১৫,৯০১.
What is the value of a, if 3x2 + ax + a + 3 divisible by x + 2?
ব্যাখ্যা
ধরি, f(x) = 3x² + ax + a +3
যেহেতু, x + 2 দ্বারা বিভাজ্য সেহেতু,
f(-2) = 0 হবে
⇒ 3(-2)2 + a(-2) + a + 3 = 0
⇒ 12 - 2a + a + 3 = 0
⇒ - a + 15 = 0
⇒ a = 15
PrepBank · বিষয়ভিত্তিক প্রশ্ন
Bank Math
Bank Math
PrepBank · পাতা ১৬০ / ১৬১ · ১৫,৯০১–১৬,০০০ / ১৬,১২৪
১৫,৯০২.
If X occupies the last chair and A occupies the 2nd chair, who must occupy chair no 1?
ব্যাখ্যা
Question: If X occupies the last chair and A occupies the 2nd chair, who must occupy chair no 1?
সমাধান:
- এখানে Y কখনোই ১ম স্থানে বসতে পারবে না, কারণ Y এর স্থান ৫ম, ৬ষ্ঠ, অথবা ৭ম।
- B কখনোই ১ম স্থানে বসতে পারবে না, কারণ A দ্বিতীয় স্থানে বসলে B এবং C পাশাপাশি বসতে পারে না।
- এছাড়া D কখনোই ১ম এবং ৭ম স্থানে বসতে পারবে না।
- তাই, ১ম স্থানে Z বসতে পারে।
সমাধান:
- এখানে Y কখনোই ১ম স্থানে বসতে পারবে না, কারণ Y এর স্থান ৫ম, ৬ষ্ঠ, অথবা ৭ম।
- B কখনোই ১ম স্থানে বসতে পারবে না, কারণ A দ্বিতীয় স্থানে বসলে B এবং C পাশাপাশি বসতে পারে না।
- এছাড়া D কখনোই ১ম এবং ৭ম স্থানে বসতে পারবে না।
- তাই, ১ম স্থানে Z বসতে পারে।
১৫,৯০৩.
How many years will it take for an investment of Tk.5000 to earn Tk. 1200 in simple interest rate of 6%?
ব্যাখ্যা
Question: How many years will it take for an investment of Tk.5000 to earn Tk. 1200 in simple interest rate of 6%?
Solution:
Given that,
Principal, P = 5000
Simple Interest, SI = 1200
Rate of interest, r = 6%
Time, n = ?
We know,
n = I/Pr
= 1200/(5000 × 6%)
= (1200 × 100)/(5000 × 6)
= 4
So, it will take 4 years for the investment to earn Tk. 1200 at 6% simple interest.
Solution:
Given that,
Principal, P = 5000
Simple Interest, SI = 1200
Rate of interest, r = 6%
Time, n = ?
We know,
n = I/Pr
= 1200/(5000 × 6%)
= (1200 × 100)/(5000 × 6)
= 4
So, it will take 4 years for the investment to earn Tk. 1200 at 6% simple interest.
১৫,৯০৪.
Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
ব্যাখ্যা
Required number
= H.C.F. of (91 - 43), (183 - 91) and (183 - 43)
= H.C.F. of 48, 92 and 140 = 4.
= H.C.F. of (91 - 43), (183 - 91) and (183 - 43)
= H.C.F. of 48, 92 and 140 = 4.
১৫,৯০৫.
If the radius of a circle is 6 cm and a circular segment subtends an angle 30° at the center, then the length of the arc is -
ব্যাখ্যা
The length of arc, s = πrθ/180 = π × 6 × 30/180 = π cm
১৫,৯০৬.
What is the value of 12 × 5 – 8 ÷ 2 = ?
ব্যাখ্যা
Question: What is the value of 12 × 5 - 8 ÷ 2 = ?
Solution:
12 × 5 - 8 ÷ 2
= 60 - 4 [ According to the BODMAS rule ]
= 56
Solution:
12 × 5 - 8 ÷ 2
= 60 - 4 [ According to the BODMAS rule ]
= 56
১৫,৯০৭.
A square room has a square carpet symmetrically placed in it. This leaves an uncovered area of 9 meter2. The area of the whole room is 25 meter2. What is the length of the one side of the carpet?
ব্যাখ্যা
Question : A square room has a square carpet symmetrically placed in it. This leaves an uncovered area of 9 meter2. The area of the whole room is 25 meter2. What is the length of the one side of the carpet?
Solution:
মনেকরি
কার্পেটের এক বাহুর দৈর্ঘ্য x মিটার
প্রশ্নমতে,
25 - 9 = x2
⇒ 16 = x2
⇒ 42 = x2
⇒ x = 4
Solution:
মনেকরি
কার্পেটের এক বাহুর দৈর্ঘ্য x মিটার
প্রশ্নমতে,
25 - 9 = x2
⇒ 16 = x2
⇒ 42 = x2
⇒ x = 4
১৫,৯০৮.
A boy walked 20 minutes at 3km/hr and ran 20 minutes at 15km/hr. The total distance covered by the boy is -
ব্যাখ্যা
Question: A boy walked 20 minutes at 3km/hr and ran 20 minutes at 15km/hr. The total distance covered by the boy is -
Solution:
first 20 minutes he covered
= 3 × 20/60 km
= 1km
in the second 20 minutes, he covered
= 15 × 20/60 km
= 5km
total distance = 1 + 5 = 6km
Solution:
first 20 minutes he covered
= 3 × 20/60 km
= 1km
in the second 20 minutes, he covered
= 15 × 20/60 km
= 5km
total distance = 1 + 5 = 6km
১৫,৯০৯.
A manufacturer marked an article at Tk.50 and sold it allowing 20% discount. If his profit was 25%, then the cost price of the article was-
ব্যাখ্যা
Selling price = 50 - (50 × 20%)
= 50 - 10
= 40
Cost Price = (100/100+25) × 40
= (100/125) × 40
= 32
১৫,৯১০.
When the price of each book goes up by Tk. 5, the librarian purchases 20 books less than the required number for Tk. 1200. The original price of the book was
ব্যাখ্যা
Question: When the price of each book goes up by Tk. 5, the librarian purchases 20 books less than the required number for Tk. 1200. The original price of the book was
Solution:
ধরি,
বইয়ের পূর্বমূল্য = x টাকা
x টাকায় পাওয়া যেতো = 1 টি বই
∴ 1 টাকায় পাওয়া যেতো = 1/x টি বই
∴ 1200 টাকায় পাওয়া যেতো = 1200/x টি বই
আবার, বইয়ের মূল্য 5 টাকা বৃদ্ধি পাওয়ায় বর্তমান মূল্য = (x + 5) টাকা
(x + 5) টাকায় পাওয়া যাবে = 1 টি বই
∴ 1 টাকায় পাওয়া যাবে = 1/(x + 5) টি বই
∴ 1200 টাকায় পাওয়া যাবে = 1200/(x + 5) টি বই
প্রশ্নমতে,
(1200/x) - {1200/(x + 5)} = 20
⇒ {1200(x + 5) - 1200x}/{x(x + 5)} = 20
⇒ {1200x + 6000 - 1200x}/(x2 + 5x) = 20
⇒ 6000/(x2 + 5x) = 20
⇒ x2 + 5x = 6000/20
⇒ x2 + 5x = 300
⇒ x2 + 5x - 300 = 0
⇒ x2 + 20x - 15x - 300 = 0
⇒ x(x + 20) - 15(x + 20) = 0
⇒ (x + 20)(x - 15) = 0
হয়, x + 20 = 0 অথবা, x - 15 = 0
x = - 20 অথবা, x = 15
কিন্তু x এর ঋণাত্মক মান গ্রহণযোগ্য নয়।
সুতরাং বইয়ের পূর্বমূল্য ছিলো = 15 টাকা
Solution:
ধরি,
বইয়ের পূর্বমূল্য = x টাকা
x টাকায় পাওয়া যেতো = 1 টি বই
∴ 1 টাকায় পাওয়া যেতো = 1/x টি বই
∴ 1200 টাকায় পাওয়া যেতো = 1200/x টি বই
আবার, বইয়ের মূল্য 5 টাকা বৃদ্ধি পাওয়ায় বর্তমান মূল্য = (x + 5) টাকা
(x + 5) টাকায় পাওয়া যাবে = 1 টি বই
∴ 1 টাকায় পাওয়া যাবে = 1/(x + 5) টি বই
∴ 1200 টাকায় পাওয়া যাবে = 1200/(x + 5) টি বই
প্রশ্নমতে,
(1200/x) - {1200/(x + 5)} = 20
⇒ {1200(x + 5) - 1200x}/{x(x + 5)} = 20
⇒ {1200x + 6000 - 1200x}/(x2 + 5x) = 20
⇒ 6000/(x2 + 5x) = 20
⇒ x2 + 5x = 6000/20
⇒ x2 + 5x = 300
⇒ x2 + 5x - 300 = 0
⇒ x2 + 20x - 15x - 300 = 0
⇒ x(x + 20) - 15(x + 20) = 0
⇒ (x + 20)(x - 15) = 0
হয়, x + 20 = 0 অথবা, x - 15 = 0
x = - 20 অথবা, x = 15
কিন্তু x এর ঋণাত্মক মান গ্রহণযোগ্য নয়।
সুতরাং বইয়ের পূর্বমূল্য ছিলো = 15 টাকা
১৫,৯১১.
