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Bank Math

মোট প্রশ্ন১৬,১২৪এই পাতা১০০প্রতি পাতা১০০
প্রশ্ন দেখুনঅনুশীলন
ঘনত্ব
উত্তর
উত্তরিতবর্তমানপুনরায় দেখুনঅসম্পূর্ণ

Bank Math

PrepBank · পাতা ৫৪ / ১৬১ · ৫,৩০১–৫,৪০০ / ১৬,১২৪

৫,৩০১.
The difference of two numbers is 11 and one-fifth of their sum is 9. Find the numbers.
  1. ক
    ক) 28 & 16
  2. খ
    খ) 28 & 17
  3. গ
    গ) 28 & 18
  4. ঘ
    ঘ) 28 & 19
  5. ঙ
    ঙ) 28 & 12
ব্যাখ্যা

Let, The numbers are x & y,
therefore,
x - y = 11 ------ (1) and
1/5(x + y) = 9 or, x + y = 45 ------ (2)
adding two equation we got,
2x = 56 or, x = 28,
putting the value of x in equation 1,
we get, y = 17

৫,৩০২.
B’s age after 12 years would be equal to 4 times his age 6 years ago. Find his age 5 years hence? 
  1. ক
    10 years
  2. খ
    12 years
  3. গ
    17 years
  4. ঘ
    20 years
ব্যাখ্যা

Question: B’s age after 12 years would be equal to 4 times his age 6 years ago. Find his age 5 years hence?
 
Solution:
Let B’s present age be ‘x’ years.

According to the question,
x + 12 = 4(x - 6)
⇒ x + 12 = 4x - 24
⇒ 3x = 36
⇒ x = 12

∴ B’s present age = 12 years

Therefore, B’s age 5 years hence = 12 + 5 = 17 years

৫,৩০৩.
A sphere of maximum volume is cut out from a solid hemisphere of radius r. The ratio of the volume of the hemisphere to that of the cut out sphere is-
  1. ক
    ক) 4 : 3
  2. খ
    খ) 3 : 2
  3. গ
    গ) 3 : 4
  4. ঘ
    ঘ) 4 : 1
ব্যাখ্যা
Question: A sphere of maximum volume is cut out from a solid hemisphere of radius r. The ratio of the volume of the hemisphere to that of the cut out sphere is-

Solution:
Volume of hemisphere = (2/3)πr3
Volume of biggest sphere = Volume of sphere with diameter r
= (4/3)π(r/2)3
= (1/6)πr3

∴ Required ratio = {(2/3)πr3}/{(1/6)πr3}
= 4/1
= 4 : 1
৫,৩০৪.
The base of an isosceles triangle is 6cm and one of the equal sides is 12cm. Find the radius of the circle through the vertices of the triangle?
  1. ক
    ক) 7√13/3
  2. খ
    খ) 7√5/6
  3. গ
    গ) 8√15/5
  4. ঘ
    ঘ) 5√5/3
ব্যাখ্যা
 
ধরি,
বৃত্তের ব্যাসার্ধ r সেন্টিমিটার।
ত্রিভুজের উচ্চতা h = (r + x) সেন্টিমিটার।

এখানে,
AB = 6 সেন্টিমিটার
AD = 6/2 = 3 সেন্টিমিটার।

সুতরাং, ΔACD  ∠D = 90°

পিথাগোরাসের সূত্র প্রয়োগ করে পাইঃ
AC2 = CD2 + AD2
122 = h2 + 32.
h2 = 135
h  = √135

ΔADE
পিথাগোরাসের সূত্র প্রয়োগ করে পাই
AE2= AD2 + DE2 
r2 = 32 + x2
r2 = 9 + (h - r)2
r2 = 9 + h2 - 2hr + r2
0 = 9 + h2 - 2hr 
2hr = 9 + h2
r  = (9 + h2)/2h
r = 9 + 135/2√135
r = 144/2√135
r = 72/√135
r =  72√135/135
r =  72√(9 × 15)/135
r = (72× 3√15)/135
r = 8√15/5
৫,৩০৫.
The average age of five members is 27. If one of them is excluded the average decreases by 2. The age of the excluded person is:
  1. ক
    ক) 40
  2. খ
    খ) 35
  3. গ
    গ) 28
  4. ঘ
    ঘ) 38
ব্যাখ্যা

The average age of five members is 27
Total age = 27× 5 = 135
After excluding one person, the new average = 27 - 2 = 25
New total age = 25× 4 = 100
Then the age of excluded person = Total age - New total age
= 135 - 100
= 35
Hence the required answer is 35.

৫,৩০৬.
Two times a number added to another number is 25. Three times the first number minus the other number is 20. Find the numbers.
  1. ক
    ক) 8,11
  2. খ
    খ) 9,12
  3. গ
    গ) 9, 7
  4. ঘ
    ঘ) 6, 8
ব্যাখ্যা
Question: Two times a number added to another number is 25. Three times the first number minus the other number is 20. find the numbers.
Solution:
প্রশ্নমতে, 
2x + y = 25 ----- (1)
3x - y = 20 -----(2)

সমীকরণ দুটি যোগ করে পাই,
5x = 45
 x = 9

x এর মান (1)নং এ বসিয়ে পাই,
   2x + y = 25
বা, 2(9) + y = 25
বা, 18+ y = 25
বা, y = 7
৫,৩০৭.
In order to maintain the price line, a trader allows a discount of 12 % on the marked price of goods in his ship. However, he still makes a gross profit of 32 % on the cost price. Find the profit percent he would have made on the selling price had he sold at the marked price.
  1. ক
    40%
  2. খ
    42%
  3. গ
    50%
  4. ঘ
    52%
ব্যাখ্যা
Question: In order to maintain the price line, a trader allows a discount of 12 % on the marked price of goods in his ship. However, he still makes a gross profit of 32 % on the cost price. Find the profit percent he would have made on the selling price had he sold at the marked price.

Solution:
Let,
CP = 100
SP = 132
This is after a discount of 12%
Thus the marked price must be = 132 + {(132 × 12)/88} = 150

∴ Profit Percent = {(150 - 100)/100} × 100% = 50%
Therefore he is marking the product 50% above the cost price. Hence the profit will be 50%
৫,৩০৮.
20000 Tk. in 10% compound interest for 2 years will be -
  1. ক
    ক) 24200 Tk.
  2. খ
    খ) 23200 Tk.
  3. গ
    গ) 22000 Tk.
  4. ঘ
    ঘ) 20980 Tk.
ব্যাখ্যা
Question: 20000 Tk. in 10% compound interest for 2 years will be - 

Solution: 
here, 
P = 20000
r = 10% = 10/100
n = 2

compound principle after 2 years,
= P(1 + r)n
= 20000(1 + 10/100)2
= 20000(110/100)2
= 2 × (110)2
= 2 × 12100
= 24200
৫,৩০৯.
If θ + ϕ = π/2, and sinθ = 1/2, then find out the value of sinϕ-
  1. ক
    √3
  2. খ
    √3/2
  3. গ
    1/√3
  4. ঘ
    2/√3
ব্যাখ্যা
Question: If θ + ϕ = π/2, and sinθ = 1/2, then find out the value of sinϕ-

Solution:
দেওয়া আছে,
θ+ϕ = π/2
⇒ θ = π/2 - ϕ
⇒ sinθ = sin(π/2 - ϕ)
⇒ 1/2 = cosϕ
⇒ cos²ϕ = 1/4
⇒ 1 - sin²ϕ = 1/4
⇒ 1 - 1/4 = sin²ϕ
⇒ sin²ϕ = 3/4
∴ sinϕ = √3/2
৫,৩১০.
A cube has a total surface area of 486 square meters. What is the volume of the cube?
  1. ক
    343 cubic meters
  2. খ
    512 cubic meters
  3. গ
    729 cubic meters
  4. ঘ
    1000 cubic meters
ব্যাখ্যা

Question: A cube has a total surface area of 486 square meters. What is the volume of the cube?

Solution:
ধরি, ঘনকের বাহুর দৈর্ঘ্য = a মিটার।

আমরা জানি, ঘনকের সম্পূর্ণ পৃষ্ঠের ক্ষেত্রফল = 6a2

প্রশ্নমতে,
6a2 = 486
⇒ a2 = 486/6
⇒ a2 = 81
∴ a = 9 মিটার

এখন, ঘনকের আয়তন = a3 = 93 = 729 ঘন মিটার

অতএব, ঘনকটির আয়তন = 729 ঘন মিটার

৫,৩১১.
What is the total surface area of a right circular cone with a base radius of 7 cm and a height of 24 cm?
  1. ক
    550 cm2
  2. খ
    704 cm2
  3. গ
    810 cm2
  4. ঘ
    840 cm2
ব্যাখ্যা

Question: What is the total surface area of a right circular cone with a base radius of 7 cm and a height of 24 cm?

Solution:
দেওয়া আছে,
ভূমির ব্যাসার্ধ r = 7 cm, উচ্চতা h = 24 cm
∴ হেলানো উচ্চতা, l = √(r2 + h2)
= √(72 + 242)
= √(49 + 576)
= √(625)
= 25 cm.

সমগ্র পৃষ্ঠতলের ক্ষেত্রফল (total surface area), = πr(l + r)
= (22/7) × 7 × (25 + 7)
= 22 × 32
= 704 cm2.

∴ সমগ্র পৃষ্ঠতলের ক্ষেত্রফল (total surface area) = 704 cm2.

৫,৩১২.
3 pumps working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?
  1. ক
    9
  2. খ
    10
  3. গ
    11
  4. ঘ
    12
ব্যাখ্যা

Question: 3 pumps working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?

