ

- 2

উত্তর

সঠিক উত্তর: ঘ

- 2

ঘ

ব্যাখ্যা

Question: If (3x + 2y) = 8 and (2x - 2y) = 2, then find the value of (4 - 3x).

Solution:

3x + 2y = 8........(1)

(2x - 2y) = 2

⇒ 2(x - y) = 2

⇒ x - y = 1

⇒ x = 1 + y ..............(2)

x এর মান (1) নং এ বসিয়ে পাই

3x + 2y = 8

⇒ 3(1 + y) + 2y = 8

⇒ 3 + 3y +2y = 8

⇒ 3 + 5y = 8

⇒ 5y = 8 - 3

⇒ 5y = 5

∴ y = 1

y এর মান (2) নং এ বসিয়ে পাই

x = 1 + y

⇒ x = 1 + 1

∴ x = 2

∴ 4 - 3x = 4 - 3 × 2 = 4 - 6 = - 2

১,৫৩০.

The single discount equivalent to two successive discount of 20% and 5% is = ?

ক
ক) 24%
খ
খ) 25%
গ
গ) 22%
ঘ
ঘ) 23%

সঠিক উত্তর: ক

ক) 24%

উত্তর

সঠিক উত্তর: ক

ক) 24%

ক

ব্যাখ্যা

Two successive discount is equivalent
= 20+5− 20×5/100
= 25−1 = 24%

১,৫৩১.

In an isosceles triangle, each of the equal sides is 16 cm long and the included angle between the equal sides is 30°. What is the area of the triangle?

ক
48 cm²
খ
64 cm²
গ
72 cm²
ঘ
80 cm²

সঠিক উত্তর: খ

64 cm²

উত্তর

সঠিক উত্তর: খ

64 cm²

খ

ব্যাখ্যা

Question: In an isosceles triangle, each of the equal sides is 16 cm long and the included angle between the equal sides is 30°. What is the area of the triangle?

Solution:
Given that,
The included angle between the equal sides, θ = 30°
Each of the equal sides of the isosceles triangle, a = b = 16 cm

We know that,
Area of the triangle = (1/2) × a × b × sin θ
= (1/2) × 16 × 16 × sin 30°
= (1/2) × 16 × 16 × (1/2)
= 8 × 8
= 64 square cm

∴ The area of the triangle is 64 cm².

১,৫৩২.

It is being given that (2³² + 1) is completely divisible by a whole number. Which of the following numbers is also completely divisible by that whole number?

ক
7 × 2²³
খ
2¹⁶ + 1
গ
2⁹⁶ + 1
ঘ
2¹⁶ - 1

সঠিক উত্তর: গ

2⁹⁶ + 1

উত্তর

সঠিক উত্তর: গ

2⁹⁶ + 1

গ

ব্যাখ্যা

Question: It is being given that (2³² + 1) is completely divisible by a whole number. Which of the following numbers is also completely divisible by that whole number?

Solution:
2⁹⁶ + 1
= (2³²)³ + 1
= (2³² + 1) {(2³²)² - 2³² + 1}
= (2³² + 1) (2⁶⁴ - 2³² + 1)

যেহেতু (2³² + 1) একটি পূর্ণসংখ্যা দ্বারা বিভাজ্য, 2⁹⁶ + 1 ও ঐ পূর্ণ সংখ্যাটি দ্বারা বিভাজ্য হবে।

১,৫৩৩.

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. How old is the mother at present?

ক
32 years
খ
36 years
গ
40 years
ঘ
48 years
ঙ
None of these

সঠিক উত্তর: গ

40 years

উত্তর

সঠিক উত্তর: গ

40 years

গ

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. How old is the mother at present?

Solution:

Let the mother's present age be x years.

Then, the person's present age = 2x/5 years.

ATQ,

(2x/5) + 8 = (1/2)(x + 8)
(2x + 40)/5 = (x + 8)/2
⇒ 2(2x + 40) = 5(x + 8)
⇒ 4x + 80 = 5x + 40
∴ x = 40

১,৫৩৪.

Sum of two numbers is 384. H.C.F. of the numbers is 48. The difference of the numbers is-

ক
336
খ
288
গ
192
ঘ
100

সঠিক উত্তর: খ

288

উত্তর

সঠিক উত্তর: খ

288

খ

ব্যাখ্যা

Question: Sum of two numbers is 384. H.C.F. of the numbers is 48. The difference of the numbers is-

Solution:
Let, the numbers be 48x and 48y
where x and y are co-primes.

ATQ,
48x + 48y = 384
⇒ 48 ( x + y) = 384
⇒ x + y = 384/48
⇒ x + y = 8 ........... (i)

Possible and acceptable pairs of x and y satisfying this condition are: (1, 7) and (3, 5).

∴ Numbers are = 48 × 1 = 48
and 48 × 7 = 336
Again 48 × 3 = 144
and 48 × 5 = 240

∴ Required difference = 336 - 48
= 288

১,৫৩৫.

A clock gains (moves ahead) 10 minutes each day. How many days will it take to reach a point where the clock will indicate the correct time?

ক
36 days
খ
56 days
গ
72 days
ঘ
84 days

সঠিক উত্তর: গ

72 days

উত্তর

সঠিক উত্তর: গ

72 days

গ

ব্যাখ্যা

Question: A clock gains (moves ahead) 10 minutes each day. How many days will it take to reach a point where the clock will indicate the correct time?

Solution:
একটি ঘড়িকে পুনরায় সঠিক সময় দেখাতে হলে তাকে 12 ঘণ্টা সময় এগিয়ে যেতে হবে।
কারণ একটি 12 ঘণ্টার ঘড়িতে যখন সঠিক সময় থেকে 12 ঘণ্টা এগিয়ে যাবে, তখন এটি আবার সঠিক সময় নির্দেশ করবে।

12 ঘণ্টা = 12 × 60 মিনিট = 720 মিনিট

এখন, যেহেতু ঘড়িটি প্রতিদিন 10 মিনিট করে সময় এগিয়ে যায়,

10 মিনিট সময় এগিয়ে যায় 1 দিনে
∴ 720 মিনিট সময় এগিয়ে যাবে = (1/10) × 720 দিনে
= 72 দিনে

সুতরাং, 72 দিন পর ঘড়িটি আবার সঠিক সময় দেখাবে।

১,৫৩৬.

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

ক
ক) 630
খ
খ) 1260
গ
গ) 2520
ঘ
ঘ) 196

সঠিক উত্তর: ক

ক) 630

উত্তর

সঠিক উত্তর: ক

ক) 630

ক

ব্যাখ্যা

The LCM of 12, 18, 21, 30 is 1260.
So, the number is 1260/2 = 630

১,৫৩৭.

If A can do 1/4 of a work in 3 days and B can do 1/9 of the same work in 4 days, how much will A get if both work together and paid Tk 800 in all?

ক
500 Tk
খ
550 Tk
গ
600 Tk
ঘ
650 Tk

সঠিক উত্তর: গ

600 Tk

উত্তর

সঠিক উত্তর: গ

600 Tk

গ

ব্যাখ্যা

Question: If A can do 1/4 of a work in 3 days and B can do 1/9 of the same work in 4 days, how much will A get if both work together and paid Tk 800 in all?