If the radious of cylinder is halved and height is doubled, then what will be the curved surface area?
ব্যাখ্যা
Curved surface এর ক্ষেত্রফল = 2Πrh
ব্যাসার্ধ হলে নতুন ব্যাসার্ধ = r/2
এবং দৈর্ঘ্য দ্বিগুণ হলে নতুন দৈর্ঘ্য = 2h
∴ নতুন ক্ষেত্রফল = 2Π(r/2)2h = 2Πrh.
সুতরাং ক্ষেত্রফল একই থাকবে।
১৫,৯১২.
A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 15 minutes. How long will it take to go 9 km in stationary water?
ব্যাখ্যা
Question: A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 15 minutes. How long will it take to go 9 km in stationary water?
Solution:
Rate downstream = (1/15 × 60) km/h
= 4 km/h
Rate upstream = 2 km/h
Speed in still water = (4 + 2)/2 km/h
= 3 km/h
Required time = (9/3) h
= 3 h
Solution:
Rate downstream = (1/15 × 60) km/h
= 4 km/h
Rate upstream = 2 km/h
Speed in still water = (4 + 2)/2 km/h
= 3 km/h
Required time = (9/3) h
= 3 h
১৫,৯১৩.
If p is a positive integer, what is the smallest possible value of p such that 2160 × p is a perfect square?
ব্যাখ্যা
Question: If p is a positive integer, what is the smallest possible value of p such that 2160 × p is a perfect square?
Solution:
আমরা জানি, একটি সংখ্যা পূর্ণবর্গ হতে হলে এর মৌলিক গুণনীয়কের ঘাতসমূহ জোড় সংখ্যা হতে হবে।
2160 = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5
= 24 × 33 × 51
2160p = 24 × 33 × 51 × p
এখানে, 2-এর ঘাত = 4 (জোড়), 3-এর ঘাত = 3 (বিজোড়), 5-এর ঘাত = 1 (বিজোড়)
পূর্ণবর্গ করতে হলে সব ঘাত জোড় হতে হবে।
তাই p = 3 × 5 = 15 হলে,
2160 × 15 = 24 × 33 × 51 × (3 × 5) = 24 × 34 × 52
যেহেতু সব মৌলিক উৎপাদকের ঘাত জোড়, তাই এটি একটি পূর্ণবর্গ সংখ্যা।
সুতরাং, p = 15 হলে, 2160 × p পূর্ণবর্গ সংখ্যা হয়।
১৫,৯১৪.
The ratio of present age Anik and Babul is 12 : 7 . After 3 years their ratio will be 30 : 20 then find the present age of Anik?
ব্যাখ্যা
Question: The ratio of present age Anik and Babul is 12 : 7 . After 3 years their ratio will be 30 : 20 then find the present age of Anik?
Solution:
Let,
present age of Anik = 12x
and present age of Babul = 7x
ATQ,
(12x + 3)/(7x + 3) = 30/20
⇒(12x + 3) × 20 = (7x + 3) × 30
⇒ 240x + 60 = 210x + 90
⇒ 30x = 30
⇒ x = 1
∴ Present age of Anik = 12 × 1 years
= 12 years
Solution:
Let,
present age of Anik = 12x
and present age of Babul = 7x
ATQ,
(12x + 3)/(7x + 3) = 30/20
⇒(12x + 3) × 20 = (7x + 3) × 30
⇒ 240x + 60 = 210x + 90
⇒ 30x = 30
⇒ x = 1
∴ Present age of Anik = 12 × 1 years
= 12 years
১৫,৯১৫.
The equation 12x2 + 4kx + 3 = 0 has real and equal roots, if-
ব্যাখ্যা
Question: The equation 12x2 + 4kx + 3 = 0 has real and equal roots, if-
Solution:
Here a = 12, b = 4k, c = 3
Since the given equation has real and equal roots
∴ b2 - 4ac = 0
⇒ (4k)2 - 4 × 12 × 3 = 0
⇒ 16k2 - 144 = 0
⇒ 16k2 = 144
⇒ k2 = 9
⇒ k = ± 3
Solution:
Here a = 12, b = 4k, c = 3
Since the given equation has real and equal roots
∴ b2 - 4ac = 0
⇒ (4k)2 - 4 × 12 × 3 = 0
⇒ 16k2 - 144 = 0
⇒ 16k2 = 144
⇒ k2 = 9
⇒ k = ± 3
১৫,৯১৬.
A worker earns Tk. 250 on the first day and spends Tk. 200 on the second day, earns Tk. 250 on the third day and again spends Tk. 200 on the fourth day and so on. On which day would he have had Tk. 1000?
ব্যাখ্যা
Question: A worker earns Tk. 250 on the first day and spends Tk. 200 on the second day, earns Tk. 250 on the third day and again spends Tk. 200 on the fourth day and so on. On which day would he have had Tk. 1000?
Solution:
১ম দিনে আয় করে ২৫০ টাকা।
২য় দিনে ব্যয় করে ২০০ টাকা।
∴ ২ দিনে তার জমা থাকে (২৫০ - ২০০) = ৫০ টাকা।
এখন, (১০০০ - ২৫০) = ৭৫০ টাকা।
৫০ টাকা জমা থাকে ২ দিনে
১ টাকা জমা থাকে ২/৫০ দিনে
৭৫০ টাকা জমা থাকে (২ × ৭৫০)/৫০ দিনে
= ৩০ দিন।
৩০ দিন পর তার হাতে থাকে ৭৫০ টাকা
এবং ৩১ তম দিনে সে আয় করে ২৫০ টাকা।
তাহলে মোট টাকা হয় (৭৫০ + ২৫০) = ১০০০ টাকা,
সুতরাং ৩১ দিনে তার কাছে ১০০০ টাকা ছিল।
১৫,৯১৭.
In a two-digit number, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is -
ব্যাখ্যা
Let the ten's digit be x.
Then, the unit's digit = x + 2.
Number = 10x + (x + 2) = 11x + 2
Sum of digits = x + (x + 2) = 2x + 2.
⇒ (11x + 2)(2x + 2) = 144
⇒ 22x2 + 26x- 140 = 0
⇒ 11x2 + 13x - 70 = 0
⇒ (x - 2)(11x + 35) = 0
⇒ x = 2
Hence, Required Number = 11x + 2 = 24
১৫,৯১৮.
Quantity A = 4/100 and Quantity B = 0.012/3
ব্যাখ্যা
Question: Quantity A = 4/100 and Quantity B = 0.012/3
Solution:
Quantity A = 4/100
Quantity B = 0.012/3
= 12/(3 × 1000)
= 4/1000
∴ Quantity A > Quantity B
Solution:
Quantity A = 4/100
Quantity B = 0.012/3
= 12/(3 × 1000)
= 4/1000
∴ Quantity A > Quantity B
১৫,৯১৯.
If nC7 = nC5 , then find the value of n.