Solution: 
3 pumps need 2 × 8 hours = 16 hours
1 pump needs  16 × 3  hours
4 pumps need (16 × 3)/4 hours
= 12 hours

৫,৩১৩.
In covering a distance of 48 km, Robin takes 2 hours more than Karim. If Robin triples his speed, he would take 2 hours less than Karim. What is Robin's original speed in km/h?
  1. ক
    8 km/h
  2. খ
    10 km/h
  3. গ
    12.5 km/h
  4. ঘ
    15 km/h
ব্যাখ্যা

Question: In covering a distance of 48 km, Robin takes 2 hours more than Karim. If Robin triples his speed, he would take 2 hours less than Karim. What is Robin's original speed in km/h?

সমাধান:
ধরি, Robin-এর মূল গতিবেগ = x কিমি/ঘন্টা
∴ Robin-এর 48 কিমি অতিক্রম করতে সময় লাগে = 48/x ঘন্টা

ধরি, Karim-এর 48 কিমি অতিক্রম করতে সময় লাগে = t ঘন্টা

প্রথম শর্ত অনুযায়ী:
Robin, Karim-এর চেয়ে 2 ঘন্টা বেশি সময় নেয়,
⇒ 48/x = t + 2 ........ (i)

দ্বিতীয় শর্ত অনুযায়ী:
Robin যদি তার গতিবেগ তিনগুণ করে (3x কিমি/ঘন্টা), তাহলে সে Karim-এর চেয়ে 2 ঘন্টা কম সময় নেয়,
⇒ 48/(3x) = t - 2 ........ (ii)

সমীকরণ (i) থেকে: t = 48/x - 2

সমীকরণ (ii)-তে বসিয়ে পাই,
48/(3x) = (48/x - 2) - 2
⇒ 16/x = 48/x - 4
⇒ 48/x - 16/x = 4
⇒ 32/x = 4
⇒ x = 32/4
⇒ x = 8 কিমি/ঘন্টা

সুতরাং, Robin-এর মূল গতিবেগ হলো 8 কিমি/ঘন্টা।

৫,৩১৪.
In how many ways 6 students can be chosen from the class of 10 students?
  1. ক
    170 ways
  2. খ
    200 ways
  3. গ
    210 ways
  4. ঘ
    218 ways
ব্যাখ্যা
Question: In how many ways 6 students can be chosen from the class of 10 students?

Solution:
ways 6 students can be chosen from the class of 10 students is = 10C6
= 10!/(6! 4!)
= 210 ways
৫,৩১৫.
After filling the car's fuel tank, a driver drove from P to Q and then to R. He used (2/5)th portion of the fuel driving from P to Q. If he used another 7 liters to drive from Q to R and still had (1/4)th of the tank left, how many liters does the tank hold?
  1. ক
    18 liters
  2. খ
    20 liters
  3. গ
    22 liters
  4. ঘ
    25 liters
ব্যাখ্যা
Question: After fillings the car's fuel tank, a driver drove from P to Q and then to R. He used (2/5)th portion of the fuel driving from P to Q. If he used another 7 liters to drive from Q to R and still had (1/4)th of the tank left,  how many liters does the tank hold?

Solution: 
Let full capacity x liters 

Fuel used from Q to R = x - (2x/5 + 1x/4)
= (20x - 8x - 5x)/20
= 7x/20

Now,
7x/20 of capacity = 7 liters
x of capacity = 7 × 20/7 liters
= 20 liters
৫,৩১৬.
X and Y Clubs consist of 300 and 370 members respectively. If the total member of the two clubs is 590 then how many members belong to both clubs?
  1. ক
    ক) 50
  2. খ
    খ) 60
  3. গ
    গ) 70
  4. ঘ
    ঘ) 80
ব্যাখ্যা
Question: X and Y Clubs consist of 300 and 370 members respectively. If the total member of the two clubs is 590 then how many members belong to both clubs?

Solution : 
সমাধান:
ধরি 
n(A) = 300 , n(B) =370 এবং n(A ∪ B) = 590

আমরা জানি 
n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
n(A ∩ B) = n(A) + n(B) - n(A ∪ B)
              = 300 + 370 - 590
              = 670 - 590
              = 80
৫,৩১৭.
Find the compound interest for Tk. 50000 at 4% interest per annum in 2 years.
  1. ক
    Tk. 8040
  2. খ
    Tk. 3080
  3. গ
    Tk. 4050
  4. ঘ
    Tk. 4080
  5. ঙ
    None
ব্যাখ্যা
Question: Find the compound interest for Tk. 50000 at 4% interest per annum in 2 years.

Solution:
Principal (P) = Tk. 50000
Rate (r) = 4%
Time (n) = 2 years

A = P[1 + (r/100)]n
A = 50000(1 + 4/100)2
= 50000 × 1.04 × 1.04
= 54080

Compound Amount (A) = Tk. 54080

Compound Interest (CI) = A - P
⇒ CI = 54080 - 50000
∴ CI = 4080

∴ Compound Interest = Tk. 4080
৫,৩১৮.
For a circle where the diameter is 4π, calculate the radius-to-circumference ratio.
  1. ক
    1 : 2π
  2. খ
    2 : 3π
  3. গ
    2π : 3
  4. ঘ
    2 : 5π
ব্যাখ্যা

Question: For a circle where the diameter is 4π, calculate the radius-to-circumference ratio.

Solution:
Here
The diameter of the circle is d = 4π
So the radius of the circle r = 2π

∴ Circumference of circle = 2. π. 2π
= 4π2

So the ratio between radius and Circumference of circle = 2π : 4π2

= 2π/4π2

= 1 : 2π

৫,৩১৯.
A box contains 20 electric bulbs, out of which 4 are defective. Two balls are chosen at random from this box. The probability that at least one of them is defective, is
  1. ক
    7/19
  2. খ
    12/19
  3. গ
    4/19
  4. ঘ
    21/95
ব্যাখ্যা

Question: A box contains 20 electric bulbs, out of which 4 are defective. Two balls are chosen at random from this box. The probability that at least one of them is defective, is

Solution:
Given that,
Total bulbs = 20
Defective bulbs = 4
Non-defective bulbs = 20 - 4 = 16
Two bulbs are chosen at random (without replacement)

Now,
P(both non-defective) = (16/20) × (15/19) = 240/380 = 12/19

And,
∴ P(at least one defective) = 1 - P(both non-defective)
= 1 - (12/19)
= (19 - 12)/19
= 7/19
∴ The probability that at least one of them is defective is 7/19

৫,৩২০.
Three friends had dinner at a restaurant. When the bill was received, Akhi paid 2/3 as much as Mira paid and Mira paid 1/2 as much as Lamia paid. What fraction of the bill did Mira pay?
  1. ক
    ক) 11/3
  2. খ
    খ) 2/13
  3. গ
    গ) 3/11
  4. ঘ
    ঘ) 13/4
  5. ঙ
    ঙ) 4/13
ব্যাখ্যা

Let Mira paid x,
so, Akhi paid 2x/3, and
Lamia paid 2x,
So total bill paid is given by,
x + (2x/3) + 2x = 1;
we get,
x = 3/11

So, Mira paid 3/11 fraction of the total bill.

৫,৩২১.
A man buys Tk. 25 shares in a company which pays 9 % dividend. The money invested is such that it gives 10 % on investment. At what price did he buy the shares?
  1. ক
    ক) Tk. 20.25
  2. খ
    খ) TK.19.50
  3. গ
    গ) Tk. 21.35
  4. ঘ
    ঘ) Tk. 22.50
  5. ঙ
    ঙ) Tk. 24.53
ব্যাখ্যা

Suppose he buys each share for Tk. x.
Then, Tk.(25 × 9/100) = (x × 10/100)
or x = Tk. 22.50.
Cost of each share = Tk. 22.50.

৫,৩২২.
The price of a phone is Tk. 8000. Its price is first increased by 25% and then decreased by 20%. What is the present price of the phone? 
  1. ক
    Tk. 5000
  2. খ
    Tk. 5550
  3. গ
    Tk. 5900
  4. ঘ
    Tk. 8000
ব্যাখ্যা

Question: The price of a phone is Tk. 8000. Its price is first increased by 25% and then decreased by 20%. What is the present price of the phone?

Solution:
Initial Cost = Tk. 8000
After 25% increase in the cost, it becomes,
(8000 + 25% of 8000)
= 8000 + 2000
= Tk. 10000

Now, cost is decreased by 20%, so cost will become,
(10000 - 20% of 10000)
= 10000 - 2000
= Tk. 8000

So, present cost is Tk. 8000.

৫,৩২৩.
Which of the following fraction is the largest?
  1. ক
    7/8
  2. খ
    13/16
  3. গ
    31/40
  4. ঘ
    63/80
ব্যাখ্যা
Question: Which of the following fraction is the largest?

Solution:
L.C.M. of 8, 16, 40 and 80 = 80.
7/8 = 70/80; 13/16 = 65/80;  31/40 = 62/80

Since, 70/80 > 65/80 > 63/80> 62/80,
so 7/8> 13/16 > 63/80 > 31/40
 
So, 7/8 is the largest.
৫,৩২৪.
Sanzida ate 3/4 of a pizza. Her brother Babu ate 1/2 of what was left. Then their friend Pavel ate 2/3 of what was still left. What fraction of the pizza remains uneaten? 
  1. ক
    1/14
  2. খ
    1/12
  3. গ
    1/24
  4. ঘ
    None
ব্যাখ্যা

Question: Sanzida ate 3/4 of a pizza. Her brother Babu ate 1/2 of what was left. Then their friend Pavel ate 2/3 of what was still left. What fraction of the pizza remains uneaten?

Solution:
Sanzida ate = 3/4
∴ Remaining = 1 - 3/4 = 1/4

Babu ate = 1/2 × 1/4 = 1/8
∴ Remaining = 1/4 - 1/8 = (2 - 1)/8 = 1/8

Pavel ate = 2/3 × 1/8 = 2/24 = 1/12
∴ Remaining = 1/8 - 1/12 = (3 - 2)/24 = 1/24

∴ Fraction of pizza remaining uneaten = 1/24.