Solution:
Whole work is done by A in (3 × 4) = 12 days
∴ A's 1 day's work = 1/12 part
Whole work is done by B in (4 × 9) = 36 days
∴ B's 1 day's work = 1/36 part

A's 1 day's work : B's 1 day's work
= A's wages : B's wages
= 1/12 : 1/36
= 3 : 1

∴ A's share = (800 × 3/4) Tk
= 600 Tk

১,৫৩৮.

While selling a watch, a shopkeeper gives a discount of 5%. If he gives a discount of 6%, he earns Tk. 15 less as profit, what is the marked price of the watch = ?

ক
ক) 1250
খ
খ) 1400
গ
গ) 1500
ঘ
ঘ) 750

সঠিক উত্তর: গ

গ) 1500

উত্তর

সঠিক উত্তর: গ

গ) 1500

গ

ব্যাখ্যা

Let the marked price = 100x
Shop Keeper gives 5% discount, therefore, Price becomes = 95x
Again if shopkeeper gives 6% discount then the price become = 94x
According to the question if he gives 6% discount his earning will Tk.15 less
∴ 95x - 94x = 15
⇒ x = 15
∴ Marked price = 100 × 15 = Tk. 1500

১,৫৩৯.

What is the average of first five multiples of 12?

ক
36
খ
38
গ
40
ঘ
42

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: What is the average of first five multiples of 12?

Solution:
Average = {12(1 + 2 + 3 + 4 + 5)}/5
= (12 × 15)/5
= 12 × 3
= 36

১,৫৪০.

The stock he bought which was 6% of face value now worth 8% of the market value.

ক
ক) Tk. 84
খ
খ) Tk. 87
গ
গ) Tk. 95
ঘ
ঘ) Tk. 92
ঙ
ঙ) Tk. 75

সঠিক উত্তর: ঙ

ঙ) Tk. 75

উত্তর

সঠিক উত্তর: ঙ

ঙ) Tk. 75

ঙ

ব্যাখ্যা

Let x be the market value,
we don't know face value so consider 100.
6% of 100 = 8% of x.
(6/100) × 100 = (8/100) × x.
6 = 8x/100.
x = 600/8.
x = 75.

Alternative Solution:
For an income of Tk. 8, investment = Tk. 100.
For an income of Tk. 6, investment = Tk.(100/8 × 6) = Tk. 75
Market value of Tk. 100 stock = Tk. 75.

১,৫৪১.

What will come in the place of question mark (?) in the following question?

ক
ক) 3
খ
খ) 5
গ
গ) 2
ঘ
ঘ) 9

সঠিক উত্তর: ঘ

ঘ) 9

উত্তর

সঠিক উত্তর: ঘ

ঘ) 9

ঘ

ব্যাখ্যা

? = {(243)²}^1/5
? = (243)^2/5
? = (3⁵)^2/5
? = 3²
? = 9

১,৫৪২.

Solve |x + 7| < 11

ক
0 < x < 4
খ
- 18 < x < 4
গ
x > 4
ঘ
- 18 < x < 0
ঙ
None of these

সঠিক উত্তর: খ

- 18 < x < 4

উত্তর

সঠিক উত্তর: খ

- 18 < x < 4

খ

ব্যাখ্যা

Question: Solve |x + 7| < 11

Solution:
We have |x + 7| < 11
⇒ - 11 < x + 7 < 11
⇒ - 11 - 7 < x + 7 - 7 < 11 - 7
⇒ - 18 < x < 4

১,৫৪৩.

In the following figure, ∠CAB = 90°, then ∠CDB =?

ক
40°
খ
60°
গ
80°
ঘ
90°

সঠিক উত্তর: ঘ

90°

উত্তর

সঠিক উত্তর: ঘ

90°

ঘ

ব্যাখ্যা

Question: In the following figure, ∠CAB = 90°, then ∠CDB =?

Solution:
বৃত্তস্থ চতুর্ভুজের বিপরীত কোণদ্বয়ের সমষ্টি ১৮০
⇒ ∠CAB + ∠CDB = 180
⇒ 90 + ∠CDB = 180
⇒ ∠CDB = 180 - 90
⇒ ∠CDB = 90°

১,৫৪৪.

One card is drawn from a pack of 52 cards. What is the probability that the card drawn is either a red card or a king?

ক
ক) 1/2
খ
খ) 6/13
গ
গ) 7/13
ঘ
ঘ) 27/52

সঠিক উত্তর: গ

গ) 7/13

উত্তর

সঠিক উত্তর: গ

গ) 7/13

গ

ব্যাখ্যা

Here, n(S) = 52
There are 26 red cards (including 2 kings) and there are 2 more kings.
Let E = event of getting a red card or a king.
Then, n(E) = 28
∴P(E)=n(E)/n(S)
=28/52
=7/13

১,৫৪৫.

What Percentage of 20 kg is 70 grams?

ক
0.035%
খ
0.45%
গ
4.5%
ঘ
0.35%

সঠিক উত্তর: ঘ

0.35%

উত্তর

সঠিক উত্তর: ঘ

0.35%

ঘ

ব্যাখ্যা

Question: What Percentage of 20 kg is 70 grams?

Solution:
Required Percentage = {(70gm/20kg) × 100}%
= {(70/20000) × 100}% ;[1kg = 1000gm]
= (7000/20000)%
= 0.35%

১,৫৪৬.

If a, b and c are positive numbers such that (a² + b²) : (b² + c²) : (c² + a²) = 34 : 61 : 45, then (b - a) : (c - b) : (c - a) = ?

ক
6 : 5 : 3
খ
4 : 3 : 2
গ
2 : 1 : 3
ঘ
5 : 2 : 7

সঠিক উত্তর: গ

2 : 1 : 3

উত্তর

সঠিক উত্তর: গ

2 : 1 : 3

গ

ব্যাখ্যা

Question : If a, b and c are positive numbers such that (a² + b²) : (b² + c²) : (c² + a²) = 34 : 61 : 45, then (b - a) : (c - b) : (c - a) = ?

Solution :
Given,
(a² + b²) : (b² + c²) : (c² + a²) = 34 : 61 : 45

Add all
2(a² + b² + c²) = 34 + 61 + 45
⇒ 2(a² + b² + c²) = 140
⇒ (a² + b² + c²) = 70
⇒ c² = 70 - 34
⇒ c² = 36
∴ c = 6

b² = 70 - 45
⇒ b² = 25
∴ b = 5

a² = 70 - 61
⇒a² = 9
∴ a = 3

(b - a) : (c - b) : (c - a)
= (5 - 3) : (6 - 5) : (6 - 3)
= 2 : 1 : 3

১,৫৪৭.

If 6 years are subtracted from the present age of Akib and the remainder is divided by 18, then the present age of Razib is obtained. If Razib is 2 years younger to Tomal whose age is 5 years, then what is Akib's present age?

ক
ক) 60 years
খ
খ) 50 years
গ
গ) 55 years
ঘ
ঘ) 62 years

সঠিক উত্তর: ক

ক) 60 years

উত্তর

সঠিক উত্তর: ক

ক) 60 years

ক

ব্যাখ্যা

The present age of Tomal = 5
Present age of Razib = 5 - 2 = 3
Let present age of Akib = x
Then, present age of Razib = (x - 6)/18

According to the question,
(x - 6)/18 = 3
x - 6 = 54
x = 54 + 6
x = 60 years.