ব্যাখ্যা
Question: If nC7 = nC5 , then find the value of n.
Solution:
We know,
If nCr = nCs , then, n = r + s
Now, nC7 = nC5
∴ n = 7 + 5
= 12
১৫,৯২০.
The present age of a son is one-fourth of the present age of his father. Eight years ago, the father's age was seven times the age of his son. What is the present age of the son?
ব্যাখ্যা
Question: The present age of a son is one-fourth of the present age of his father. Eight years ago, the father's age was seven times the age of his son. What is the present age of the son?
Solution: Let the father's age be 4x years
Then, Son's age = x years
ATQ,
4x - 8 = 7(x - 8)
or, 4x - 8 = 7x - 56
or, -8 + 56 = 7x - 4x
or, 48 = 3x
or, x = 16
∴ The present age of the son = 16 years.
১৫,৯২১.
Kamal went to a shop and bought things worth Tk 25, out of which 30 paisa went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
ব্যাখ্যা
25 টাকার মধ্যে 30 পয়সা ট্যাক্স হলে পণ্যের প্রকৃত মূল্য (25 - 0.3) = 24.7 টাকা। X টাকার পণ্য যদি ট্যাক্স ফ্রি হয় তবে বাকি জিনিসের উপর প্রশ্নানুসারে 6% হারে ট্যাক্স আরোপ হয়।
∴ (24.7 - x)×.06 = .3
⇒ 1.482 - 0.06x = .3
⇒0.06x = 1.482 - .3 = 1.182
⇒ x = 1.182/0.06 = 19.70
∴ (24.7 - x)×.06 = .3
⇒ 1.482 - 0.06x = .3
⇒0.06x = 1.482 - .3 = 1.182
⇒ x = 1.182/0.06 = 19.70
১৫,৯২২.
P is a girl and has the same number of brothers as sisters. Q is a boy and has thrice as many sisters as brothers. P and Q are the children of R. How many children does R have?
ব্যাখ্যা
Question: P is a girl and has the same number of brothers as sisters. Q is a boy and has thrice as many sisters as brothers. P and Q are the children of R. How many children does R have?
Solution: Let d and s represent the number of daughters and sons respectively.
Then, we have
d - 1 = s
⇒ d = s + 1
and
3(s - 1) = d
⇒ 3s - 3 = s + 1
⇒ 3s - s = 1 + 3
⇒ 2s = 4
⇒ s = 2
∴ d = 2 + 1 = 3
∴ Total children = 2 + 3 = 5
১৫,৯২৩.
What is the slope of a line containing the points (1, 13) and (-3, 6)?
ব্যাখ্যা
Here the points line are (1, 13) and (-3, 6)
∴ Slope, m = Y1 - Y2 / X1 - X2
= (13 - 6)/(1 + 3)
= 7/4
= 1.75
১৫,৯২৪.
Jamil's average score in 4 tests was 85 out of a possible 100. If his scores in 2 of the tests were 70, and 80. What is the lowest that either of his other scores could have been?
ব্যাখ্যা
Question: Jamil's average score in 4 tests was 85 out of a possible 100. If his scores in 2 of the tests were 70, and 80. What is the lowest that either of his other scores could have been?
Solution:
Average of 4 test was 85
Total marks = 85 × 4 = 340
Marks of other 2 subjects = (340 - 70 - 80)= 290
He can get highest 100 marks in one of the subjects.
∴ Lowest marks will be = (290 - 100) = 190
Solution:
Average of 4 test was 85
Total marks = 85 × 4 = 340
Marks of other 2 subjects = (340 - 70 - 80)= 290
He can get highest 100 marks in one of the subjects.
∴ Lowest marks will be = (290 - 100) = 190
১৫,৯২৫.
A sum of Tk.312 was divided among 100 boys and girls in such a way that the boy gets Tk..3.60 and each girl Tk.. 2.40 the number of girls is -
ব্যাখ্যা
Let x be the number of boys and y be the number of girls.
Given total number of boys and girls = 100
x + y = 100 --------- (i)
A boy gets Tk. 3.60 and a girl gets Tk. 2.40
The amount given to 100 boys and girls = Tk. 312
3.60x + 2.40y = 312 ---------- (ii)
Solving (i) and (ii)
3.60x + 3.60y = 360 ---------- Multiply (i) by 3.60
3.60x + 2.40y = 312 ------------ (ii)
Equation (i) - (ii)
1.20y = 48
⇒ y = 48/1.20
⇒ y = 40
Number of girls = 40.
১৫,৯২৬.
What is the total interest on Tk. 1,200 at 10% per annum for 9 months?
ব্যাখ্যা
Question: What is the total interest on Tk. 1,200 at 10% per annum for 9 months?
Solution:
Given,
Principal (P) = Tk. 1200
Rate (R) = 10%
Time (T) = 9 months
= 9/12 year
= 3/4 year
By Formula,
SI = PRT/100
= {1200 × 10 × (3/4)}/100
= (1200 × 10 × 3)/400
= 90 Tk
১৫,৯২৭.
The ratio of two numbers is 5 : 7 and their L.C.M is 420. What is the sum of the numbers?
ব্যাখ্যা
Question: The ratio of two numbers is 5 : 7 and their L.C.M is 420. What is the sum of the numbers?
Solution:
Let, the numbers be 5x and 7x
∴ Their L.C.M = 35x
ATQ,
35x = 420
⇒ x = 420/35
∴ x = 12
∴ The numbers are (5 × 12) = 60 and (7 × 12) = 84
∴ Sum of the numbers = 60 + 84 = 144
Solution:
Let, the numbers be 5x and 7x
∴ Their L.C.M = 35x
ATQ,
35x = 420
⇒ x = 420/35
∴ x = 12
∴ The numbers are (5 × 12) = 60 and (7 × 12) = 84
∴ Sum of the numbers = 60 + 84 = 144
১৫,৯২৮.
Given that a square and a rectangle share the same area, and the square’s perimeter is 32 meters, while the rectangle’s length is 4 meters, calculate the rectangle’s width.
ব্যাখ্যা
Question: Given that a square and a rectangle share the same area, and the square’s perimeter is 32 meters, while the rectangle’s length is 4 meters, calculate the rectangle’s width.
Solution:
Given that,
Perimeter of square = 32 m
Area of rectangle = Area of square
And length of rectangle = 4 m
Now,
Perimeter of square,
4s = 32
⇒ s = 32/4 = 8
∴ s = 8 m
∴ Area of square = s2 = 82 = 64 m2
According to the Question,
Area of rectangle = Area of square
∴ Area of rectangle = 64 m2
∴ Area of rectangle = length × width
64 = 4 × w
⇒ w = 64/4
∴ w = 16 m
So the width of the rectangle = 16 meters
১৫,৯২৯.
What is the value of
ব্যাখ্যা
Question: What is the value of
Solution:
{√(2 × 2 × 6) + √(6 × 6 × 6)}/√(4 × 4 × 6 )
= (2√6 + 6√6)/4√6
= 8√6/4√6
= 2
Solution:
{√(2 × 2 × 6) + √(6 × 6 × 6)}/√(4 × 4 × 6 )
= (2√6 + 6√6)/4√6
= 8√6/4√6
= 2
১৫,৯৩০.
Two pipes A and B can fill a tank in 24 and 32 min, respectively. If both the pipes are opened together, after how much time pipe B should be closed so that the tank is full in 9 min?
ব্যাখ্যা
Let, the total capacity of the tank be 96 units (LCM of 24 & 32).
A fills = 96/24 = 4 units / minute.
B fills = 96/32 = 3 units / minute
Let the time for which B is opened is x minutes.
According to the question,
4 × 9 + 3 × x = 96
3x = 96 - 36
3x = 60
x = 20 minutes.
The pipe B should be closed after 20 minutes
১৫,৯৩১.
What is the difference between the compound interests on Tk. 5000 for 1 (1/2) years at 4% per annum compounded yearly and half-yearly?
ব্যাখ্যা
C.I. when interest compound yearly = Tk. [5000 × (1 + 4/100) (1 + 1/2 × 4/100)]
= Tk. 5304.