৫,৩২৫.
How many permutations of 12 different letters may be made?
  1. ক
    1
  2. খ
    12!
  3. গ
    12!/12
  4. ঘ
    None of these
ব্যাখ্যা
There are 12 different letters. No letter can be repeated.
So, number of permutations = 12!
৫,৩২৬.
The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?
  1. ক
    ক) 8 : 7
  2. খ
    খ) 1 : 1
  3. গ
    গ) 7 : 8
  4. ঘ
    ঘ) 21 : 22
ব্যাখ্যা
প্রশ্ন: The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?

সমাধান: 
ধরি,
বালকের সংখ্যা ৭ক জন
বালিকার সংখ্যা ৮ক জন 

বালকের সংখ্যা ২০% বাড়লে,
বালকের সংখ্যা হয় ৭ক + {৭ক × (২০/১০০)} জন
= ৭ক + ১.৪ক জন
= ৮.৪ক 

বালিকার সংখ্যা ১০% বাড়লে,
বালিকার সংখ্যা হয় ৮ক + {৮ক × (১০/১০০)} জন
= ৮ক + ০.৮ক
= ৮.৮ক

বালক : বালিকা = ৮.৪ক : ৮.৮ক = ৮.৪ : ৮.৮ = ৮৪ : ৮৮ = ২১ : ২২ 
৫,৩২৭.
If the workforce is doubled, how much longer will it take to finish the task?
  1. ক
    3 times
  2. খ
    2 times
  3. গ
    0.5 times
  4. ঘ
    None of these
ব্যাখ্যা

Question: If the workforce is doubled, how much longer will it take to finish the task?
​
Solution:
ধরি,
শ্রমিক সংখ্যা = x, এর দিগুণ = 2x,
সময় = n
x জন কাজটি করে n সময়ে

১ জন কাজটি করে = xn সময়ে
২x জন কাজটি করে = xn/২x
= n/২ সময়ে বা ১/২ সময়ে।

৫,৩২৮.
The difference between the ages of a father and his son is 40% of the father’s age. If the son is 18 years old, find the father’s age.
  1. ক
    38 years
  2. খ
    45 years
  3. গ
    30 years
  4. ঘ
    40 years
ব্যাখ্যা

Question: The difference between the ages of a father and his son is 40% of the father’s age. If the son is 18 years old, find the father’s age.

Solution:
Let
Let father’s age = x

Then,
x - 18 = 40% of x
⇒ x - 18 = 40x/100
⇒ x - 18 = 2x/5
⇒ x - 2x/5 = 18
⇒ (5x - 2x)/5 = 18
⇒ 3x = 90
∴ x = 30

So the father’s age is 30 years.

৫,৩২৯.
Tickets numbered 1 to 30 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 4 or 5?
  1. ক
    11/30
  2. খ
    2/5 
  3. গ
    7/15
  4. ঘ
    1/2
ব্যাখ্যা

Question: Tickets numbered 1 to 30 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 4 or 5?

Solution:
Here, S = {1, 2, 3, 4, ...., 29, 30}
n(S) = 30

Let E = event of getting a multiple of 4 or 5
∴ n(E) = {4, 5, 8, 10, 12, 15, 16, 20, 24, 25, 28, 30}

∴ P(E) = n(E)/n(S)
= 12/30
= 2/5

৫,৩৩০.
The value of 'A' varies in verse in inverse proportion as the square of 'B'.If the value of 'A' is equal to 40 when 'B' is equal to 12. What would be the value of 'A' when 'B' is equal to 24?
  1. ক
    ক) 15
  2. খ
    খ) 20
  3. গ
    গ) 10
  4. ঘ
    ঘ) 22
ব্যাখ্যা
দেয়া আছে
A = k/B2 ......... (i) 
k= AB2
=40×122
= 40×144

(i) নং সমীকরণ থেকে পাই 
A = k/B2
   = 40×144/24×24 
    = 10
৫,৩৩১.
If the ratio of principal and the simple interest of 5 year is 10:3, then the rate of interest is = ?
  1. ক
    ক) 6%
  2. খ
    খ) 8%
  3. গ
    গ) 3%
  4. ঘ
    ঘ) 5%
ব্যাখ্যা

P/S.I.=10/3
Let Principal = 10
S.I. for 5 year = 3
S.I. for 1 year = 0.6
Rate = S.I./Principal×100
Rate = 0.6/10×100
=6%

৫,৩৩২.
Arif travels 1/3rd of the distance at an average speed of 5 km/hr, 2/5the of the distance at an average speed of 4 km/hr and the rest 12 miles in 2 hours. What is the total distance traveled by Arif?
  1. ক
    45
  2. খ
    48
  3. গ
    52
  4. ঘ
    54
  5. ঙ
    None of these
ব্যাখ্যা

Distance = X
Distance covered at 5km and 4 km = x/3 + 2x/5
= (5x + 6x)/15
= 11x/15
Rest of the distance = 1 - 11x/15 = 4x/15
ATQ,
4x/15 = 12
or, x = (12 × 15)/4
or, x = 45.

৫,৩৩৩.
What is the probability of getting a sum 9 from two throws of a dice?
  1. ক
    1/9
  2. খ
    13/36
  3. গ
    4/38
  4. ঘ
    1/12
  5. ঙ
    None of the above
ব্যাখ্যা
Question: What is the probability of getting a sum 9 from two throws of a dice?

Solution: 
total event for two dice = 6 × 6 = 36
total event of getting 9 is = {(6, 3),(5, 4),(4, 5),(3, 6)} = 4

probability = 4/36 = 1/9
৫,৩৩৪.
The product of two different irrational numbers is always -
  1. ক
    ক) rational
  2. খ
    খ) irrational
  3. গ
    গ) both of above
  4. ঘ
    ঘ) none
ব্যাখ্যা

Product of two different irrational numbers is sometimes irrational and sometimes rational. 
For example, product of √2 and √3 is √6, which is irrational
but product of √3 and √12 is √36, which is rational number 6. 

৫,৩৩৫.
Rohit lends his 40800 Tk in two parts at simple interest. He lends one part for a period of 8 years at a rate of 6.25%. The other part he lends for 5 years at a rate of 7%. Both the parts earn him the same interest. Find the value of the smaller part of money.
  1. ক
    ক) Tk. 13000
  2. খ
    খ) Tk. 16800
  3. গ
    গ) Tk. 19200
  4. ঘ
    ঘ) Tk. 20100
ব্যাখ্যা

Two parts are = A and (40800 - A)
Time period and Simple interest are same for both

Simple Interest = (P × R × T)/100

∴ (A × 6.25 × 8)/100 = {(40800 - A) × 7 × 5}/100
∴ 50A = 35 × 40800 - 35A
∴ 85A = 35 × 40800
∴ A = 8400

Smaller amount is Tk. 16800
By direct observation, we can say that 16800 is smaller - as it is smaller than half of 40800.

৫,৩৩৬.
If a = bc and c = a - b, then the value of a is-
  1. ক
    ক) 2b2/(b - 1)
  2. খ
    খ) b/(b - 1)
  3. গ
    গ) b2/(b + 1)
  4. ঘ
    ঘ) b2/(b - 1)
ব্যাখ্যা
Given that 
a = bc and c = a - b
a = b(a - b)
a = ab - b2
b2 = ab - a
b2 = a(b - 1)
a = b2/(b - 1)
৫,৩৩৭.
In a badminton tournament, every player plays against every other player exactly once. If there were 66 matches played in total, how many players participated in the tournament?
  1. ক
    11
  2. খ
    12
  3. গ
    13
  4. ঘ
    15
ব্যাখ্যা

Question: In a badminton tournament, every player plays against every other player exactly once. If there were 66 matches played in total, how many players participated in the tournament?

Solution:
ধরি, টুর্নামেন্টে মোট খেলোয়াড়ের সংখ্যা = x

যেহেতু প্রতিটি খেলোয়াড় অন্য সকল খেলোয়াড়ের সাথে একবার করে ম্যাচ খেলে, তাই মোট ম্যাচের সংখ্যা হবে:
xC2 = 66
⇒ x!/{2!(x - 2)!} = 66
⇒ x(x - 1)/2 = 66
⇒ x(x - 1) = 132
⇒ x² - x - 132 = 0
⇒ x² - 12x + 11x - 132 = 0
⇒ x(x - 12) + 11(x - 12) = 0
⇒ (x - 12)(x + 11) = 0
⇒ x = 12 অথবা x = -11

যেহেতু খেলোয়াড়ের সংখ্যা ঋণাত্মক হতে পারে না, তাই x = 12

∴ টুর্নামেন্টে মোট খেলোয়াড়ের সংখ্যা = 12 জন।

৫,৩৩৮.
If 56Pr + 6 : 54Pr + 3 = 30800 : 1 then the value of r is?
  1. ক
    36
  2. খ
    41
  3. গ
    47
  4. ঘ
    None
ব্যাখ্যা
Question: If 56Pr + 6 : 54Pr + 3 = 30800 : 1 then the value of r is?