১,৫৪৮.

How much water be mixed in 45 litre of milk worth Tk. 6.40 per litre, so that value of mixture is Tk. 4.80 per litre?

ক
10 litres
খ
12 litres
গ
15 litres
ঘ
20 litres

সঠিক উত্তর: গ

15 litres

উত্তর

সঠিক উত্তর: গ

15 litres

গ

ব্যাখ্যা

Question: How much water be mixed in 45 litre of milk worth Tk. 6.40 per litre, so that value of mixture is Tk. 4.80 per litre?

Solution:
মনে করি, x লিটার পানি মেশাতে হবে।

মিশ্রণের মোট পরিমাণ = (45 + x) লিটার
45 লিটার দুধের দাম = 45 × 6.40 = 288 টাকা
পানির দাম = 0 টাকা

প্রশ্নমতে, মিশ্রণের মোট দাম = (45 + x) × 4.80
যেহেতু পানি বিনামূল্যে পাওয়া যায়, তাই মোট দাম অপরিবর্তিত থাকবে:
288 = (45 + x) × 4.80
⇒ 288/4.80 = 45 + x [উভয় পক্ষকে 4.80 দ্বারা ভাগ করে পাই]
⇒ 60 = 45 + x
⇒ x = 60 - 45
⇒ x = 15 litres

∴ 15 লিটার পানি মেশাতে হবে।

১,৫৪৯.

A water tank can hold 500 liters of water. In the first 2 hours, water is filled at the rate of 60 liters per hour. What should be the filling rate in the remaining 4 hours to completely fill the tank?

ক
78 liters/hour
খ
89 liters/hour
গ
95 liters/hour
ঘ
102 liters/hour

সঠিক উত্তর: গ

95 liters/hour

উত্তর

সঠিক উত্তর: গ

95 liters/hour

গ

ব্যাখ্যা

Question: A water tank can hold 500 liters of water. In the first 2 hours, water is filled at the rate of 60 liters per hour. What should be the filling rate in the remaining 4 hours to completely fill the tank?

Solution:
Water filled in the first 2 hours = (60 × 2) liters
= 120 liters

Water left to be filled = (500 − 120) liters
= 380 liters

Required filling rate for the next 4 hours = (380 ÷ 4) liters/hour
= 95 liters/hour

১,৫৫০.

The weight of an empty bucket is 25% of the weight of the bucket when filled with some liquid. Some of the liquid has been removed. Then, the bucket, along with the remaining liquid, weighed three-fifths of the original weight. What percentage of the liquid has been removed?

ক
40%
খ
(123/2)%
গ
(160/3)%
ঘ
None of the Above

সঠিক উত্তর: গ

(160/3)%

উত্তর

সঠিক উত্তর: গ

(160/3)%

গ

ব্যাখ্যা

Question: The weight of an empty bucket is 25% of the weight of the bucket when filled with some liquid. Some of the liquid has been removed. Then, the bucket, along with the remaining liquid, weighed three-fifths of the original weight. What percentage of the liquid has been removed?

Solution:
let, weight of empty bucket is x liter

x = 25% (x + some liquid)
⇒ x = (1/4) (x + some liquid)
⇒ 4x = x + some liquid
⇒ 3x = some liquid
⇒ some liquid = 3x

Then, the bucket, along with the remaining liquid, weighed three-fifths of the original weight.
weight of removed liquid = (2/5) × 4x = 8x/5

%percentage removed = (8x/5/3x ) × 100%
= (160/3)%

১,৫৫১.

(10.3×10.3×10.3+1) /(10.3×10.3−10.3+1) is equal to :

ক
ক) 10.3
খ
খ) 10.5
গ
গ) 11.3
ঘ
ঘ) 13.3

সঠিক উত্তর: গ

গ) 11.3

উত্তর

সঠিক উত্তর: গ

গ) 11.3

গ

ব্যাখ্যা

Given expression :
= (10.3)³+1³/ (10.3)²−(10.3×1)+1²= (a³+b³/ a²−ab+b²)
=(a+b)
=(10.3+1)
=11.3

১,৫৫২.

A man spends 75% of his income. If his income increases by 25% and expenditure increases by 15%, find the percentage increase in his savings.

ক
50%
খ
55%
গ
60%
ঘ
65%

সঠিক উত্তর: খ

55%

উত্তর

সঠিক উত্তর: খ

55%

খ

ব্যাখ্যা

Question: A man spends 75% of his income. If his income increases by 25% and expenditure increases by 15%, find the percentage increase in his savings.

Solution:
Let,
Original income = 100 Taka
Original expenditure = 75% of 100 = 75 Taka
Original savings = Income - Expenditure = 100 - 75 = 25 Taka

After increase,
New income = 100 + 25% of 100 = 100 + 25 = 125 Taka
New expenditure = 75 + 15% of 75 = 75 + 11.25 = 86.25 Taka
New savings = 125 - 86.25 = 38.75 Taka

Percentage increase = [(New savings - Original savings) / Original savings] × 100
= [(38.75 - 25) / 25] × 100
= [13.75/ 25] × 100
= 0.55 × 100
= 55%

∴ Saving increased = 55%

১,৫৫৩.

ক
ক) a
খ
খ) a + 1
গ
গ) 1
ঘ
ঘ) a²

সঠিক উত্তর: গ

গ) 1

উত্তর

সঠিক উত্তর: গ

গ) 1

গ

ব্যাখ্যা

Question:

Solution:

১,৫৫৪.

Which is the better investment: 9% stock at Tk 90 or 12% stock at Tk 120?

ক
9% stock at Tk 90
খ
12% stock at Tk 120
গ
Both are same
ঘ
Cannot say

সঠিক উত্তর: গ

Both are same

উত্তর

সঠিক উত্তর: গ

Both are same

গ

ব্যাখ্যা

Question: Which is the better investment: 9% stock at Tk 90 or 12% stock at Tk 120?

Solution:
→ Yield of 9% stock = (9 / 90) × 100 = 10%
→ Yield of 12% stock = (12 / 120) × 100 = 10%
On every taka you put in, both give the same 10 % return.
correct answer: Both are same

১,৫৫৫.

A pump can fill a tank with water in 2 hours. Because of a leak, it took 140 minutes to fill the tank. The leak can drain all the water of the tank in-

ক
ক) 4.5 hr
খ
খ) 9 hr
গ
গ) 12 hr
ঘ
ঘ) 14 hr

সঠিক উত্তর: ঘ

ঘ) 14 hr

উত্তর

সঠিক উত্তর: ঘ

ঘ) 14 hr

ঘ

ব্যাখ্যা

Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 140 minutes to fill the tank. The leak can drain all the water of the tank in-

Solution:
একটি পাইপ চৌবাচ্চা পূর্ণ করতে পারে ২ ঘণ্টায় বা ১২০ মিনিটে
১ মিনিটে পূর্ণ করে ১/১২০ অংশ

একটি ছিদ্র থাকায় তা পূর্ণ করতে পারে ১৪০ মিনিটে
১ মিনিটে পূর্ণ হয় ১/১৪০ মিনিটে

ছিদ্র দিয়ে ১ মিনিটে খালি হয় = (১/১২০) - (১/১৪০)
= (৭ - ৬)/৮৪০
= ১/৮৪০ অংশ

সম্পূর্ণ অংশ খালি করতে সময় লাগে = ১/১/৮৪০ মিনিট
= ৮৪০ মিনিটে
= ৮৪০/৬০ ঘণ্টায়
= ১৪ ঘণ্টায়

১,৫৫৬.