C.I. when interest is compounded half-yearly = Tk. 5000 (1 + 2/100)3
= Tk. 5306.04
Difference = Tk. (5306.04 - 5304)
= Tk. 2.04
১৫,৯৩২.
The ratio of total surface area to curved surface area of a cone whose radius is 5cm and height 12 cm is :
ব্যাখ্যা
Question: The ratio of total surface area to curved surface area of a cone whose radius is 5cm and height 12 cm is :
Solution:
দেওয়া আছে,
কোণকের ব্যাসার্ধ, r = 5 cm
কোণকের উচ্চতা, h = 12 cm
এখন,কোণকের হেলানো উচ্চতা (slant height) বের করতে হবে।
কোণকের হেলানো উচ্চতা ((slant height), l = √(r2 + h2)
= √(52 + 122)
= √(25 + 144)
= √(169)
= 13 cm
এখন, কোণকের সমগ্র পৃষ্ঠতলের ক্ষেত্রফল ও বক্রতলের ক্ষেত্রফলের অনুপাত নির্ণয় করি।
সমগ্র পৃষ্ঠতলের ক্ষেত্রফল (total surface area) = πrl + πr2
বক্রতলের ক্ষেত্রফল (curved surface area) = πrl
অনুপাত = ( πrl + πr2 ) : ( πrl )
= πr(l + r) : πrl
= (l + r) : l (উভয় পক্ষকে πr দ্বারা ভাগ করে)
= (13 + 5) : 13
= 18 : 13
∴ কোণকের সমগ্র পৃষ্ঠতলের ক্ষেত্রফল ও বক্রতলের ক্ষেত্রফলের অনুপাত = 18 : 13.
১৫,৯৩৩.
A student scores 55% marks in 8 papers of 100 marks each. He scores 15% of his total marks in English. How much does he score in English?
ব্যাখ্যা
Total marks obtained by the student
= 55% of 800 = (55/100)×800 = 440
∴ Marks scored in English
= 15% of 440 = (15/100)×440 = 66
১৫,৯৩৪.
Train A passes a lamp post in 3 seconds and 900 meter long platform in 30 seconds. How much time will the same train take to cross a platform which is 800 meters long? (in seconds)
ব্যাখ্যা
Question: Train A passes a lamp post in 3 seconds and 900 meter long platform in 30 seconds. How much time will the same train take to cross a platform which is 800 meters long? (in seconds)
Solution:
Let, the length of the train is = x m.
and its speed is = v. m/s.
∴ Distance = Speed × time [S = V × T]
x = v × 3 .........(i)
(x + 900) = v × 30 ........(ii)
Dividing the eqn. (i) by (ii)
x/(x + 900) = 1/10
⇒ 10x = x + 900
⇒ 9x = 900.
⇒ x = 900/9
⇒ x = 100 m.
putting x = 100 in eqn. (1).
100 = v × 3
⇒ v = 100/3 m/s.
Let, the train crosses a 800 m. long platform in t seconds.
(x + 800) = v × t .........(iii) [ S = V × T]
⇒ (100 + 800) = (100/3) × t [putting x= 100 and v= 100/3]
⇒ 900 = (100/3) × t
⇒ t = (900 × 3)/100
⇒ t = 2700/100
⇒ t = 27 seconds.
Solution:
Let, the length of the train is = x m.
and its speed is = v. m/s.
∴ Distance = Speed × time [S = V × T]
x = v × 3 .........(i)
(x + 900) = v × 30 ........(ii)
Dividing the eqn. (i) by (ii)
x/(x + 900) = 1/10
⇒ 10x = x + 900
⇒ 9x = 900.
⇒ x = 900/9
⇒ x = 100 m.
putting x = 100 in eqn. (1).
100 = v × 3
⇒ v = 100/3 m/s.
Let, the train crosses a 800 m. long platform in t seconds.
(x + 800) = v × t .........(iii) [ S = V × T]
⇒ (100 + 800) = (100/3) × t [putting x= 100 and v= 100/3]
⇒ 900 = (100/3) × t
⇒ t = (900 × 3)/100
⇒ t = 2700/100
⇒ t = 27 seconds.
১৫,৯৩৫.
A worker earns Tk. 300 on the first day and spends Tk. 150 on the second day, earns Tk. 300 on the third day and again spends Tk. 150 on the fourth day, and so on. On which day would he have had Tk. 1500?
ব্যাখ্যা
Question: A worker earns Tk. 300 on the first day and spends Tk. 150 on the second day, earns Tk. 300 on the third day and again spends Tk. 150 on the fourth day, and so on. On which day would he have had Tk. 1500?
Solution:
1ম দিনে আয় = 300 টাকা
2য় দিনে ব্যয় = 150 টাকা
∴ প্রতি 2 দিনে জমা হয় = 300 - 150 = 150 টাকা
শুধু 1ম দিনে আয় করায় হাতে থাকে = 300 টাকা
অতএব, 1500 - 300 = 1200 টাকা আরও জমা করতে হবে।
150 টাকা জমা হয় 2 দিনে,
∴ 1200 টাকা জমা হয় = (2 × 1200)/150 = 16 দিনে
অর্থাৎ, 16 দিনের শেষে জমা থাকবে = 1200 টাকা
17-তম দিনে আবার আয় হবে = 300 টাকা
∴ মোট সঞ্চয় হবে = 1200 + 300 = 1500 টাকা
∴ 17-তম দিনে তার কাছে মোট 1500 টাকা জমা থাকবে।
১৫,৯৩৬.
Find the angle of elevation of the sun if the length of a tree's shadow is √3 times its actual height.
ব্যাখ্যা
Question: Find the angle of elevation of the sun if the length of a tree's shadow is √3 times its actual height.
Solution:
Let,
AB = height of tree
BC= Shadow of tree
angle of elevation = C
∴ BC = √3 AB
We know,
tanC = AB/BC
⇒ tanC = AB/√3AB
⇒ tanC = 1/√3
⇒ tanC = tan30°
∴ C = 30°
১৫,৯৩৭.
It was Friday on January 1, 2016. What was the day of the week on January 1, 2017?
ব্যাখ্যা
Question: It was Friday on January 1, 2016. What was the day of the week on January 1, 2017?
Solution:
The year 2016 is a leap year. So, it has 2 odd days.
Given,
1st day of the year 2016 is Friday
So, 1st day of the year 2017 is 2 days beyond Friday.
Friday + 1 day = Saturday
Saturday + 1 day = Sunday
Hence, it will be Sunday.
১৫,৯৩৮.
What is the sum of all two-digit numbers that gives a remainder of 3 when they are divided by 7?
ব্যাখ্যা
Question: What is the sum of all two-digit numbers that gives a remainder of 3 when they are divided by 7?
Solution:
general formula for that number = 7n + 3
n = 1, then the number is = 7 + 3 = 10
n = 2, then the number is =14 + 3 = 17
.
.
.
n= 13, then the number is = 94
sum = 10 + 17 + ... + 94
= 13 (10 + 94)/2
= 676
১৫,৯৩৯.
Equation of the straight line parallel to X-axis and also 4 units below X-axis is:
ব্যাখ্যা
Question: Equation of the straight line parallel to X-axis and also 4 units below X-axis is:
Solution:
Equation of the straight line parallel to X-axis and also 4 units below X-axis is y = - 4
১৫,৯৪০.
Which of the following three side of the triangle?
ব্যাখ্যা
আমরা জানি,
ত্রিভুজের যেকোনো দুই বাহুর সমষ্টি তৃতীয় বাহু অপেক্ষা বৃহত্তম।
এখানে একমাত্র 5 + 6 > 7 বাহু গুলো দ্বারা ত্রিভুজ অঙ্কন সম্ভব।
ত্রিভুজের যেকোনো দুই বাহুর সমষ্টি তৃতীয় বাহু অপেক্ষা বৃহত্তম।
এখানে একমাত্র 5 + 6 > 7 বাহু গুলো দ্বারা ত্রিভুজ অঙ্কন সম্ভব।
১৫,৯৪১.
The average age of 15 colleague of a office is 23. If the minimum age requirement for being a member of the office is 19 years, what is the possible maximum range of the ages?