Solution:
56Pr + 6 : 54Pr + 3 = 30800 : 1
⇒ 56!/(50 - r)! = (30800 × 54!)/(51 - r!)
⇒ 56 × 55 = 30800/(51 - r)
⇒ 51 - r = 10
∴ r = 41
৫,৩৩৯.
A man decided to cover a distance of 6 km in 84 minutes. He decided to cover two-thirds of the distance at 4 km/hr and the remaining at some different speed. Find the speed after the two third distance has been covered -
  1. ক
    ক) 5 kmph
  2. খ
    খ) 7 kmph
  3. গ
    গ) 9 kmph
  4. ঘ
    ঘ) 3 kmph
ব্যাখ্যা

Given that,
Two thirds of the 6 km was covered at 4 km/hr
i.e. 4 km distance was covered at 4 km/hr.
Time taken to cover 4 km = 4 km/(4 km/hr)
= 1 hr
= 60 minutes
Time left = (84 – 60) minutes.
= 24 minutes
Now,
The man has to cover remaining 2 km in 24 minutes
or 24/60
= 2/5 hours
Speed required for remaining 2 km
= 2 km/(2/5)hr
= 5 km/hr.

৫,৩৪০.
If X5 = 32  and Y3 = 343 then, Y - X = ?
  1. ক
    10
  2. খ
    14
  3. গ
    5
  4. ঘ
    7
ব্যাখ্যা
Question: If X5 = 32  and Y3 = 343 then, Y - X = ?

Solution:
Given that,
X5 = 32
⇒ X5 = 25
∴ X = 2
and
Y3 = 343
⇒ Y3 = 73
∴ Y = 7

Y - X
= 7 - 2
= 5
৫,৩৪১.
Find the value of log22 + log222 + log223 + ........ + log22n.
  1. ক
    n(n + 1)/2
  2. খ
    n + 1
  3. গ
    n
  4. ঘ
    2n
  5. ঙ
    None of these
ব্যাখ্যা
Question: Find the value of log22 + log222 + log223 + ........ + log22n.

Solution:
log22 + log222 + log223 + ........ + log22n
= log22 + 2log22 + 3log22 + ........ + nlog22
= 1 + 2 + 3 + ........ + n
= n(n+1)/2
৫,৩৪২.
If Discriminant > 0, then the equation has-
  1. ক
    Two distinct real roots
  2. খ
    No real roots
  3. গ
    Two equal real roots
  4. ঘ
    None of these
ব্যাখ্যা
Question: If Discriminant > 0, then the equation has-

Solution:
Discriminant (নিশ্চায়ক),
ax2 + bx + c = 0 দ্বিঘাত সমীকরণের নিশ্চায়কের মান b² - 4ac

দ্বিঘাত সমীকরণের মূলের প্রকৃতি:
1. যদি b2 - 4ac = 0 হয় তবে দ্বিঘাত সমীকরণের মূলদ্বয় বাস্তব ও সমান হবে।
2. যদি b2 - 4ac > 0 হয় তবে দ্বিঘাত সমীকরণের মূলদ্বয় বাস্তব ও অসমান হবে।
3. যদি b2 - 4ac < 0 হয় তবে দ্বিঘাত সমীকরণের মূলদ্বয় অবাস্তব ও অসমান হবে।
4. যদি b2 - 4ac পূর্ণবর্গ সংখ্যা হয় তবে দ্বিঘাত সমীকরণের মূলদ্বয় মূলদ ও অসমান হবে।
৫,৩৪৩.
The interest charged on a loan is p dollars per $1,000 for the first month and q dollars per $1000 for each month after the first month. How much interest will be charged during the first three months on a loan of $10,000?
  1. ক
    ক) 10p + 20q
  2. খ
    খ) 30q
  3. গ
    গ) 30p
  4. ঘ
    ঘ) 20p + 10q
ব্যাখ্যা

Interest for the first month = p×(10000/1000) = 10p
Interest for the 2nd month will be =  q×(10000/1000) = 10q
Interest for the 3rd month will be = q×(10000/1000) = 10q

∴ Total Interest = 10p + 20q

৫,৩৪৪.
10 people shake their hands with each other. How many handshakes occurred?
  1. ক
    ক) 40
  2. খ
    খ) 22
  3. গ
    গ) 45
  4. ঘ
    ঘ) 20
ব্যাখ্যা

যে কোন করমর্দন অথবা কোলাকুলির অংকে শুধু কত জন করমর্দন (Handshake), বা কোলাকুলি করল তা দেয়া থাকবে।
এক্ষেত্রে মনে রাখতে হবে যে প্রত্যেক বার করমর্দন বা কোলাকুলি করার সময় মোট ২ জন লোকের প্রয়োজন।
তাই এক্ষেত্রে সূত্রটি হবে nC2 = মোট লোকC২ জন সব সময়
10C2 = 10!/2!(10 - 2)!
= 10!/2!8!
= (10 × 9)/2
= 5 × 9
= 45.

৫,৩৪৫.
If 3 jackets and 5 sweaters cost Tk. 12,000, and 5 jackets and 3 sweaters cost Tk. 13,600, what is the cost of one jacket?
  1. ক
    Tk. 15000
  2. খ
    Tk. 2000
  3. গ
    Tk. 2500
  4. ঘ
    Tk. 3000
ব্যাখ্যা

Question: If 3 jackets and 5 sweaters cost Tk. 12,000, and 5 jackets and 3 sweaters cost Tk. 13,600, what is the cost of one jacket?

Solution:
ধরি, একটি জ্যাকেটের মূল্য x টাকা এবং একটি সোয়েটারের মূল্য y টাকা।

প্রশ্নমতে,
3x + 5y = 12000 ............... (i) 
5x + 3y = 13600 .............. (ii)

(ii) × 5 - (i) × 3 ⇒
(25x + 15y) - (9x + 15y) = 68000 - 36000
⇒ 25x - 9x = 32000
⇒ 16x = 32000
⇒ x = 32000/16
⇒ x = 2000

সুতরাং, একটি জ্যাকেটের মূল্য 2000 টাকা।

৫,৩৪৬.
A train 180 meters long passes a pole in 12 seconds. How long will it take to pass a platform that is 420 meters long?
  1. ক
    30 seconds
  2. খ
    40 seconds
  3. গ
    80 seconds
  4. ঘ
    60 seconds
ব্যাখ্যা

Question: A train 180 meters long passes a pole in 12 seconds. How long will it take to pass a platform that is 420 meters long?

Solution:
Train's speed = Distance/Time
= 180/12 = 15 m/s

Total distance to pass the platform,
= Length of train + Length of platform
= 180 m + 420 m
= 600 m

∴ Required time = Distance/Speed
= 600/15
= 40 seconds

∴ The train will take 40 seconds to pass platform.

৫,৩৪৭.
Yesterday was Powel's birthday. His father brought a cake for their family, Powel took 1/2 of the cake and had 3 times as much as each of the other family members had. The total number of family member is-
  1. ক
    4
  2. খ
    5
  3. গ
    6
  4. ঘ
    3
ব্যাখ্যা
Question: Yesterday was Powel's birthday. His father brought a cake for their family, Powel took 1/2 of the cake and had 3 times as much as each of the other family members had. The total number of family member is-

Solution: 
Let the total number of the family member excluding Powel be 'x' and the amount of cake be 100 units

Share of cake taken by Powel = 100 × 1/2 = 50 units
Remaining share of cake taken by family member = (100 - 50)/x  = 50/x
Now
50 = 3 × 50/x
⇒ 50x = 3 × 50 
⇒ x = 3

∴ Total number of the family members including Powel = 3 + 1 = 4
৫,৩৪৮.
A man buys doughnuts at the rate of Tk. 35 per 100 pieces and sells them at Tk. 7.20 per dozen. If the profit is Tk. 30, how many doughnuts did he buy?
  1. ক
    ক) 60
  2. খ
    খ) 120
  3. গ
    গ) 180
  4. ঘ
    ঘ) 210
ব্যাখ্যা

Cost price of one doughnut = 35/100 = 0.35
Selling price of one doughnuts = 7.20/12 = 0.6 tk
Profit in one doughnuts = 0.6 - 0.35 = 0.25 tk
So, Total doughnuts bought = 30 / 0.25 = 120

৫,৩৪৯.
A sum of money is borrowed and paid back in two annual instalments of Tk. 882 each allowing 5% compound interest. The sum borrowed was -
  1. ক
    Tk. 1640
  2. খ
    Tk. 1830
  3. গ
    Tk. 1250
  4. ঘ
    Tk. 1440
ব্যাখ্যা

Question: A sum of money is borrowed and paid back in two annual instalments of Tk. 882 each allowing 5% compound interest. The sum borrowed was -

Solution:
Principle,
= (P.W. of Tk. 882 due 1 year hence) + (P.W of Tk. 882 due 2 years hence)
= [{882/(1 + 5/100)} + {882/(1 + 5/100)2}]
= [{(882 × 20)/21} + {(882 × 400)/441}]
= 840 + 800
= Tk. 1640

The sum borrowed was Tk. 1640.

৫,৩৫০.
  1. ক
    12
  2. খ
    2
  3. গ
    5
  4. ঘ
    0
ব্যাখ্যা

Question:

Solution:

৫,৩৫১.
What is the volume of a cylinder with radius 6 and height of 7?
  1. ক
    ক) 284π 
  2. খ
    খ) 252π 
  3. গ
    গ) 181π
  4. ঘ
    ঘ) 294π
ব্যাখ্যা
সিলিন্ডারের ব্যাসার্ধ r = 6 একক এবং উচ্চতা h = 7 একক।

নির্ণেয় আয়তন =πr2h ঘন একক
                        = π × 62 × 7
                        = 252π ঘন একক
৫,৩৫২.
What is the angle between the hour and minute hand of a clock when it is 4 : 40 pm?
  1. ক
    120°
  2. খ
    100°
  3. গ
    150°
  4. ঘ
    80°
ব্যাখ্যা

Question: What is the angle between the hour and minute hand of a clock when it is 4 : 40 pm?