A number when divided by 91 gives a remainder 17. When the same number is divided by 13, the remainder will be?

ক
2
খ
4
গ
5
ঘ
6

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: A number when divided by 91 gives a remainder 17. When the same number is divided by 13, the remainder will be?

Solution:
Here,
the first divisor (91) is a multiple of the second divisor (13).

∴ Required remainder = Remainder obtained on dividing 17 by 13
⇒ 17 = ( 13 × 1 ) + 4

∴ Hence Required remainder = 4

১,৫৫৭.

Of three numbers, the average of the first and third number is greater than the average of the second and third number by 14. What is the difference between the first and the second number?

ক
24
খ
25
গ
27
ঘ
28

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

ব্যাখ্যা

Question: Of three numbers, the average of the first and third number is greater than the average of the second and third number by 14. What is the difference between the first and the second number?

Solution:
Let, these numbers are x, y and z respectively.

ATQ,
{(x + z)/2} - {(y + z)/2} = 14
Or, (x + z) - (y + z) = 28
Or, x + z - y - z = 28
Or, x - y = 28

∴ the difference between the first and the second number is = 28.

১,৫৫৮.

The average of the largest and smallest 3 digits numbers formed by 0, 2 and 4 would be :

ক
213
খ
232
গ
312
ঘ
320

সঠিক উত্তর: গ

312

উত্তর

সঠিক উত্তর: গ

312

গ

ব্যাখ্যা

Question: The average of the largest and smallest 3 digits numbers formed by 0, 2 and 4 would be :

Solution:
largest = 420
smallest = 204

Average = (420 + 204)/2
= 624/2
= 312

১,৫৫৯.

A square is inscribed in a circle of diameter 2a and another square is circumscribing circle. The difference between the areas of outer and inner squares is -

ক
ক) a²
খ
খ) 2a²
গ
গ) 3a²
ঘ
ঘ) 4a²

সঠিক উত্তর: খ

খ) 2a²

উত্তর

সঠিক উত্তর: খ

খ) 2a²

খ

ব্যাখ্যা

Area or outer space = 2a x 2a = 4a²
From ABCD rectangle, In ΔBAD,
BD² = (AD)² + (AB)²
⇒ (2a)²= x² + x²
⇒ 4a²= 2x²
⇒ 2a²= x²
∴ x = √2a

Area of inner square = √2a × √2a = 2a²

∴ The difference between the areas of outer and inner squares is = 4a² - 2a² = 2a²

১,৫৬০.

A ferry can carry 25 trucks or 40 motorcycles at a time. If there are 15 trucks on the ferry, how many motorcycles can be loaded onto it?

ক
18 motorcycles
খ
8 motorcycles
গ
12 motorcycles
ঘ
16 motorcycles

সঠিক উত্তর: ঘ

16 motorcycles

উত্তর

সঠিক উত্তর: ঘ

16 motorcycles

ঘ

ব্যাখ্যা

Question: A ferry can carry 25 trucks or 40 motorcycles at a time. If there are 15 trucks on the ferry, how many motorcycles can be loaded onto it?

Solution:
Here,
25 trucks = 40 motorcycles
∴ 1 trucks = 40/25 = 8/5 motorcycles
∴ 15 trucks = = (8 × 15)/5 = 24 motorcycles

∴ Required number of motorcycles = 40 - 24 = 16

So the ferry can carry 16 more motorcycles along with the 15 trucks.

১,৫৬১.

Two pipes A and B can fill a cistern in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the cistern from the empty state if B is used for half the time, and A and B fill it together for the other half?

ক
ক) 30
খ
খ) 20
গ
গ) 45
ঘ
ঘ) 50

সঠিক উত্তর: ক

ক) 30

উত্তর

সঠিক উত্তর: ক

ক) 30

ক

ব্যাখ্যা

Question: Two pipes A and B can fill a cistern in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the cistern from the empty state if B is used for half the time, and A and B fill it together for the other half?

Solution:
part filled by (A + B) in 1 minute = 1/60 + 1/40 = 1/24

suppose, the cistern is filled in x minutes

according to the question,
{(x/2) × (1/40)} + {(x/2) × (1/24)} = 1
⇒ x/80 + x/48 =1
⇒ 8x/240 = 1
⇒ x = 30

১,৫৬২.

যদি log₂₇x + log₂₇(1/6) = 1/3 হয়, তবে x এর মান কত?

ক
18
খ
12
গ
9
ঘ
24

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

প্রশ্ন: যদি log₂₇x + log₂₇(1/6) = 1/3 হয়, তবে x এর মান কত?

সমাধান:
log₂₇x + log₂₇(1/6) = 1/3
⇒ log₂₇{x × (1/6)} = 1/3
⇒ log₂₇(x/6) = 1/3
⇒ 27^1/3 = x/6
⇒ (3³)^1/3 = x/6
⇒ 3 = x/6
∴ x = 18

১,৫৬৩.

Shonghoti and Shouhardo Clubs consist of 200 and 270 members respectively. If the total member of the two clubs is 420 then how many members belong to both clubs?

ক
ক) 30
খ
খ) 40
গ
গ) 50
ঘ
ঘ) 60

সঠিক উত্তর: গ

গ) 50

উত্তর

সঠিক উত্তর: গ

গ) 50

গ

ব্যাখ্যা

প্রশ্ন: Shonghoti and Shouhardo Clubs consist of 200 and 270 members respectively. If the total member of the two clubs is 420 then how many members belong to both clubs?

সমাধান:
ধরি
n(A) = 200 , n(B) =270 এবং n(A ∪ B) = 420

আমরা জানি
n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
n(A ∩ B) = n(A) + n(B) - n(A ∪ B)
= 200 + 270 - 420
= 470 - 420
= 50

১,৫৬৪.

The solution of (2x + 3)/(2x - 1) = (3x - 1)/(3x + 1) is:

ক
- 1/8
খ
- 7/3
গ
8/5
ঘ
None of the above

সঠিক উত্তর: ক

- 1/8

উত্তর

সঠিক উত্তর: ক

- 1/8

ক

ব্যাখ্যা

Question:
The solution of (2x + 3)/(2x - 1) = (3x - 1)/(3x + 1) is:

Solution:

১,৫৬৫.

Which is the correct factor analysis of 2√2x³ + 125?

ক
ক) (√2x + 5)(2x² - 5√2 x - 25)
খ
খ) (√2x + 5)(2x² - 5√2x + 25)
গ
গ) (√2x + 5)(2x² +5√2x - 25)
ঘ
ঘ) (√2x - 5)(2x² -5√2x - 25)

সঠিক উত্তর: খ

খ) (√2x + 5)(2x² - 5√2x + 25)

উত্তর

সঠিক উত্তর: খ

খ) (√2x + 5)(2x² - 5√2x + 25)

খ

ব্যাখ্যা

Question: Which is the correct factor analysis of 2√2x³ + 125?