ব্যাখ্যা
প্রশ্ন: The average age of 15 colleague of a office is 23. If the minimum age requirement for being a member of the office is 19 years, what is the possible maximum range of the ages?
সমাধান:
15 জনের গড় বয়স 23 বছর
∴ 15 জনের মোট বয়স = 15 × 23 = 345 বছর
1 জনের সর্বনিম্ন বয়স 19 বছর
∴ 14 জনের সর্বনিম্ন মোট বয়স = 19 × 15 = 266 বছর
অতএব, একজনের সর্বোচ্চ বয়স হতে পারে = 345 - 266 = 79 বছর
সমাধান:
15 জনের গড় বয়স 23 বছর
∴ 15 জনের মোট বয়স = 15 × 23 = 345 বছর
1 জনের সর্বনিম্ন বয়স 19 বছর
∴ 14 জনের সর্বনিম্ন মোট বয়স = 19 × 15 = 266 বছর
অতএব, একজনের সর্বোচ্চ বয়স হতে পারে = 345 - 266 = 79 বছর
১৫,৯৪২.
If the sum of 3 consecutive integer is 240, then the sum of the two smaller integer is-
ব্যাখ্যা
Question: If the sum of 3 consecutive integer is 240, then the sum of the two smaller integer is-
Solution:
Let,
Three consecutive integer is, x - 1, x, x + 1.
ATQ,
x - 1 + x + x + 1 = 240
⇒ 3x = 240
∴ x = 80
The sum of the two smaller integer is : x - 1 + x
= 80 - 1 + 80
= 160 - 1
= 159
Solution:
Let,
Three consecutive integer is, x - 1, x, x + 1.
ATQ,
x - 1 + x + x + 1 = 240
⇒ 3x = 240
∴ x = 80
The sum of the two smaller integer is : x - 1 + x
= 80 - 1 + 80
= 160 - 1
= 159
১৫,৯৪৩.
A man runs opposite to a train at 10 km/hr. The relative speed between them is 40 km/hr. If it takes 18 seconds for the train to pass the man when he is at rest, find the length of the train.
ব্যাখ্যা
Question: A man runs opposite to a train at 10 km/hr. The relative speed between them is 40 km/hr. If it takes 18 seconds for the train to pass the man when he is at rest, find the length of the train.
Solution:
Relative speed = Train’s speed + Man’s speed
⇒ vt + 10 = 40
⇒ vt = 40 - 10
⇒ vt = 30 × (5/18) = 25/3 m/s
∴ vt = 25/3 m/s
∴ Length of the train = Speed × Time to cross
= (25/3) × 18
= 150 meters
Solution:
Relative speed = Train’s speed + Man’s speed
⇒ vt + 10 = 40
⇒ vt = 40 - 10
⇒ vt = 30 × (5/18) = 25/3 m/s
∴ vt = 25/3 m/s
∴ Length of the train = Speed × Time to cross
= (25/3) × 18
= 150 meters
১৫,৯৪৪.
Difference of numerator and denominator of a proper fraction is 1; if 2 is subtracted from numerator and 2 is added to denominator of the fraction, it will be equal to 1/6. Find the fraction.
ব্যাখ্যা
Solution: Difference of numerator and denominator of a proper fraction is 1; if 2 is subtracted from numerator and 2 is added to denominator of the fraction, it will be equal to 1/6. Find the fraction.
Solution:
ধরি,
ভগ্নাংশটির লব = x
ভগ্নাংশটির হর = x + 1
∴ ভগ্নাংশটি = x/x + 1
প্রশ্নমতে,
(x - 2)/(x + 1 + 2) = 1/6
(x - 2)/(x + 3) = 1/6
6x - 12 = x + 3
6x - x = 12 +3
5x = 15
x = 3
∴ ভগ্নাংশটি = 3/4
Solution:
ধরি,
ভগ্নাংশটির লব = x
ভগ্নাংশটির হর = x + 1
∴ ভগ্নাংশটি = x/x + 1
প্রশ্নমতে,
(x - 2)/(x + 1 + 2) = 1/6
(x - 2)/(x + 3) = 1/6
6x - 12 = x + 3
6x - x = 12 +3
5x = 15
x = 3
∴ ভগ্নাংশটি = 3/4
১৫,৯৪৫.
The sum of three consecutive even integers is 30 more than the first of the numbers. What is the middle number?
ব্যাখ্যা
Question: The sum of three consecutive even integers is 30 more than the first of the numbers. What is the middle number?
Solution:
ধরি, তিনটি ক্রমিক জোড় সংখ্যা হলো x, x + 2, x + 4.
প্রশ্নমতে,
x + (x + 2) + (x + 4) = x + 30
⇒ 3x + 6 = x + 30
⇒ 3x − x = 30 − 6
⇒ 2x = 24
⇒ x = 24/2
⇒ x = 12
∴ প্রথম সংখ্যা = x = 12
দ্বিতীয় সংখ্যা (মাঝের সংখ্যা) = x + 2 = 14
তৃতীয় সংখ্যা = x + 4 = 16
∴ মাঝের সংখ্যাটি হলো = 14
১৫,৯৪৬.
The angle of depression of an object on the ground, from the top of a 25 m high tower is 30°. The distance of the object from the base of tower is
ব্যাখ্যা
Let AB be the tower and BC be the distance of the object (at C) from the base of the tower.
In right triangle ABC,
tan 30° = AB/BC
1/√3 = 25/BC
BC = 25√3 m
In right triangle ABC,
tan 30° = AB/BC
1/√3 = 25/BC
BC = 25√3 m
১৫,৯৪৭.
If f(y) = y3 + ky2 - 4y - 8 , then for what value of k will f(- 2) = 0?
ব্যাখ্যা
Question: If f(y) = y3 + ky2 - 4y - 8 , then for what value of k will f(- 2) = 0 ?
Solution:
Given that,
f(y) = y3 + ky2 - 4y - 8
f(- 2) = (- 2)3 + k(- 2)2 - 4(- 2) - 8
= - 8 + 4k + 8 - 8
∴ f(- 2) = 4k - 8
Set f(- 2) = 0
⇒ 4k - 8 = 0
⇒ 4k = 8
⇒ k = 8/4
∴ k = 2
So the value of k is 2.
১৫,৯৪৮.
The difference between two numbers is 960. When the larger number is divided by the smaller, the quotient is 5 and the remainder is 12. What is the smaller number?
ব্যাখ্যা
Question: The difference between two numbers is 960. When the larger number is divided by the smaller, the quotient is 5 and the remainder is 12. What is the smaller number?
Solution:
Given that,
The difference of two numbers = 960
Quotient when the larger number is divided by the smaller number = 5
Remainder when the larger number is divided by the smaller number = 12
Now,
Let the smaller number be x.
Larger number = 5x + 12
ATQ,
⇒ 5x + 12 - x = 960
⇒ 4x + 12 = 960
⇒ 4x = 960 - 12
⇒ 4x = 948
⇒ x = 948/4
∴ x = 237
So the smaller number is 237.
১৫,৯৪৯.
The value of log2{log4(log42564)} =?
ব্যাখ্যা
Question: The value of log2{log4(log42564)} =?
Solution:
= log2{log4(log42564)}
= log2{log4(log4(44)4}
= log2{log4(16log44)}
= log2{log442}
= log22(log44)
= log22
= 1
∴ The value of the expression is 1.
Solution:
= log2{log4(log42564)}
= log2{log4(log4(44)4}
= log2{log4(16log44)}
= log2{log442}
= log22(log44)
= log22
= 1
∴ The value of the expression is 1.
১৫,৯৫০.
Age of the father is equal to the sum of ages of his three sons. If in 19 years, one third of father's age will be equal to one fifth the sum of the ages of the sons. What is the age of the father?
ব্যাখ্যা
Question: Age of the father is equal to the sum of ages of his three sons. If in 19 years, one third of father's age will be equal to one fifth the sum of the ages of the sons. What is the age of the father?