সমাধান:
4টা 40 মিনিট = 4 + (40/60) ঘন্টা
= 4 + 2/3 = 14/3 ঘন্টা

আমরা জানি,
ঘণ্টার কাঁটা 12 ঘণ্টায় 360° ঘোরে।
∴ 1 ঘণ্টায় ঘোরে = 360°/12 = 30°
∴ 14/3 ঘণ্টায় ঘোরে = (30° × 14)/3
= 140°

আবার,
মিনিটের কাঁটা 60 মিনিটে 360° ঘোরে।
∴ 1 মিনিটে ঘোরে = 360°/60 = 6°
∴ 40 মিনিটে ঘোরে = 40 × 6° = 240°

ঘড়ির কাঁটা দুটির মধ্যবর্তী কোণ = |240° - 140°| = 100°

৫,৩৫৩.
A lent Tk. 5,000 to B for 2 years and Tk. 3,000 to C for 4 years on simple interest at the same rate of interest and received Tk. 2,200 in all from both of them as interest. The rate of interest per annum is:
  1. ক
    ক) 9%
  2. খ
    খ) 20%
  3. গ
    গ) 10%
  4. ঘ
    ঘ) 25%
ব্যাখ্যা
Let the rate be R%p.a.
Then,
5000 × R × 2/100 + 3000 × R × 4/100 = 2200.
⇒ 100R + 120R = 2200
⇒ R = 2200/220 =10
∴Rate = 10%
৫,৩৫৪.
What is the value of 5/(x - x) = ?
  1. ক
    5
  2. খ
    0
  3. গ
    2.5
  4. ঘ
    undefined
  5. ঙ
    None of these
ব্যাখ্যা
Question: What is the value of 5/(x - x) = ?

Solution:
Given that,
5/(x - x)
= 5/0 = Undefined
Division by zero is undefined in mathematics.
৫,৩৫৫.
Calculate the area of a rhombus if the length of its side is 4 cm and one of its angles A is 120 degrees.
  1. ক
    16√3 cm2
  2. খ
    16 cm2
  3. গ
    6√2 cm2
  4. ঘ
    8√3 cm2
ব্যাখ্যা

Question: Calculate the area of a rhombus if the length of its side is 4 cm and one of its angles A is 120 degrees.

Solution:
Given that,
Side of rhombus, a = 4 cm
And One angle, A = 120°

We know,
Area of a rhombus = a2 × sin⁡A [Where a = side of rhombus, A = any interior angle.]
= 42  × sin⁡120°
= 16 × (√3/2)
= 8√3

So the area of the rhombus is 8√3 cm2

Note:
sin(180∘ - θ) = sinθ,
So sin120° = sin⁡(180° - 60°) = sin⁡60° = √3/2

৫,৩৫৬.
If tan(θ + 30°) = √3, then what is the value of cosθ?
  1. ক
    1
  2. খ
    1/2
  3. গ
    √3/2
  4. ঘ
    1/√2
  5. ঙ
    0
ব্যাখ্যা

Question: If tan(θ + 30°) = √3, then what is the value of cosθ?

Solution:
Given that,
tan(θ + 30°) = √3
⇒ tan(θ + 30°) = tan60°
⇒ (θ + 30°) = 60°
∴  θ = 30°

Now,
cosθ
= cos30°
= √3/2

৫,৩৫৭.
A cuboid has dimensions in the ratio 1 : 2 : 4 and a total surface area of 112 cm2. What is its volume?
  1. ক
    48 cm3
  2. খ
    84 cm3
  3. গ
    64 cm3
  4. ঘ
    72 cm3
ব্যাখ্যা

Question: A cuboid has dimensions in the ratio 1 : 2 : 4 and a total surface area of 112 cm2. What is its volume?

Solution:
দেয়া আছে,
 আয়তাকার ঘনবস্তুর মাত্রাগুলির অনুপাত = 1 : 2 : 4
এবং সমগ্র পৃষ্ঠতলের ক্ষেত্রফল = 112 cm²

ধরি , আয়তাকার ঘনবস্তুর মাত্রাগুলির অনুপাত যথাক্রমে x, 2x এবং 4x

আমরা জানি,
আয়তাকার ঘনবস্তুর সমগ্র পৃষ্ঠতলের ক্ষেত্রফল = 2(lb + bh + lh)
⇒ সমগ্র পৃষ্ঠতলের ক্ষেত্রফল = 2(x)(2x) + (2x)(4x) + (4x)(x)
⇒ 112 = 2(2x2 + 8x2 + 4x2)
⇒ 112 = 2(14x2)
⇒ 112 = 28x2
⇒ x2 = 112/28
⇒ x2 = 4
⇒ x = 2

সুতরাং, ঘনবস্তুটির মাত্রাগুলি হল,
দৈর্ঘ্য (l) = x = 2 cm
প্রস্থ (b) = 2x = 2 × 2 = 4 cm
উচ্চতা (h) = 4x = 4 × 2 = 8 cm

এখন, আয়তাকার ঘনবস্তুর আয়তন, V = l × b × h
⇒ V = 2 × 4 × 8
⇒ V = 64 ঘন সেমি।

সুতরাং, নির্ণেয় আয়তন হল 64 cm3।

৫,৩৫৮.
A tank is 25 m long, 12 m wide and 6 m deep. The core of plastering its walls and bottom at 75 paisa per m2 is:
  1. ক
    ক) tk. 456
  2. খ
    খ) tk. 458
  3. গ
    গ) tk. 558
  4. ঘ
    ঘ) tk. 568
ব্যাখ্যা

Area to be plastered = [2(l + b)×h] + (l×b)
= [2(25 + 12)×6] + (25×12)
= 744 m2 
Cost of plastering = 744 × 75/100 = 558 tk

৫,৩৫৯.
Two trains, each 50 m long, moving in opposite directions, cross each other in 4 seconds. If one is moving twice as fast the other, then the speed of the faster train is:
  1. ক
    ক) 16.67 m/sec
  2. খ
    খ) 33.33 m/sec
  3. গ
    গ) 35.5 m/sec
  4. ঘ
    ঘ) 40 m/sec
ব্যাখ্যা
Question: Two trains, each 50 m long, moving in opposite directions, cross each other in 4 seconds. If one is moving twice as fast the other, then the speed of the faster train is:

Solution:
Let the speed of the slower train be x m/sec.
∴ speed of the faster train = 2x m/sec.

Relative speed = (x + 2x) m/sec = 3x m/sec.

Now,
(50 + 50)/4 = 3x
⇒ 12x = 100
⇒ x = 100/12
∴ x = 8.333

∴ speed of the faster train = 2 × 8.333 = 16.67 m/sec.
৫,৩৬০.
A can complete a piece of work in 18 days, B in 20 days and C in 30 days. B and C together start the work and are forced to leave after 2 days. The time taken by A alone to complete the remaining work is-
  1. ক
    20 days
  2. খ
    18 days
  3. গ
    15 days
  4. ঘ
    12 days
ব্যাখ্যা
Question: A can complete a piece of work in 18 days, B in 20 days and C in 30 days. B and C together start the work and are forced to leave after 2 days. The time taken by A alone to complete the remaining work is-

Solution:
Here,
B's 1 day's work = 1/20 part
C's 1 day's work = 1/30 part

∴ (B + C)'s 1 day's work = (1/20 + 1/30) part
∴ (B+C)'s 2 day's work = {(1/20 + 1/30) × 2} part
= [{(3+2)/60} × 2] part
= (5/60 × 2) part
= 1/6 part

Remaining work = (1 -1/6) part
= 5/6 part

A's one day's work = 1/18 part
∴ The time taken by A alone to complete the remaining work is = (5/6)/(1/18) days
= 15 days
৫,৩৬১.
The supplement of an angle exceeds twice the angle by 30°. Then the angle is equal to-
  1. ক
    60°
  2. খ
    45°
  3. গ
    50°
  4. ঘ
    35°
ব্যাখ্যা

Question: The supplement of an angle exceeds twice the angle by 30°. Then the angle is equal to-

Solution:
Let the angle be x
Then, its supplement = 180 - x

According to the question,
180 - x = 2x + 30
⇒ 180 - 30 = 3x
⇒ 150 = 3x
⇒ x = 50°

৫,৩৬২.
In a code FLOWER is written as EMPXER, GARDEN is written as FBSEEN, then how can PLANET be written in the same code?
  1. ক
    QMBOFS
  2. খ
    OMBOET
  3. গ
    NNAODU
  4. ঘ
    PNCPFS
ব্যাখ্যা
Question: In a code FLOWER is written as EMPXER, GARDEN is written as FBSEEN, then how can PLANET be written in the same code?

Solution:

Given,
F         L          O          W          E        R
↓(- 1)  ↓(+ 1)   ↓(+ 1)   ↓(+ 1)    ↓(0)    ↓(0)
E        M         P           X           E        R

G         A          R          D         E        N
↓(- 1)   ↓(+ 1)   ↓(+ 1)   ↓(+ 1)  ↓(0)    ↓(0)
F         B           S          E          E        N

Similarly,
P          L          A          N         E        T
↓(- 1)   ↓(+ 1)   ↓(+ 1)   ↓(+ 1)  ↓(0)    ↓(0)
O         M         B          O         E        T
৫,৩৬৩.
Three pipes A, B, and C are connected to a tank. Out of the three, A is the inlet pipe and B and C are the outlet pipes. If opened separately, A fills the tank in 10 hours, B empties the tank in 12 hours and C empties the tank in 30 hours. If all three are opened simultaneously, how much time does it take to fill/empty the tank?
  1. ক
    120 hours to fill
  2. খ
    60 hours to empty
  3. গ
    45 hours to empty
  4. ঘ
    30 hours to fill
ব্যাখ্যা
Question: Three pipes A, B, and C are connected to a tank. Out of the three, A is the inlet pipe and B and C are the outlet pipes. If opened separately, A fills the tank in 10 hours, B empties the tank in 12 hours and C empties the tank in 30 hours. If all three are opened simultaneously, how much time does it take to fill / empty the tank?