সমাধান:
2√2x³ + 125
= (√2x)³ + 5³
= (√2x + 5) (2x² - 5√2x + 25)

১,৫৬৬.

The sum of four consecutive two-digit odd numbers, when divided by 10, becomes a perfect square. Which of the following can be the set of the four numbers?

ক
27, 29, 31 and 33
খ
37, 39, 41 and 43
গ
47, 49, 51 and 53
ঘ
None of the above

সঠিক উত্তর: খ

37, 39, 41 and 43

উত্তর

সঠিক উত্তর: খ

37, 39, 41 and 43

খ

ব্যাখ্যা

Question: The sum of four consecutive two-digit odd numbers, when divided by 10, becomes a perfect square. Which of the following can be the set of the four numbers?

Solution:
Using options,
We find that four consecutive odd numbers are 37, 39, 41 and 43

Here, 37 + 39 + 41 + 43 = 160

The sum of these 4 numbers is 160, when divided by 10 we get 16 which is a perfect square.

Hence, the required set = 37, 39, 41 and 43

১,৫৬৭.

If cot3A = 1, what is the value of 1/cos2A?

ক
√3
খ
3/√2
গ
2/√3
ঘ
√2/3

সঠিক উত্তর: গ

2/√3

উত্তর

সঠিক উত্তর: গ

2/√3

গ

ব্যাখ্যা

Question: If cot3A = 1, what is the value of 1/cos2A?

Solution:
cot3A = 1
cot3A = cot45°
3A = 45°
A = 15°

1/cos2A = sec2A
= sec30°
= 2/√3

১,৫৬৮.

If m/n = 1/4, then the value of (m² + n²)/(m² - n²) is-

ক
5/7
খ
- √7/√5
গ
15/17
ঘ
- 17/15

সঠিক উত্তর: ঘ

- 17/15

উত্তর

সঠিক উত্তর: ঘ

- 17/15

ঘ

ব্যাখ্যা

Question: If m/n = 1/4, then the value of (m² + n²)/(m² - n²) is-

Solution:
Given that,
m/n = 1/4

Now,
(m/n) = (1/4)
⇒ (m/n)² = (1/4)²
⇒ m²/n² = 1/16
∴ (m² + n²)/(m² - n²) = (1 + 16)/(1 - 16); [যোজন-বিয়োজন]
= 17/(- 15)
= - 17/15

১,৫৬৯.

A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?

ক
ক) 7 liters
খ
খ) 15 liters
গ
গ) 10 liters
ঘ
ঘ) 9 liters

সঠিক উত্তর: গ

গ) 10 liters

উত্তর

সঠিক উত্তর: গ

গ) 10 liters

গ

ব্যাখ্যা

Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 × 150 = 30 liters.
P liters of water added to the mixture to make water 25% of the new mixture.
Total amount of water becomes (30 + P) and total volume of mixture is (150 + P).
(30 + P) = 25/100 × (150 + P)
120 + 4P = 150 + P
=> P = 10 liters.

১,৫৭০.

Choose analogous pair.
Shrub : Prune

ক
Beard : Shave
খ
Hair : Trim
গ
Lawn : Mow
ঘ
Wool : Shear

সঠিক উত্তর: খ

Hair : Trim

উত্তর

সঠিক উত্তর: খ

Hair : Trim

খ

ব্যাখ্যা

Question: Choose analogous pair.
Shrub : Prune

Solution:
Shrub - ঝোপঝাড়
Prune - ছাঁটাই

Beard - দাড়ি
Shave - মুণ্ডণ, চাঁচা

Hair - চুল
Trim - ছাঁটা

Lawn - বনভূমি
Mow - কাস্তে দ্বারা কাটা

Wool - পশম
Shear - ফাড়িয়া ফেলা

ঝোপঝাড় যেমন ছাঁটাই করে সুন্দর করে রাখা হয়, তেমনি চুল ও ছেঁটে সুন্দর রাখা হয়।

১,৫৭১.

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

ক
2
খ
3
গ
18
ঘ
21

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

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

Solution:
23 ) 1056 ( 45
92
_______
136
115
_______
21

∴ Required number = (23 - 21) = 2

১,৫৭২.

A train travels 90 km at a speed of 45 km/h. How much time would it take for the same train to travel 180 km at a speed of 60 km/h?

ক
3 hours
খ
4 hours
গ
6 hours
ঘ
7.5 hours

সঠিক উত্তর: ক

3 hours

উত্তর

সঠিক উত্তর: ক

3 hours

ক

ব্যাখ্যা

Question: A train travels 90 km at a speed of 45 km/h. How much time would it take for the same train to travel 180 km at a speed of 60 km/h?

Solution:
Here, the distance is 180 km and the speed is 60 km/h

∴ Time = distance/speed
= 180/60
= 3 hour

১,৫৭৩.

Two dice are thrown simultaneously. What is the probability of getting the sum of the face number is odd?

ক
ক) 1/2
খ
খ) 2/3
গ
গ) 3/4
ঘ
ঘ) 1/3

সঠিক উত্তর: ক

ক) 1/2

উত্তর

সঠিক উত্তর: ক

ক) 1/2

ক

ব্যাখ্যা

প্রশ্ন: Two dice are thrown simultaneously. What is the probability of getting the sum of the face number is odd?

সমাধান:
The odd sum is 3, 5, 7, 9, 11
The number of ways getting 3 = (1, 2), (2, 1) = 2
The number of ways getting 5 = (1, 4), (2, 3), (3, 2), (4, 1) = 4
The number of ways getting 7 = (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) = 6
The number of ways getting 9 = (3, 6), (4, 5), (5, 4), (6, 3) = 4
The number of ways getting 11 = (5, 6), (6,5) = 2
The number of ways = 2 + 4 + 6 + 4 + 2 = 18
The total number of ways = 6 × 6 = 36

Probability = 18/36 = 1/2
∴ The probability of getting an odd sum is 1/2

১,৫৭৪.

From a point P on a level ground, the angle of elevation of the top tower is 30°. If the tower is 100 m high, the distance of point P from the foot of the tower is:

ক
149 m
খ
156 m
গ
173 m
ঘ
200 m

সঠিক উত্তর: গ

173 m

উত্তর

সঠিক উত্তর: গ

173 m

গ

ব্যাখ্যা

Question: From a point P on a level ground, the angle of elevation of the top tower is 30°. If the tower is 100 m high, the distance of point P from the foot of the tower is:

Solution:

Let AB be the tower.
Then, ∠APB = 30° and AB = 100 m.

AB/AP = tan 30° = 1/√3
⇒ AP = (AB × √3) m
= 100 × √3 m
= (100 × 1.73) m
= 173 m.

১,৫৭৫.

A biker travels at 60 km/h. If instead, he had traveled at 80 km/h for the same duration, he would have covered 100 km more. How far did he actually travel?

ক
320 km
খ
300 km
গ
290 km
ঘ
270 km

সঠিক উত্তর: খ

300 km

উত্তর

সঠিক উত্তর: খ

300 km

খ

ব্যাখ্যা

Question: A biker travels at 60 km/h. If instead, he had traveled at 80 km/h for the same duration, he would have covered 100 km more. How far did he actually travel?