Solution:
Let,
The age of the father now = a
Sum of the ages of three sons = b
Now, a = b
After 19 years, Father's age = a + 19
Age's of three son's = b + (3 × 19) = b + 57
ATQ, (1/3)(a + 19) = (1/5)(b + 57)
⇒ 5a + 95 = 3b + 171
⇒ 5a - 3a = 171 - 95 [∵ b = a]
⇒ 2a = 76
∴ a = 38
Solution:
Let,
The age of the father now = a
Sum of the ages of three sons = b
Now, a = b
After 19 years, Father's age = a + 19
Age's of three son's = b + (3 × 19) = b + 57
ATQ, (1/3)(a + 19) = (1/5)(b + 57)
⇒ 5a + 95 = 3b + 171
⇒ 5a - 3a = 171 - 95 [∵ b = a]
⇒ 2a = 76
∴ a = 38
১৫,৯৫১.
A man sells two books at Tk. 120 each and by doing so he gains 25% on one book and loses 25% on the other. His loss on the whole in Tk. is = ?
ব্যাখ্যা
Question: A man sells two books at Tk. 120 each and by doing so he gains 25% on one book and loses 25% on the other. His loss on the whole in Tk. is = ?
Solution:
Sells price of two books = (120 × 2) = Tk. 240
Cost price of first book = (100/125) × 120
= Tk. 96
Cost price of second book = (100/75) × 120
= Tk. 160
∴ Loss = (160 + 96) - 240
= 256 - 240
= Tk. 16
Solution:
Sells price of two books = (120 × 2) = Tk. 240
Cost price of first book = (100/125) × 120
= Tk. 96
Cost price of second book = (100/75) × 120
= Tk. 160
∴ Loss = (160 + 96) - 240
= 256 - 240
= Tk. 16
১৫,৯৫২.
A clock seen through a mirror reads a quarter to nine. What is the actual time?
ব্যাখ্যা
Question: A clock seen through a mirror reads a quarter to nine. What is the actual time?
Solution:
The quarter to nine = 8 : 45
So the actual time = (11 : 60 - 8 : 45)
= 3 : 15
Solution:
The quarter to nine = 8 : 45
So the actual time = (11 : 60 - 8 : 45)
= 3 : 15
১৫,৯৫৩.
What is the solution of the equation 3/(y + 1) = 4/(y - 2)?
ব্যাখ্যা
Question: What is the solution of the equation 3/(y + 1) = 4/(y - 2)?
Solution:
3/(y + 1) = 4/(y - 2)
⇒ 3/(y + 1) - 4/(y - 2) = 0
⇒ (3y - 6 - 4y - 4)/(y + 1) (y - 2) = 0
⇒ - y - 10 = 0
∴ y = - 10
Solution:
3/(y + 1) = 4/(y - 2)
⇒ 3/(y + 1) - 4/(y - 2) = 0
⇒ (3y - 6 - 4y - 4)/(y + 1) (y - 2) = 0
⇒ - y - 10 = 0
∴ y = - 10
১৫,৯৫৪.
Rizvi and Shafi take a project to work together. However, Shafi falls sick after working for 20 days and Rizvi works alone on the project for the last 6 days. They submit the project in 26 days. Had Rizvi and Shafi worked on the project for all the days together, they could have submitted it in 24 days. How many days will Shafi take to complete the project alone?
ব্যাখ্যা
Let work is done by Rizvi in 1 day = 1/R & Shafi in 1/S day
Both complete work in 24 days. So in 1 day, together they complete = 1/24 = 1/R + 1/S
For 20 days both work together, so work done by them = 20(1/R + 1/S) = 5/6
Remaining work = {1 - (5/6)= 1/6} is done by Rizvi alone in 6 days
Work done by Rizvi in 6 days = 1/6 = 6(1/R)
∴ R = 36 = days needed by Rizvi to complete the work alone
According to the question,
∴ (1/36) + 1/S = 1/24
1/S = (1/24) - (1/36)
1/S = (3 - 2)/72
1/S = 1/72
S = 72 days needed by Shafi to complete the work alone.
১৫,৯৫৫.
Compute the total surface area of the cylinder, with a radius of 5cm and height of 10cm?
ব্যাখ্যা
Question: Compute the total surface area of the cylinder, with a radius of 5cm and height of 10cm?
Solution:
Since, we know,
Total surface area of a cylinder, A = 2πr(r + h) square units
Therefore, A = 2π × 5(5 + 10) = 2π × 5(15)
= 2π × 75 = 150 × 3.14
= 471 cm2
Solution:
Since, we know,
Total surface area of a cylinder, A = 2πr(r + h) square units
Therefore, A = 2π × 5(5 + 10) = 2π × 5(15)
= 2π × 75 = 150 × 3.14
= 471 cm2
১৫,৯৫৬.
Speed of a boat in standing water is 10 kmph and the speed of the stream is 2.5 kmph. A man rows to a place at a distance of 112.5 km and comes back to the starting point. The total time taken by him is:
ব্যাখ্যা
Speed upstream = 7.5 kmph.
Speed downstream = 12.5 kmph.
∴ Total time taken =(112.5/7.5) +(112.5/12.5)
= (15 + 9) hours
= 24 hours
Speed downstream = 12.5 kmph.
∴ Total time taken =(112.5/7.5) +(112.5/12.5)
= (15 + 9) hours
= 24 hours
১৫,৯৫৭.
Which is the larger between two numbers if they are in the ratio of 6 : 13 and their least common multiple is 312?
ব্যাখ্যা
Question: Which is the larger between two numbers if they are in the ratio of 6 : 13 and their least common multiple is 312?
Solution:
Let, the numbers be 6x, 13x
HCF is x and LCM is 312
6x × 13x = 312 × x
⇒ x = 312/(6 × 13)
= 4
Larger number = 13 × 4 = 52
১৫,৯৫৮.
The graph of linear equation x + 2y = 2, cuts the y-axis at:
ব্যাখ্যা
x + 2y = 2
y = (2 - x)/2
If x = 0, then,
y = (2 - 0)/2
= 2/2
= 1
Hence, x + 2y = 2 cuts the y-axis at (0, 1).
১৫,৯৫৯.
The average of 10 numbers is 23. If each number is increased by 4, what will the new average be?
ব্যাখ্যা
Question: The average of 10 numbers is 23. If each number is increased by 4, what will the new average be?
Solution:
Given,
Given,
Average of 10 numbers = 23
⇒ Sum/Total numbers = 23
⇒ Sum/10 = 23
∴ Sum of the 10 numbers = 230
If each number is increased by 4, the total increase = 4 × 10 = 40
New sum = 230 + 40 = 270
Therefore, the new average = 270/10 = 27
১৫,৯৬০.
Three taps A, B, and C can fill a tank in 12,15, and 20 hours respectively. If A is open all the time and B, and C are open for one hour each alternatively, the tank will be full in:
ব্যাখ্যা
Question: Three taps A, B, and C can fill a tank in 12,15, and 20 hours respectively. If A is open all the time and B, and C are open for one hour each alternatively, the tank will be full in:
Solution:
A ১ ঘণ্টায় করে ১/১২ অংশ
B ১ ঘণ্টায় পূর্ণ করে ১/১৫ অংশ
C ১ ঘণ্টায় পূর্ণ করে ১/২০ অংশ
A ও B ১ ঘন্টায় করে (১/১২) + (১/১৫) অংশ
= ৩/২০ অংশ
A ও C অংশ ১ ঘণ্টায় করে (১/১২) + (১/২০) অংশ
= ২/১৫ অংশ
২ ঘণ্টায় পূর্ণ হয় = (৩/২০) + (২/১৫)
= ১৭/৬০ অংশ
৪ ঘণ্টায় পূর্ণ হয় (২ × ১৭)/৬০ অংশ
= ৩৪/৬০ অংশ
৬ ঘণ্টায় পূর্ণ হয় (৩৪/৬০) + (১৭/৬০)
= (৩৪ + ১৭)/৬০ অংশ
= ৫১/৬০ অংশ
বাকি থাকে (১ - ৫১/৬০)
= ৯/৬০ অংশ
= ৩/২০ অংশ
A ও B ১ ঘন্টায় করে (১/১২) + (১/১৫) অংশ
= ৩/২০ অংশ
∴ মোট সময় লাগবে = ৬ + ১ ঘণ্টা
= ৭ ঘণ্টা
Solution:
A ১ ঘণ্টায় করে ১/১২ অংশ
B ১ ঘণ্টায় পূর্ণ করে ১/১৫ অংশ
C ১ ঘণ্টায় পূর্ণ করে ১/২০ অংশ
A ও B ১ ঘন্টায় করে (১/১২) + (১/১৫) অংশ
= ৩/২০ অংশ
A ও C অংশ ১ ঘণ্টায় করে (১/১২) + (১/২০) অংশ
= ২/১৫ অংশ
২ ঘণ্টায় পূর্ণ হয় = (৩/২০) + (২/১৫)
= ১৭/৬০ অংশ
৪ ঘণ্টায় পূর্ণ হয় (২ × ১৭)/৬০ অংশ
= ৩৪/৬০ অংশ
৬ ঘণ্টায় পূর্ণ হয় (৩৪/৬০) + (১৭/৬০)
= (৩৪ + ১৭)/৬০ অংশ
= ৫১/৬০ অংশ
বাকি থাকে (১ - ৫১/৬০)
= ৯/৬০ অংশ
= ৩/২০ অংশ
A ও B ১ ঘন্টায় করে (১/১২) + (১/১৫) অংশ
= ৩/২০ অংশ
∴ মোট সময় লাগবে = ৬ + ১ ঘণ্টা
= ৭ ঘণ্টা
১৫,৯৬১.