Solution:
Part of tank filled by pipe A in one hour working alone = 1/10
Part of tank emptied by pipe B in one hour working alone = 1/12
Part of tank emptied by pipe C in one hour working alone = 1/30

∴ Part of tank filled by pipes A, B and C in one hour working together = (1/10) - (1/12) - (1/30) =  - (1/60)
Therefore, time taken to completely empty the tank if all pipes are opened simultaneously = 1/60 hours = 60 hours
৫,৩৬৪.
What is the ratio of 5 inches to 9 feet? 
  1. ক
    7 : 108
  2. খ
    6 : 108
  3. গ
    5 : 108
  4. ঘ
    5 : 18
  5. ঙ
    None
ব্যাখ্যা

Question: What is the ratio of 5 inches to 9 feet?

Solution:
We know, 1 foot = 12 inches
So, 9 feet = 9 × 12 = 108 inches

Now,
5 inches : 9 feet = 5 : 108

∴ The ratio = 5 : 108

৫,৩৬৫.
A tap can completely fill a water tank in 8 hours. The water tank has a hole in it through which the water leaks out. The leakage will cause the full water tank to empty in 10 hours. How much time will it take for the tap to fill the tank completely with the hole?
  1. ক
    18 hours
  2. খ
    20 hours
  3. গ
    24 hours
  4. ঘ
    40 hours
  5. ঙ
    48 hours
ব্যাখ্যা

Question: A tap can completely fill a water tank in 8 hours. The water tank has a hole in it through which the water leaks out. The leakage will cause the full water tank to empty in 10 hours. How much time will it take for the tap to fill the tank completely with the hole?

Solution: 
Tap alone fills the tank in 8 hours
⇒ Filling rate = 1/8 tank/hour
Leakage alone empties the full tank in 10 hours
⇒ Emptying rate = 1/10 tank/hour

∴ Net rate = Filling rate - Emptying rate
= (1/8) - (1/10)
= (5 - 4)/40
= 1/40

Time to fill the tank with the hole = 1 full tank/Net rate
= 1/(1/40) hours
= 40 hours 

৫,৩৬৬.
The income of A, B, and C are in the ratio 7 : 9 : 12 and their spending are in the ratio 8 : 9 : 15. If A saves 1/4 th of his income then the savings of A, B, and C are in the ratio of -
  1. ক
    ক) 56 : 99 : 69
  2. খ
    খ) 69 : 56 : 99
  3. গ
    গ) 99 : 56 : 69
  4. ঘ
    ঘ) 99 : 69 : 56
ব্যাখ্যা
Question: The income of A, B, and C are in the ratio 7 : 9 : 12 and their spending are in the ratio 8 : 9 : 15. If A saves 1/4 th of his income then the savings of A, B, and C are in the ratio of -

Solution:
Let the income of A, B and C are 7x, 9x, and 12x respectively
and expenditure of A, B and C are 8y, 9y and 15y respectively

ATQ,
7x - 8y = 7x × 1/4
⇒ 28x - 32y = 7x
⇒21x = 32y
⇒ x : y = 32 : 21

∴ The ratio of savings of A, B, and C
⇒ (7x - 8y) : (9x - 9y) : (12x - 15y)
⇒ (7 × 32 - 8 × 21) : (9 × 32 - 9 × 21) : (12 × 32 - 15 × 21)
⇒ (224 - 168) : (288 - 189) : (384 - 315)
⇒ 56 : 99 : 69
৫,৩৬৭.
Four years ago, the average age of A and B was 18 years. At present the average age of A, B and C is 24 years. What would be the age of C after 4 years.
  1. ক
    ক) 26 years
  2. খ
    খ) 28 years
  3. গ
    গ) 32 years
  4. ঘ
    ঘ) 34 years
ব্যাখ্যা
Sum of the ages of A and B, 4 years ago = 18 × 2 = 36 years
Sum of the present age of A and B = 4 + 4 + 36 = 44 years
Sum of the present ages of A, B and C = 24 × 3 = 72 years
⇒ Present age of C = 72 - 44 = 28 years

∴ C's age after 4 years = 28 + 4 = 32 years.
৫,৩৬৮.
A number is decreased by 10% and then increased by 10%. The number so obtained is 10 less than the original number. What was the original number?
  1. ক
    ক) 1000
  2. খ
    খ) 2000
  3. গ
    গ) 3000
  4. ঘ
    ঘ) 4000
  5. ঙ
    ঙ) 5000
ব্যাখ্যা

x + y + xy/100
= 10 - 10 - (100/100)
= -1%
so, 1% = 10
and 100% = 10 × 100
= 1000

৫,৩৬৯.
If the difference between the circumference and diameter of a circle is 60 cm, then the radius of the circle is
  1. ক
    7cm
  2. খ
    9cm
  3. গ
    10cm
  4. ঘ
    14cm
ব্যাখ্যা
Question: If the difference between the circumference and diameter of a circle is 60 cm, then the radius of the circle is

Solution:
ধরি,
বৃত্তের ব্যাসার্ধ = r
বৃত্তের ব্যাস = 2r
বৃত্তের পরিধি = 2πr

প্রশ্নমতে,
2πr - 2r = 60
⇒ 2r(π - 1) = 60
⇒ r = (60/2)/{(22/7) - 1}
⇒ r = 30/{(22 - 7)/7}
⇒ r = (30 × 7)/15
∴ r = 14

∴ বৃত্তের ব্যাসার্ধ = r = 14 সে.মি.
৫,৩৭০.
A candidate has to obtain a minimum of 40% of the total marks to pass. He got 30% of the total marks and failed by 50 marks. What are the maximum marks?
  1. ক
    400
  2. খ
    425
  3. গ
    475
  4. ঘ
    500
ব্যাখ্যা

Question: A candidate has to obtain a minimum of 40% of the total marks to pass. He got 30% of the total marks and failed by 50 marks. What are the maximum marks?

Solution: 
Let the maximum marks be x.

Then,
40% of x - 30% of x = 50
⇒ 10% of x = 50
⇒ 10x/100 = 50
⇒ x= (50 × 100)/10
∴  x = 500

৫,৩৭১.
To complete a piece of work, Hasib takes 6 days and Tanveer takes 8 days alone respectively. Hasib and Tanveer took Tk.2400 to do this work. When Hamza joined them, the work was done in 3 days. What amount was paid to Hamza?
  1. ক
    ক) Tk.200
  2. খ
    খ) Tk.350
  3. গ
    গ) Tk.300
  4. ঘ
    ঘ) None of these
ব্যাখ্যা
প্রশ্ন: To complete a piece of work, Hasib takes 6 days and Tanveer takes 8 days alone respectively. Hasib and Tanveer took Tk.2400 to do this work. When Hamza joined them, the work was done in 3 days. What amount was paid to Hamza?

সমাধান: 
হাসিব ১ দিনে করে ১/৬ অংশ
তানভীর ১ দিনে করে ১/৮ অংশ 
হাসিব ও তানভীর একত্রে ১ দিনে করে (১/৬ + ১/৮) অংশ
= ৭/২৪ অংশ

হামজা সহ আসলে কাজ ৩ দিনে শেষ হয়।
তাহলে ৩ জনে একত্রে ১ দিনে করে ১/৩ অংশ

হামজা ১ দিনে করে ১/৩ - ৭/২৪ অংশ
= ১/২৪ অংশ

হামজা ৩ দিনে করে ৩/২৪ অংশ = ১/৮ অংশ 

১ বা সম্পূর্ণ অংশের জন্য দেয়া হয় ২৪০০ টাকা 
∴ ১/৮ অংশের জন্য দেয়া হয় ২৪০০/৮ টাকা 
= ৩০০ টাকা
৫,৩৭২.
The average runs of a cricket player of 10 innings was 32. How many runs must he make in his next innings to increase his average of runs by 4?
  1. ক
    ক) 76
  2. খ
    খ) 79
  3. গ
    গ) 85
  4. ঘ
    ঘ) 87
ব্যাখ্যা
10টি ম্যাচের রানের গড় হলো 32
10টি ম্যাচের মোট রান = 32 × 10 = 320

11 তম ম্যাচ শেষে গড় রান = 32 + 4 = 36  রান
11 তম ম্যাচ শেষে মোট হবে = 36 x 11 = 396 রান

11 তম ম্যাচে করতে হবে = 396 - 320 = 76 রান।
৫,৩৭৩.
If annual income from 6% stock at 80 is Tk. 50 more than 7% stock at 120, then the investment is-
  1. ক
    Tk. 3000
  2. খ
    Tk. 2500
  3. গ
    Tk. 4500
  4. ঘ
    Tk. 5000
ব্যাখ্যা
Question: If annual income from 6% stock at 80 is Tk. 50 more than 7% stock at 120, then the investment is-

Solution:
Let,
The investment is Tk. x

6% stock at 80,
income from Tk. 80 is 6
∴ income from Tk. x is 6x/80

7% stock at 120,
income from Tk. 120 is 7
∴ income from Tk. x is 7x/120

ATQ,
6x/80 - 7x/120 = 50
⇒ 18x - 14x = 50 × 240
⇒ 4x = 50 × 240
∴ x = 3000
৫,৩৭৪.
A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is:
  1. ক
    5 : 4
  2. খ
    3 : 2
  3. গ
    5 : 2
  4. ঘ
    3 : 1
ব্যাখ্যা
Question: A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is:

Solution:
Let man's rate upstream be x kmph.
Then, his rate downstream = 2x kmph.

∴ (Speed in still water) : (Speed of stream) = {(2x + x)/2} : {(2x - x)/2}
= (3x/2) : (x/2)
= 3 : 1
৫,৩৭৫.
A contractor employs 45 persons to do a job in 40 days. After 10 days, it was found that only one-sixth of the work was finished. How many more persons are to be employed to finish the job as per schedule? 
  1. ক
    15
  2. খ
    25
  3. গ
    40
  4. ঘ
    30 
ব্যাখ্যা

Question: A contractor employs 45 persons to do a job in 40 days. After 10 days, it was found that only one-sixth of the work was finished. How many more persons are to be employed to finish the job as per schedule?