Solution:
Let, the actual distance travelled be x km.
Then,
x/60 = (x + 100)/80
⇒ x/6 = (x + 100)/8
⇒ 6(x + 100) = 8x
⇒ 6x + 600 = 8x
⇒ 8x - 6x = 600
⇒ 2x = 600
⇒ x = 600/2
⇒ x = 300 km

১,৫৭৬.

If √2 : (1 + √3 ) :: √6 : x, then x is equal to-

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

সঠিক উত্তর: খ

খ) √3 + 3

উত্তর

সঠিক উত্তর: খ

খ) √3 + 3

খ

ব্যাখ্যা

√2 : (1 + √3 ) :: √6 : x
√2/ (1 + √3) = √6 / x
x√2 = √6(1 + √3)
x = √6(1 + √3)/√2
x = √3(1 + √3)
x =√3 + 3

১,৫৭৭.

If 5 workers can collect 75 kg wheat in 3 days, how many kilograms of wheat will 8 workers collect in 5 days?

ক
160 kg
খ
200 kg
গ
320 kg
ঘ
175 kg

সঠিক উত্তর: খ

200 kg

উত্তর

সঠিক উত্তর: খ

200 kg

খ

ব্যাখ্যা

Question: If 5 workers can collect 75 kg wheat in 3 days, how many kilograms of wheat will 8 workers collect in 5 days ?

Solution:
5 workers 3 days collection = 75 kg
1 worker 1 day collection = (75/15) kg
8 workers 5 days collection = (75 × 40)/15 kg
= 200 kg

∴ 8 workers will collect 200 kg in 5 days.

১,৫৭৮.

A trader sets his products 50% above cost price and gives a discount of 20%. Find his profit percent.

ক
30% profit
খ
25% profit
গ
20% profit
ঘ
15% profit

সঠিক উত্তর: গ

20% profit

উত্তর

সঠিক উত্তর: গ

20% profit

গ

ব্যাখ্যা

Question: A trader sets his products 50% above cost price and gives a discount of 20%. Find his profit percent.

Solution:
Let the cost price (CP) = Tk. 100

Marked Price (MP)
MP = CP + 50% of CP
= 100 + 50
= 150

Selling Price (SP) after discount:
SP = MP - 20% of MP
= 150 - 30
= 120

Profit = SP - CP
= 120 - 100
= 20

Profit percent:
Profit % = (Profit/CP) × 100
= (20/100) × 100
= 20%

∴ Profit = 20%

১,৫৭৯.

What is the least multiple of 7 which leaves a remainder of 4 when divided by 6, 9, 15 and 18?

ক
ক) 343
খ
খ) 350
গ
গ) 371
ঘ
ঘ) 364

সঠিক উত্তর: ঘ

ঘ) 364

উত্তর

সঠিক উত্তর: ঘ

ঘ) 364

ঘ

ব্যাখ্যা

LCM of 6, 9, 15 and 18 = 90
Required Number = (90k + 4) which is a multiple of 7
Put k = 1. We get numbers as (90 × 1) + 4 = 94. But this is not a multiple of 7
Put k = 2. We get numbers as (90 × 2) + 4 = 184. But this is not a multiple of 7
Put k = 3. We get numbers as (90 × 3) + 4 = 274. But this is not a multiple of 7
Put k = 4. We get numbers as (90 × 4) + 4 = 364. This is a multiple of 7
Hence 364 is the answer.

১,৫৮০.

The sum of values of x satisfying x^2/3 + x^1/3 = 2 is-

ক
- 3
খ
3
গ
- 7
ঘ
7

সঠিক উত্তর: গ

- 7

উত্তর

সঠিক উত্তর: গ

- 7

গ

ব্যাখ্যা

Question: The sum of values of x satisfying x^2/3 + x^1/3 = 2 is-

Solution:
x^2/3 + x^1/3 = 2
⇒ (x^2/3 + x^1/3)³ = 2³
⇒ (x^2/3)³ + (x^1/3)³ + 3.x^2/3.x^1/3(x^2/3 + x^1/3) = 8
⇒ x² + x + 3x(x^2/3 + x^1/3) = 8
⇒ x² + x + 3x(2) = 8
⇒ x² + 7x - 8 = 0
⇒ x² + 8x - x - 8 = 0
⇒ x (x + 8) - 1 (x + 8) = 0
⇒ (x + 8)(x - 1) = 0
⇒ x = - 8 or x = 1

∴ Sum of values of x = - 8 + 1 = - 7.

১,৫৮১.

The cost of a table and a chair are in the ratio of 10 : 7. If the cost of table and a chair is increased by 8% and 20% respectively, then what will be the new ratio?

ক
12 : 13
খ
7 : 12
গ
9 : 7
ঘ
24 : 55

সঠিক উত্তর: গ

9 : 7

উত্তর

সঠিক উত্তর: গ

9 : 7

গ

ব্যাখ্যা

Question : The cost of a table and a chair are in the ratio of 10 : 7. If the cost of table and a chair is increased by 8% and 20% respectively, then what will be the new ratio?

Solution :
Let the cost of the table and chair be Tk. 10x and Tk. 7x respectively

New cost of table = 108% of 10x
= (108 × 10x)/100
= 54x/5

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

So the new ratio = 54x/5 : 42x/5
= 54 : 42
= 9 : 7

১,৫৮২.

The selling price of 8 cots is equal to the purchase price of 10 cots. What is the profit margin?

ক
ক) 15%
খ
খ) 20%
গ
গ) 25%
ঘ
ঘ) 24%

সঠিক উত্তর: গ

গ) 25%

উত্তর

সঠিক উত্তর: গ

গ) 25%

গ

ব্যাখ্যা

Question: The selling price of 8 cots is equal to the purchase price of 10 cots. What is the profit margin?

Solution:
Let,
The CP of 10 cots = 10 Tk.
∴ The CP of 8 cots = 8 Tk.
∴ The SP of 8 cots = 10 Tk.

∴ Profit margin = {(10 - 8) × 100}/8 %
= 200/8 %
= 25%

১,৫৮৩.

When a commodity is sold for Tk. 49, there is a loss of 2%. What is the cost price of the commodity?

ক
ক) 50
খ
খ) 60
গ
গ) 40.50
ঘ
ঘ) 45.50

সঠিক উত্তর: ক

ক) 50

উত্তর

সঠিক উত্তর: ক

ক) 50

ক

ব্যাখ্যা

প্রশ্ন: When a commodity is sold for Tk. 49, there is a loss of 2%. What is the cost price of the commodity?

সমাধান:
একটি পণ্যের বিক্রয়মূল্য ৪৯ টাকা
ক্ষতি ২%

ধরি, ক্রয়মূল্য x টাকা

প্রশ্নমতে,
x - x × 2% = 49
⇒ x - (x/50) = 49
⇒ (50x - x)/50 = 49
⇒ 49x/50 = 49
∴ x = 50

অতএব, দ্রব্যটির ক্রয়মূল্য ৫০ টাকা।

১,৫৮৪.