If A's income is 80% of B's income, then B's income is more than A's income by -
ব্যাখ্যা
When A’s income is Tk 80 B’s Income is Tk 100
when A’s income is Tk 1 B’s Income is Tk 100/80
when A’s income is Tk 100 B’s Income is Tk (100/80) × 100 = 125%
So, A’s income is 125 - 100 = 25% more
Short-cut,
A’s income is 20% less than B’s
r = 20%
(r/100 - r) × 100
(20/100) × 100
= 25%
১৫,৯৬২.
A fruit seller sells mangoes at the rate of Tk. 9 per kg and thereby loses 20%. At what price per kg, he should have sold, them to make a profit of 5%?
ব্যাখ্যা
Let the new S.P. be Tk. x
Then,80:9=105:x
⇒x=(9×105/ 80)=11.81
১৫,৯৬৩.
Abir is paid an hourly wage totalling Tk 500 for 50 hours of work in a week. If his hourly wage increases by 20% and he decides to work 20% fewer hours each week, how much will Abir be paid in a week?
ব্যাখ্যা
Question: Abir is paid an hourly wage totalling Tk 500 for 50 hours of work in a week. If his hourly wage increases by 20% and he decides to work 20% fewer hours each week, how much will Abir be paid in a week ?
Solution:
Here,
Hourly wage = 500/50 = 10
The hourly wage increases by 20%;
Then, the present hourly wage = 10 + (10 × 20%)
= 10 + [10 × (20/100)]
= (10 + 2) Tk
= 12 Tk/hour
The work hour decreases by 20%;
Then, the present work hour = 50 - (50 × 20%)
= 50 - [50 × (20/100)]
= (50 - 10) hour
= 40 hour
∴ Present weekly income = 12 × 40 = 480 Tk.
১৫,৯৬৪.
The difference between three times and seven times of a number comes to 36. What is the number?
ব্যাখ্যা
Question: The difference between three times and seven times of a number comes to 36. What is the number?
Solution:
let, the number be x
ATQ,
7x - 3x = 36
⇒ 4x = 36
⇒ x =36/4 = 9
Solution:
let, the number be x
ATQ,
7x - 3x = 36
⇒ 4x = 36
⇒ x =36/4 = 9
১৫,৯৬৫.
A number when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing the same number by 31?
ব্যাখ্যা
Let the number be P.
So,
P ÷ 44 = 432
⇒ P = 432 * 44
= 19008
P/31 = 19008 / 31
= 613, Remainder = 5
১৫,৯৬৬.
What decimal of an hour is 45 seconds?
ব্যাখ্যা
Question: What decimal of an hour is 45 seconds?
Solution:
1 hour = 60 × 60 = 3600 seconds
∴ Required decimal
= 45/3600
= 1/80
= 0.0125
১৫,৯৬৭.
A father said to his son, ''I was as old as you are at the present at the time of your birth''. If the father's age is 38 years now, what was the son's age five years back?
ব্যাখ্যা
Fathers age when his son was born= son's present age
Fathers age when his son was born + son's present age = father's present age
Therefore, 2 (Son's present age) = 38
=> Son's present age = 19
=> Son's age five years back = 19 − 5 = 14
১৫,৯৬৮.
A company makes a profit of 5% on its first TK. 1000 of sales each day, and 4% on all sales in excess of 1000 for that day. What would be the profit of the company in a day when sales are TK. 6000?
ব্যাখ্যা
Question:
A company makes a profit of 5% on its first TK. 1000 of sales each day, and 4% on all sales in excess of 1000 for that day. What would be the profit of the company in a day when sales are TK. 6000?
Solution:
Profit for first TK. 1000 = 1000 × (5/100) = TK. 50
Total sales excess of Tk. 1000 = (6000 - 1000) = Tk. 5000
∴ Profit for excess of Tk. 1000 = 5000 × (4/100) = Tk. 200
∴ Total Profit (50+ 200) = Tk. 250
A company makes a profit of 5% on its first TK. 1000 of sales each day, and 4% on all sales in excess of 1000 for that day. What would be the profit of the company in a day when sales are TK. 6000?
Solution:
Profit for first TK. 1000 = 1000 × (5/100) = TK. 50
Total sales excess of Tk. 1000 = (6000 - 1000) = Tk. 5000
∴ Profit for excess of Tk. 1000 = 5000 × (4/100) = Tk. 200
∴ Total Profit (50+ 200) = Tk. 250
১৫,৯৬৯.
The length of one side of a square inscribed in a circle is 2. What is the area of the circle?
ব্যাখ্যা
Question: The length of one side of a square inscribed in a circle is 2. What is the area of the circle?
Solution:
বৃত্তের অন্তর্লিখিত বর্গের বাহুর দৈর্ঘ্য ২ একক
∴ বর্গের কর্ণের দৈর্ঘ্য = ২√২ একক
এখানে বর্গের কর্ণ বৃত্তটির ব্যাসের সমান।
∴ বৃত্তের ব্যাসার্ধ = (২√২)/২ একক = √২ একক
বৃত্তের ক্ষেত্রফল = π(√২)২ বর্গএকক
= ২π বর্গএকক
Solution:
বৃত্তের অন্তর্লিখিত বর্গের বাহুর দৈর্ঘ্য ২ একক
∴ বর্গের কর্ণের দৈর্ঘ্য = ২√২ একক
এখানে বর্গের কর্ণ বৃত্তটির ব্যাসের সমান।
∴ বৃত্তের ব্যাসার্ধ = (২√২)/২ একক = √২ একক
বৃত্তের ক্ষেত্রফল = π(√২)২ বর্গএকক
= ২π বর্গএকক
১৫,৯৭০.
A coin is thrown 3 times. What is the probability that atleast one head is obtained?
ব্যাখ্যা
Question: A coin is thrown 3 times. What is the probability that atleast one head is obtained?
Solution:
Sample space = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}
Total number of ways = 23 = 8.
Fav. Cases = 7
∴ Probability that atleast one head is obtained = 7/8
Solution:
Sample space = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}
Total number of ways = 23 = 8.
Fav. Cases = 7
∴ Probability that atleast one head is obtained = 7/8
১৫,৯৭১.
At what rate percent of simple interest will a sum of money double itself in 10 years?
ব্যাখ্যা
Question: At what rate percent of simple interest will a sum of money double itself in 10 years?