Solution:
দেওয়া আছে:
মোট লোক = 45 জন
নির্ধারিত সময় = 40 দিন
10 দিনে সম্পন্ন কাজ = 1/6 অংশ

ধরি, সম্পূর্ণ কাজ = 1 একক

45 জন লোক 10 দিনে করে = 1/6 অংশ কাজ
∴ 45 জন লোক 1 দিনে করে = (1/6) ÷ 10 = 1/60 অংশ
∴ 1 জন লোক 1 দিনে করে = (1/60) ÷ 45 = 1/2700 অংশ

অবশিষ্ট কাজ = 1 - 1/6 = 5/6 অংশ
অবশিষ্ট সময় = 40 - 10 = 30 দিন

∴ অবশিষ্ট 5/6 অংশ কাজ 30 দিনে করতে হবে

∴ প্রতিদিনের প্রয়োজনীয় কাজের হার = (5/6) ÷ 30 অংশ
= 5/180 = 1/36 অংশ

এখন,
প্রতিদিন 1/2700 অংশ কাজ করে 1 জন
∴ 1 অংশ কাজ করে = 1 ÷ (1/2700) জন
∴ 1/36 অংশ কাজ করে = (2700/36) জন
= 75 জন

∴ অতিরিক্ত লোকের প্রয়োজন = 75 - 45 = 30 জন

৫,৩৭৬.
If a 32-year-old man is replaced by a new man, then the average age of 42 men increases by 1 year. What is the age of the new man?
  1. ক
    ক) 72 years
  2. খ
    খ) 74 years
  3. গ
    গ) 76 years
  4. ঘ
    ঘ) 77 years
ব্যাখ্যা
প্রশ্ন : If a 32 year old man is replaced by a new man, then the average age of 42 men increases by 1 year. What is the age of the new man?
সমাধান :
Let initially the average age of 42 men be x
⇒ Total age of 42 men = 42x

Now,  a 32 year old man is replaced by a new man
⇒ New Total age = 42 × (x + 1)

∴ 42 × (x + 1) - 42x = Age of the New man - 32
⇒ 42x + 42 - 42x = Age of the New man - 32
⇒ Age of the New man - 32 = 42

∴  Age of the New man = 42 + 32 = 74 years
৫,৩৭৭.
Three candidates, Salman, Parimal & Maruf contested an election and received 1800, 3300 and votes 3900 respectively. What percent of the total votes did Salman get?
  1. ক
    20%
  2. খ
    40%
  3. গ
    45%
  4. ঘ
    70%
ব্যাখ্যা
Question: Three candidates, Salman, Parimal & Maruf contested an election and received 1800, 3300 and votes 3900 respectively. What percent of the total votes did Salman get?

Solution:
Total no. of votes polled = (1800 + 3300 + 3900) = 9000.
Required percentage = (1800/9000) × 100% = 20%.
৫,৩৭৮.
If cosA = 8/17 than, what is the value of tanA = ?
  1. ক
    15/17 
  2. খ
    15/8
  3. গ
    17/8
  4. ঘ
    8/15
ব্যাখ্যা

Question: If cosA = 8/17 than, what is the value of tanA = ?

Solution:
Given that, 
cosA = 8/17

We know, 
sin2A = 1 - cos2A = 1 - (8/17)2
= 1 - (64/289)
= (289 - 64)/289
= 225/289
∴ sinA = √(225/289) = 15/17

Now, 
tanA = sinA/cosA = (15/17)/(8/17) = 15/8
∴ tanA = 15/8

৫,৩৭৯.
In a rainfall, 7 cm of rain falls. What is the volume of water that falls on 2 hectares of ground?
  1. ক
    700 cubic meters
  2. খ
    850 cubic meters
  3. গ
    1400 cubic meters
  4. ঘ
    1700 cubic meters
ব্যাখ্যা
Question: In a rainfall, 7 cm of rain falls. What is the volume of water that falls on 2 hectares of ground?

Solution:
1 hectare = 10,000 m2
So, Area = (2 × 10000) m2 = 20000 m2
Depth = 7 cm = 7/100 m

Volume = (Area × Depth) = 20000 × (7/100) m3
= 1400 m3
∴ The volume of water that falls on 2 hectares of ground is 1,400 cubic meters.
৫,৩৮০.
The price of a math book is Tk. 500, but you have only Tk. 350 with you. If you get a discount of 20%, how much money do you need to borrow from a friend so that you can buy the book?
  1. ক
    Tk. 150
  2. খ
    Tk. 125
  3. গ
    Tk. 100
  4. ঘ
    Tk. 50
ব্যাখ্যা
Question: The price of a math book is Tk. 500, but you have only Tk. 350 with you. If you get a discount of 20%, how much money do you need to borrow from a friend so that you can buy the book?

Solution:
In 20% discount,
Original price 100 taka then discount price 80 taka
Original price 1 taka then discount price 80/100 taka
Original price 500 Taka then discount price (80 × 500)/100 Taka
= 400 taka

I need  to borrow = (400 - 350) Taka
= 50 taka
৫,৩৮১.
Find the area of the circle whose circumference is equal to the perimeter of a square of side 22 cm.
  1. ক
    ক) 767 cm2
  2. খ
    খ) 156 cm2
  3. গ
    গ) 263 cm2
  4. ঘ
    ঘ) 616 cm2
ব্যাখ্যা
Given that
Side of the square = 22 cm
According to the question,
Circumference of the circle = Perimeter of the square
⇒ 2πr = 4a
⇒ 2πr = 4 × 22
⇒ 2 × (22 / 7) × r = 88
⇒ r = 14 cm

Area of the circle = πr2 ⇒ (22/ 7) × 14 × 14 = 616 cm2
∴ Area of circle is 616 cm2.
৫,৩৮২.
What is the slope of the line perpendicular to the line y = -5x + 9?
  1. ক
    ক) 5
  2. খ
    খ) -5
  3. গ
    গ) 1/5
  4. ঘ
    ঘ) -1/5
ব্যাখ্যা

y = -5x + 9
⇒ y + 5x = 9 .....(i)
সুতরাং (i) নং রেখাটির লম্বরেখার সমীকরণ 5y - x = k
⇒ y = 1/5x + k
∴ লম্ব রেখাটির ঢাল = 1/5

৫,৩৮৩.
A rectangular plot measuring 90 metre by 50 metre needs to be enclosed by wire fencing such that poles of the fence will be kept 5 metre apart. How many poles will be needed?
  1. ক
    30
  2. খ
    60
  3. গ
    44
  4. ঘ
    56
ব্যাখ্যা

Length of the wire fencing
= perimeter
= 2 (90+ 50) = 280 metre

Two poles are kept 5 metre apart. Note that the poles are placed along the perimeter of the rectangular plot, not in a single straight line.

Hence, number of poles required
= 280/5
= 56 metre

৫,৩৮৪.
If (2p + 1) is a prime number, which one of the following digits could be the value of p?
  1. ক
    6
  2. খ
    5
  3. গ
    4
  4. ঘ
    3
ব্যাখ্যা
Question: If (2p + 1) is a prime number, which one of the following digits could be the value of p?

Solution:
If P= 6, we will get; 26 + 1 = 64 + 1= 65

If P = 5, we will get; 25 + 1 = 32 + 1 = 33

If P = 4, we will get; 24 + 1 = 16 + 1 = 17

If P = 3, we will get; 23 + 1 = 8 + 1= 9

Out of the four results, only 17 is the prime number. So, the required value of the P is 4.
৫,৩৮৫.
The bus fare was recently raised from Tk. 3.70 to Tk. 4.00 per kilometer. What is the approximate percentage increase?
  1. ক
    8%
  2. খ
    5%
  3. গ
    6%
  4. ঘ
    10%
ব্যাখ্যা

Question: The bus fare was recently raised from Tk. 3.70 to Tk. 4.00 per kilometer. What is the approximate percentage increase?

Solution: 
বাস ভাড়া বাড়ে = (4.00 - 3.70) টাকা
= 0.30 টাকা

বাস ভাড়া শতকরা বাড়ে = (0.30/3.70) × 100%
= 8.1 %
≈ 8%

৫,৩৮৬.
A student scored 30% marks and failed by 12 marks. Another student scored 55% marks and secured 38 marks more than the pass marks. What is the pass percentage?
  1. ক
    33%
  2. খ
    37.5%
  3. গ
    42%
  4. ঘ
    36%
ব্যাখ্যা

Question: A student scored 30% marks and failed by 12 marks. Another student scored 55% marks and secured 38 marks more than the pass marks. What is the pass percentage?

Solution:
Let total marks = x

According to the question,
30% of x + 12 = 55% of x - 38
⇒ 0.3x + 12 = 0.55x - 38
⇒ 0.55x - 0.3x = 12 + 38
⇒ 0.25x = 50
⇒ x = 50/0.25
∴ x = 200

∴ Pass marks = 30% of x + 12
= 0.3 × 200 + 12
= 60 + 12
= 72

∴ Pass percentage = (72/200) × 100
= 36%

৫,৩৮৭.
A certain sum of money is invested at an interest rate of 5% per annum and a second sum twice as large as the first is invested at 5.5% p. a. The total amount of interest earned from two investments together is Tk. 1000 per year and the interest is withdrawn every year. The second sum invested is: 
  1. ক
    ক) Tk.18750
  2. খ
    খ) Tk.6250
  3. গ
    গ) Tk.12500
  4. ঘ
    ঘ) Tk.6500
ব্যাখ্যা
Let 
Two sums Tk. x and Tk. 2x

Now
{(x × 5 × 1)/100} + {(2x × 5.5× 1)/100} = 1000
5x + 11x = 100000
16x = 100000
x = 6250

Second sum =Tk. (6250 × 2) =  Tk. 12500
৫,৩৮৮.
If the day before yesterday was Thursday, when will Sunday be?
  1. ক
    Day after tomorrow
  2. খ
    Tomorrow
  3. গ
    Two days after today
  4. ঘ
    Today
  5. ঙ
    None of these
ব্যাখ্যা

Question: If the day before yesterday was Thursday, when will Sunday be?