The sum of three consecutive multiples of 4 is 312. Find the largest number.

ক
108
খ
208
গ
123
ঘ
311

সঠিক উত্তর: ক

108

উত্তর

সঠিক উত্তর: ক

108

ক

ব্যাখ্যা

Question: The sum of three consecutive multiples of 4 is 312. Find the largest number.

Solution:
Let,
First multiple = 4x
Second multiple = 4(x + 1) = 4x + 4
Third multiple = 4(x + 2) = 4x + 8

According to the question,
4x + (4x + 4) + (4x + 8) = 312
⇒ 12x + 12 = 312
⇒ 12x = 300
⇒ x = 25

∴ The largest number = 4x + 8
= 4 × 25 + 8
= 108

১,৫৮৫.

ক
0.4
খ
0.5
গ
0.6
ঘ
0.8

সঠিক উত্তর: খ

0.5

উত্তর

সঠিক উত্তর: খ

0.5

খ

ব্যাখ্যা

Question:

Solution:

১,৫৮৬.

The sum of ages of 4 children born at the intervals of 3 years each is 54 years. What is the age of elder child?

ক
18 years
খ
9 years
গ
12 years
ঘ
15 years

সঠিক উত্তর: ক

18 years

উত্তর

সঠিক উত্তর: ক

18 years

ক

ব্যাখ্যা

Question: The sum of ages of 4 children born at the intervals of 3 years each is 54 years. What is the age of elder child?

Solution:
Let,
The age of 4 children = x years, x + 3 years, x + 6 years, x + 9 years

ATQ,
x + (x + 3) + (x + 6) + (x + 9) = 54
⇒ 4x + 18 = 54
⇒ 4x = 54 - 18
⇒ 4x = 36
⇒ x = 36 ÷ 4
∴ x = 9

So the age of the elder children is = 9 + 9
= 18 years

১,৫৮৭.

The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6m away from the wall. The length of the ladder is

ক
ক) 2.3 m
খ
খ) 9.2 m
গ
গ) 4.6 m
ঘ
ঘ) 7.8 m

সঠিক উত্তর: খ

খ) 9.2 m

উত্তর

সঠিক উত্তর: খ

খ) 9.2 m

খ

ব্যাখ্যা

Let AB be the wall and BC be the ladder
Then, ACB = 60°
and AC = 4.6 m.
AC/BC = cos 60° = 1/2
BC = 2 × AC = (2 × 4.6) m = 9.2 m.

১,৫৮৮.

A monkey climbs a 60 m high pole. In the first minute, he climbs 6m and slips down 3m in the next minute. How much time is required by it to reach the top?

ক
ক) 35 minutes
খ
খ) 33 minutes
গ
গ) 37 minutes
ঘ
ঘ) 40 minutes

সঠিক উত্তর: গ

গ) 37 minutes

উত্তর

সঠিক উত্তর: গ

গ) 37 minutes

গ

ব্যাখ্যা

শেষের মিনিটে সে slip করবে না, অর্থাৎ 54 মিটার উঠার পর 6 মিটার উঠে গেলে সে আর নিচে নামবে না।
তাই এখন দেখি এই 54 মিটার সে কত মিনিটে উঠে।
প্রতি 2 মিনিটে বানরটি উঠে = 6 - 3 = 3 মিটার।
অর্থাৎ 3 মিটার উঠে = 2 মিনিটে
∴ 54 মিটার উঠে = (2 × 54)/3
= 36 মিনিটে
∴ খুটি বেয়ে উঠতে সময় লাগবে = 36 + 1 = 37 মিনিট

১,৫৮৯.

A person needs to pay Tk. 500 to buy pencils and Tk. X for any additional unit of pencil. If the customer pays a total of Tk. 4,700 for 1200 pencils, what is the value of X?

ক
ক) 4.0
খ
খ) 3.91
গ
গ) 3.85
ঘ
ঘ) 3.5

সঠিক উত্তর: ঘ

ঘ) 3.5

উত্তর

সঠিক উত্তর: ঘ

ঘ) 3.5

ঘ

ব্যাখ্যা

সমাধান:
মোট খরচ = নির্দিষ্ট (বরাদ্দকৃত) টাকা + প্রতি পেন্সিলের অতিরিক্ত মূল্য × পেন্সিলের সংখ্যা

এখানে,
নির্দিষ্ট টাকা = ৫০০ টাকা
মোট পেন্সিল = ১২০০ টি
মোট প্রদানকৃত টাকা = ৪৭০০ টাকা
প্রতি পেন্সিলের অতিরিক্ত মূল্য = X টাকা

সুতরাং সমীকরণ,
৪৭০০ = ৫০০ + ১২০০X
বা। ৪৭০০ − ৫০০ = ১২০০X
বা, ৪২০০ = ১২০০X
বা, X = ৪২০০ ÷ ১২০০
বা, X = ৪২ ÷ ১২
∴ X = ৩.৫

সুতরাং, প্রতিটি অতিরিক্ত পেন্সিলের জন্য মূল্য X = ৩.৫ টাকা

১,৫৯০.

The ages of Sabit and Sumit are in the ratio of 7 : 3 respectively. After 6 years, the ratio of their ages will be 5 : 3. What is the sum of their ages?

ক
20 years
খ
8 years
গ
16 years
ঘ
10 years

সঠিক উত্তর: ক

20 years

উত্তর

সঠিক উত্তর: ক

20 years

ক

ব্যাখ্যা

Question: The ages of Sabit and Sumit are in the ratio of 7 : 3 respectively. After 6 years, the ratio of their ages will be 5 : 3. What is the sum of their ages?

Solution:
Let, their ages are 7x, 3x

ATQ,
(7x + 6)/(3x + 6) = 5/3
⇒ 3(7x + 6) = 5(3x + 6)
⇒ 21x + 18 = 15x + 30
⇒ 21x - 15x = 30 - 18
⇒ 6x = 12
∴ x = 2

The difference in their ages is = 7x + 3x
= 10x
= 10 × 2
= 20 years

১,৫৯১.

A large tanker can be filled by two pipes A and B in 60 minutes and 40 minutes, respectively. How many minutes will it take to fill the empty tanker if only B is used in the first-half of the time and A and B are both used in the second-half of the time?

ক
ক) 27.5 minutes
খ
খ) 15 minutes
গ
গ) 30 minutes
ঘ
ঘ) 20 minutes

সঠিক উত্তর: গ

গ) 30 minutes

উত্তর

সঠিক উত্তর: গ

গ) 30 minutes

গ

ব্যাখ্যা

Question: A large tanker can be filled by two pipes A and B in 60 minutes and 40 minutes, respectively. How many minutes will it take to fill the empty tanker if only B is used in the first-half of the time and A and B are both used in the second-half of the time?

Solution:
Part filled by (A + B) in 1 minute = 1/60 + 1/40
= (2 + 3)/120
= 1/24

(A + B) will take half of total time= (x/2)× (1/24)
The rest half will be filled by B only in half of total time = (x/2) × (1/40)

Now
x/48 + x/80 = 1
(5x + 3x)/240 = 1
8x/240 = 1
x/30 = 1
x = 30

১,৫৯২.

The height of a cylinder is four times its radius. If the cylinder’s volume is 32π cm³, what is the radius of the cylinder?

ক
2 cm
খ
4 cm
গ
6 cm
ঘ
8 cm

সঠিক উত্তর: ক

2 cm

উত্তর

সঠিক উত্তর: ক

2 cm

ক

ব্যাখ্যা

Question: The height of a cylinder is four times its radius. If the cylinder’s volume is 32π cm³, what is the radius of the cylinder?

Solution:
ধরি,
সিলিন্ডারের ব্যাসার্ধ = r সেমি
∴ সিলিন্ডারের উচ্চতা = 4r সেমি

আমরা জানি,
সিলিন্ডারের আয়তন = πr²h ঘন সেমি
প্রশ্নমতে,
πr²h = 32π
⇒ πr² × 4r = 32π
⇒ 4πr³ = 32π
⇒ 4r³ = 32
⇒ r³ = 32/4
⇒ r³ = 8
⇒ r = 2

১,৫৯৩.

Let M be the median and m the mode of the following set of numbers : 10, 70, 20, 40, 70, 90. What is the average (arithmetic) mean of M and m?

ক
ক) 50
খ
খ) 60
গ
গ) 62.5
ঘ
ঘ) 65

সঠিক উত্তর: গ

গ) 62.5

উত্তর

সঠিক উত্তর: গ

গ) 62.5

গ

ব্যাখ্যা

Median is the middle element or the mean of two middle elements in a numerical data set with the elements ordered by their value.
The mode is the value in a set of data that has the most occurrences.
The mode is not unique and a data set may have more than one mode of no mode as well
Given set of numbers are 10, 70, 20, 40, 70, 90
Arrange in order: 10, 20, 40, 70, 70, 90
So, Median M = ( 40 + 70)/2 = 55
and, Mode m = 70

∴ average of M and m = (55 + 70)/2 = 62.5

১,৫৯৪.

A craft store has ribbons of lengths 36 cm, 48 cm, and 60 cm. What is the longest possible length that can evenly cut all ribbons without waste?

ক
15 cm
খ
18 cm
গ
9 cm
ঘ
12 cm

সঠিক উত্তর: ঘ

12 cm

উত্তর

সঠিক উত্তর: ঘ

12 cm

ঘ

ব্যাখ্যা

Question: A craft store has ribbons of lengths 36 cm, 48 cm, and 60 cm. What is the longest possible length that can evenly cut all ribbons without waste?

Solution:
Prime factorization of
36 = 2 × 2 × 3 × 3
48 = 2 × 2 × 2 × 2 × 3
60 = 2 × 2 × 3 × 5

∴ HCF = 2 × 2 × 3 = 12

So, the longest ribbon length that can evenly cut all three without waste is 12 cm.

১,৫৯৫.

Express A = {2, 4, 6, 8, 10, 12, 14, 16, 18} in set builder form.

ক
A = {x : x ∈ N, x is an even number < 20}
খ
A = {x = 2n : n ∈ N and n < 20}
গ
A = {x : x ∈ N, x is an even number < 10}
ঘ
None of these

সঠিক উত্তর: ক

A = {x : x ∈ N, x is an even number < 20}

উত্তর

সঠিক উত্তর: ক

A = {x : x ∈ N, x is an even number < 20}

ক

ব্যাখ্যা

Question: Express A = {2, 4, 6, 8, 10, 12, 14, 16, 18} in set builder form.

Solution:
A = {2, 4, 6, 8, 10, 12, 14, 16, 18}
All the elements of A is even Natural number and less than 20.
∴ The builder from is A = {x : x ∈ N, x is an even number < 20}

Now, If we take A = {x = 2n : n ∈ N and n < 20}
Then the set will be A = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38}

∴ Option 1 is the correct answer.

১,৫৯৬.

A committee of 3 members is to be selected out of 3 men and 2 women. What is the probability that the committee has at least one woman?

ক
11/20
খ
2/3
গ
3/8
ঘ
9/10

সঠিক উত্তর: ঘ

9/10

উত্তর

সঠিক উত্তর: ঘ

9/10

ঘ

ব্যাখ্যা

Question: A committee of 3 members is to be selected out of 3 men and 2 women. What is the probability that the committee has at least one woman?

Solution:
Total member = 3 + 2 = 5

Committee can be form with at least 1 one woman:
1 woman, 2 men : ²C₁× ³C₂ = 2 × 3 = 6
2 women, 1 man: ²C₂ × ³C₁ = 1 × 3 = 3
∴ The total number of ways to make committe with at least 1 one woman: 6 + 3 = 9

The total number of ways to make committe with all members = ⁵C₃ = 10

∴ The probability that the committee has at least woman = 9/10

১,৫৯৭.

A circle and a rectangle have the same perimeter. The sides of the rectangle are 9 cm and 13 cm. What is the area of the circle?

ক
ক) 124 cm²
খ
খ) 144 cm²
গ
গ) 154 cm²
ঘ
ঘ) 164 cm²

সঠিক উত্তর: গ

গ) 154 cm²

উত্তর

সঠিক উত্তর: গ

গ) 154 cm²

গ

ব্যাখ্যা

Question: A circle and a rectangle have the same perimeter. The sides of the rectangle are 9 cm and 13 cm. What is the area of the circle?

Solution:
The sides of the rectangle are 9 cm and 13 cm.
Perimeter of the rectangle =2(9 + 13) = 44 cm
Circumference of circle = 44 cm.

Here
2πr = 44
(22/7)r = 22
r/7 = 1
r = 7

Area of circle = πr²
= (22/7) × 7²
= (22/7) × 49
= (22 × 7)
= 154 cm²

১,৫৯৮.

One pipe can fill a tank four times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the faster pipe alone will be able to fill the tank in:

ক
40 minutes
খ
45 minutes
গ
50 minutes
ঘ
55 minutes

সঠিক উত্তর: খ

45 minutes

উত্তর

সঠিক উত্তর: খ

45 minutes

খ

ব্যাখ্যা

Question: One pipe can fill a tank four times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the faster pipe alone will be able to fill the tank in:

Solution:
Let,
the slower pipe alone fill the tank in x minutes.
Then, Faster pipe alone will fill it in x/4 minutes.

ATQ,
(1/x) + (4/x) = 1/36
⇒ 5/x = 1/36
∴ x = 180

The slower pipe alone fill the tank in 180 minutes.
the faster pipe alon will be able to fill the tank in = (180 ÷ 4) minutes.
= 45 minutes

১,৫৯৯.

Find out the missing number : 52, 64, 76, ____ , 100

ক
78
খ
82
গ
86
ঘ
88

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

ব্যাখ্যা

Question: Find out the missing number : 52, 64, 76, ____ , 100

Solution:
52 + 12 = 64
64 + 12 = 76
76 + 12 = 88
88 + 12 = 100

১,৬০০.

An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?

ক
144°
খ
150°
গ
168°
ঘ
180°

সঠিক উত্তর: ঘ

180°

উত্তর

সঠিক উত্তর: ঘ

180°

ঘ

ব্যাখ্যা

Question: An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?

Solution:

Time between 8 o'clock in the morning to 2 o'clock in the afternoon = 6 hours

Angle traced by the hour hand in 6 hours = {(360/12) × 6}° = 180°