Solution:
Day before yesterday = Thursday
Yesterday = Friday
Today = Saturday
Tomorrow = Sunday

Therefore, Sunday will be tomorrow.

৫,৩৮৯.
If sin(θ + 15°) = 3/√12 then 2sin2θ = ?
  1. ক
    ক) 1/2
  2. খ
    খ) 2
  3. গ
    গ) 1
  4. ঘ
    ঘ) 1/4
ব্যাখ্যা
Question: If sin(θ + 15°) = 3/√12 then 2sin2θ = ?

Solution:
sin(θ + 15°) = 3/√12
⇒ sin(θ + 15°) = 3/(2√3)
⇒ sin(θ + 15°) = √3/2
⇒ sin(θ + 15°) = sin60°
⇒ θ + 15° = 60°
⇒ θ = 45°

Now,
2sin2θ = 2(sin 45°)2
= 2 . (1/√2)2
= 2 . 1/2
= 1
৫,৩৯০.
If a+b = 8 and ab = 15, what is the value of a2+b2?
  1. ক
    ক) 94
  2. খ
    খ) 79
  3. গ
    গ) 34
  4. ঘ
    ঘ) 30
ব্যাখ্যা
দেওয়া আছে, a+b = 8, ab = 15
আমরা জানি, a2+b2 = (a+b)2-2ab
= 82-2×15 = 34
৫,৩৯১.
A man invested TK 4500 in a stock at 108 to obtain an income of TK 250. What is the dividend from the stock?
  1. ক
    4%
  2. খ
    5%
  3. গ
    6%
  4. ঘ
    7%
ব্যাখ্যা

Question: A man invested TK 4500 in a stock at 108 to obtain an income of TK 250. What is the dividend from the stock?

Solution:
By investing TK 4500, income  = TK 250
By investing TK 108 = (108 × 250)/4500 = 6

Hence, the dividend is 6%.

৫,৩৯২.
A man takes 3 hours 45 minutes to row a boat 22.5 km downstream of a river and 2 hours 30 minutes to cover a distance of 10 km upstream . Find the speed of the river current in km /hr.
  1. ক
    ক) 1 km/hr
  2. খ
    খ) 2 km/ hr
  3. গ
    গ) 3 km /hr
  4. ঘ
    ঘ) 4km/ hr
ব্যাখ্যা

We have to find the speed of a current.
t (downstream) = 3 h 45 min = 3.75 h
t (upstream) = 2 h 30 min = 2.5 h
Speed downstream = 22.5 km / 3.75 h = 6 km/h
Speed upstream = 10 km / 2.5 h = 4 km/h

So, Speed of the current = (Speed downstream - speed upstream) / 2
= (6 - 4) / 2
= (2 / 2) km/h
= 1 km/h

৫,৩৯৩.
Masum performs 6/15 of the total journey by rail, 8/20 by bus and the remaining 12 km on foot, his total journey is: 
  1. ক
    60 km
  2. খ
    58 km
  3. গ
    30 km
  4. ঘ
    50 km
ব্যাখ্যা
Question: Masum performs 6/15 of the total journey by rail, 8/20 by bus and the remaining 12 km on foot, his total journey is:

Solution: 
Let, the total journey be x km.

ATQ,
(6x/15) + (8x/20) + 12 = x
or,  (24x + 24x + 720)/60 = x
or, 24x + 24x + 720 = 60x
or, 60x - 48x = 720
or, 12x = 720
or, x = 60

∴ Total journey = 60 km.
৫,৩৯৪.
Of the following list of numbers, which has the greatest standard deviation?
  1. ক
    ক) 1, 2, 3
  2. খ
    খ) 6, 8, 10
  3. গ
    গ) 2, 4, 6
  4. ঘ
    ঘ) 4, 7, 10
ব্যাখ্যা
অপশন ক এর ক্ষেত্রে 
  x                 x2 
 1                  1 
2                   4 
3                    9          
∑x = 6            ∑x2 =14

SD =√{(∑x2/n) - (∑x/n)2}
       = √{(14/3) - (6/3)2}
        =√(4.67 - 4)
         = 1.63


অপশন খ এর ক্ষেত্রে 
  x                 x2 
 6                  36 
 8                   64
 10                 100          
∑x = 24            ∑x2 =200

SD =√{(∑x2/n) - (∑x/n)2}
       = √{(200/3) - (24/3)2}
        =√(66.666 - 64)
         = 1.63

অপশন গ এর ক্ষেত্রে 
 x                 x2 
 2                  4 
4                   16 
6                    36          
∑x = 12            ∑x2 =56

SD =√{(∑x2/n) - (∑x/n)2}
       = √{(56/3) - (12/3)2}
        =√(18.67 - 16)
         = 1.63


অপশন ঘ এর ক্ষেত্রে 
  x                 x2 
4                  16 
7                  49
 10                 100          
∑x = 21            ∑x2 =165

SD =√{(∑x2/n) - (∑x/n)2}
       = √{(165/3) - (21/3)2}
        =√(55 - 49)
         = 2.45
৫,৩৯৫.
An art box contains 3 blue pens, 4 green pens, and 5 red pens. In how many ways can a student choose 3 pens such that at least one blue pen is included in the selection?
  1. ক
    112 ways
  2. খ
    124 ways
  3. গ
    136 ways
  4. ঘ
    152 ways
  5. ঙ
    None
ব্যাখ্যা
Question: An art box contains 3 blue pens, 4 green pens, and 5 red pens. In how many ways can a student choose 3 pens such that at least one blue pen is included in the selection?

Solution:
Total number of pens = 3 + 4 + 5
= 12 pens

Total ways to choose any 3 pens from 12 = 12C3
= 220 ways

Ways to choose 3 pens with no blue pen (only green and red pens) = 9C3
= 84 ways 

∴ So, ways to choose 3 pens with at least one blue pen = (220 - 84) ways
= 136 ways
৫,৩৯৬.
Find the value of 'x' if the mean of the set of the numbers 8, 5, a, 10, 15, 21 is given as 11.
  1. ক
    5
  2. খ
    6
  3. গ
    7
  4. ঘ
    8
ব্যাখ্যা
Question: Find the value of 'x' if the mean of the set of the numbers 8, 5, a, 10, 15, 21 is given as 11.

Solution:
ATQ,
(8 + 5 + a + 10 + 15 + 21)/6 = 11
⇒ (59 + a)/6 = 11
⇒ 59 + a  = 66
⇒ a = 66 - 59
∴ a = 7
৫,৩৯৭.
A man travels at 3 mph in still water. If the current’s velocity is 1 mph, it takes 3 hours to row to a place and come back. How far is the place?
  1. ক
    ক) 2 miles
  2. খ
    খ) 3 miles
  3. গ
    গ) 4 miles
  4. ঘ
    ঘ) 5 miles
ব্যাখ্যা
প্রশ্ন: A man travels at 3 mph in still water. If the current’s velocity is 1 mph, it takes 3 hours to row to a place and come back. How far is the place?

সমাধান: 
Let,
the distance be d miles.

Time taken to cover the distance upstream + Time taken to cover the distance downstream = 3 hours 
Here,
Speed upstream = 3 - 1 = 2 mph

Speed downstream = 3 + 1 = 4 mph

So, our equation would be,
d/2 + d/4 = 3 
⇒ (2d + d)/4 = 3
⇒ 3d = 12
⇒ d = 12/3 
∴ d = 4 

The distance is 4 miles.
৫,৩৯৮.
A man rows downstream at 20 km/hr and rows upstream at 15 km/hr. At what speed he can row in still water?
  1. ক
    22 km/hr
  2. খ
    20.5 km/hr
  3. গ
    17.5 km/hr
  4. ঘ
    18 km/hr
ব্যাখ্যা
Question: A man rows downstream at 20 km/hr and rows upstream at 15 km/hr. At what speed he can row in still water?

Solution:
Speed downstream = 20 km/hr
Speed upstream = 15 km/hr

∴ Required speed = (20 + 15)/2 km/hr
= 35/2 = 17.5 km/hr
৫,৩৯৯.
A jar contains milk and water in the ratio 5:1. If the quantity of milk is more than that of water by 8 liters, then what is the quantity of water?
  1. ক
    1.5 liters
  2. খ
    2 liters
  3. গ
    2.5 liters
  4. ঘ
    3.5 liters
  5. ঙ
    4 liters
ব্যাখ্যা
let, A jar contains milk and water be 5x and X

the quantity of milk is more than that of water (5x -x ) = 4x

so, the quantity of water = (x * 8)/4x = 2
৫,৪০০.
A works twice as fast as B. If B can complete a work in 18 days independently, the number of days in which A and B can together finish the work is:
  1. ক
    ক) 4 days
  2. খ
    খ) 6 days
  3. গ
    গ) 8 days
  4. ঘ
    ঘ) 10 days
  5. ঙ
    ঙ) None of these
ব্যাখ্যা

Ratio of rates of working of A and B = 2:1.
So, ratio of times taken = 1:2
Therefore, A's 1 day's work = 1/9
B's 1 day's work = 1/18
(A + B)'s 1 day's work = 1/9 + 1/18 = 1/6
So, A and B together can finish the work in 6 days.