Solution:
ধরি,
আসল = ১০০ টাকা
তাহলে ১০ বছর পর দ্বিগুণ অর্থ সুদ সহ আসল হবে = ২ × ১০০ = ২০০
∴ মোট সুদ = (২০০ - ১০০) টাকা = ১০০ টাকা
∴ ১০ বছরের সুদ ১০০ টাকা হলে ১ বছরের সুদ = ১০০/১০ = ১০%
Solution:
ধরি,
আসল = ১০০ টাকা
তাহলে ১০ বছর পর দ্বিগুণ অর্থ সুদ সহ আসল হবে = ২ × ১০০ = ২০০
∴ মোট সুদ = (২০০ - ১০০) টাকা = ১০০ টাকা
∴ ১০ বছরের সুদ ১০০ টাকা হলে ১ বছরের সুদ = ১০০/১০ = ১০%
১৫,৯৭২.
The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8 is-
ব্যাখ্যা
Question: The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8 is-
Solution:
The number leaves a remainder 8 when divided by 12, 15, 20 and 54.
So the required number = LCM(12, 15, 20, 54) + 8
Now,
12 = 2 × 2 × 3
15 = 3 × 5
20 = 2 × 2 × 5
54 = 2 × 3 × 3 × 3
∴ LCM(12, 15, 20, 54) = 540
∴ Required Number = 540 + 8 = 548
১৫,৯৭৩.
Which of the following has most number of divisors?
ব্যাখ্যা
66 = 1 × 3 × 2 × 11
103 = 1 × 103
176 = 1 × 2 × 2 × 2 × 2 × 11
182 = 1 × 2 × 7 × 13
So, divisor of 66 are 1, 3, 6, 11, 22, 33 and 66
Divisor of 103 are 1 and 103
Divisor of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88 and 176
Divisor of 182 are 1, 2, 7, 13, 14, 26, 91 and 182
Hence, 176 has the most number of divisors.
103 = 1 × 103
176 = 1 × 2 × 2 × 2 × 2 × 11
182 = 1 × 2 × 7 × 13
So, divisor of 66 are 1, 3, 6, 11, 22, 33 and 66
Divisor of 103 are 1 and 103
Divisor of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88 and 176
Divisor of 182 are 1, 2, 7, 13, 14, 26, 91 and 182
Hence, 176 has the most number of divisors.
১৫,৯৭৪.
From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings?
ব্যাখ্যা
Let S be the sample space
Then,
n(S) = 52C2
= 52 × 51/2 × 1
= 1326
Let E = event of getting 2 kings out of 4.
n(E) = 4C2
=> 4 × 3/2 × 1
P(E) = n(E)/n(S)
= 6/1326
= 1/221
১৫,৯৭৫.
If a2 + b2 = 61 and ab = 30, find (1/a) + (1/b).
ব্যাখ্যা
Question: If a2 + b2 = 61 and ab = 30, find (1/a) + (1/b).
Solution:
দেওয়া আছে,
ab = 30
a2 + b2 = 61
⇒ (a + b)2 - 2ab = 61
⇒ (a + b)2 - 60 = 61
⇒ (a + b)2 = 121
∴ a + b = 11
এখন,
(1/a) + (1/b)
= (b + a)/ab
= 11/30
Solution:
দেওয়া আছে,
ab = 30
a2 + b2 = 61
⇒ (a + b)2 - 2ab = 61
⇒ (a + b)2 - 60 = 61
⇒ (a + b)2 = 121
∴ a + b = 11
এখন,
(1/a) + (1/b)
= (b + a)/ab
= 11/30
১৫,৯৭৬.
If a3 - b3 = 208 and a - b = 4, then ab = ?
ব্যাখ্যা
Question: If a3 - b3 = 208 and a - b = 4, then ab = ?
Solution:
Given,
a3 - b3 = 208
a - b = 4
We know,
a3 - b3 = (a - b)3 + 3ab(a - b)
⇒ 208 = 43 + 3ab · 4
⇒ 208 = 64 + 12ab
⇒ 12ab = 208 - 64
⇒ 12ab = 144
∴ ab = 12
Solution:
Given,
a3 - b3 = 208
a - b = 4
We know,
a3 - b3 = (a - b)3 + 3ab(a - b)
⇒ 208 = 43 + 3ab · 4
⇒ 208 = 64 + 12ab
⇒ 12ab = 208 - 64
⇒ 12ab = 144
∴ ab = 12
১৫,৯৭৭.
If x is doubled and y is tripled in the expression z = (4x/y), then the value of z is _____.
ব্যাখ্যা
Question: If x is doubled and y is tripled in the expression z = (4x/y), then the value of z is _____.
Solution:
x এর দ্বিগুণ = 2x
y এর দিগুণ = 3y
এখন
z = (4 × 2x/3y)
= 8x/3y
= (4x/y) × (2/3)
The value of z is multiplied by a factor 2/3.
১৫,৯৭৮.
If the perimeter of square region S and the perimeter of circular region C are equal, then the ratio of the area of S to the area of C is closest to-
ব্যাখ্যা
Question: If the perimeter of square region S and the perimeter of circular region C are equal, then the ratio of the area of S to the area of C is closest to-
Solution:
If Perimeter of square = Perimeter of Circle,
then:
4a = 2πr, where a = side of square and r is radius of the circle
a/r = π/2
Area of S/Area of C = a2/(πr2)
= (π/2)2 × (1/π)
= π/4
= 3.14/4
≈ 3/4
Solution:
If Perimeter of square = Perimeter of Circle,
then:
4a = 2πr, where a = side of square and r is radius of the circle
a/r = π/2
Area of S/Area of C = a2/(πr2)
= (π/2)2 × (1/π)
= π/4
= 3.14/4
≈ 3/4
১৫,৯৭৯.
A pipe can fill a tank in 6 hours. Because of a leak, it took 1 hour more to fill the tank. The leak can drain all the water from the tank in -
ব্যাখ্যা
Question: A pipe can fill a tank in 6 hours. Because of a leak, it took 1 hour more to fill the tank. The leak can drain all the water from the tank in -
Solution:
Because of the leak, it took 6 + 1 = 7 hours to fill the tank
Work done by pipe + leak in 1 hour = 1/7 part
Work done by pipe in 1 hour = 1/6 part
So, Work done by the leak in 1 hour = 1/6 - 1/7 part
= 1/42 part
∴ the leak will empty the tank in 42 hours
Solution:
Because of the leak, it took 6 + 1 = 7 hours to fill the tank
Work done by pipe + leak in 1 hour = 1/7 part
Work done by pipe in 1 hour = 1/6 part
So, Work done by the leak in 1 hour = 1/6 - 1/7 part
= 1/42 part
∴ the leak will empty the tank in 42 hours
১৫,৯৮০.
The ratio between the speeds of two trains is 5 : 8. If the second train runs 600 km in 5 hours, then the speed of the first train is -
ব্যাখ্যা
Question: The ratio between the speeds of two trains is 5 : 8. If the second train runs 600 km in 5 hours, then the speed of the first train is -
Solution:
Let the speed of the trains are 5x and 8x
the speed of the second train = 600/5 kmph = 120 kmph
∴ 8x = 120
x = 15
∴ speed of first train = 5x = 75 kmph
Solution:
Let the speed of the trains are 5x and 8x
the speed of the second train = 600/5 kmph = 120 kmph
∴ 8x = 120
x = 15
∴ speed of first train = 5x = 75 kmph
১৫,৯৮১.
In how many different ways can be letters of the word 'CYCLE' be arranged?
ব্যাখ্যা
Question: In how many different ways can be letters of the word 'CYCLE' be arranged?
Solution:
CYCLE whereas total 5 letters and C comes two times.
So, arrangements are = 5!/2!
= 60 ways
Solution:
CYCLE whereas total 5 letters and C comes two times.
So, arrangements are = 5!/2!
= 60 ways
১৫,৯৮২.
A number for each figures are given from 1 to 9. Find out the best method of classification and identify this amongst the four alternatives.
ব্যাখ্যা
A number for each figure is given from 1 to 9. Find out the best method of classification and identify this amongst the four alternatives.
Solution:
১, ৩, ৫ চিত্রে বৃত্ত বা অর্ধবৃত্ত আছে।
২, ৬, ৮ চিত্রগুলো ত্রিভুজ আকৃতির।
৪, ৭, ৯ চিত্রগুলো চতুর্ভুজ আকৃতির।
Solution:
১, ৩, ৫ চিত্রে বৃত্ত বা অর্ধবৃত্ত আছে।
২, ৬, ৮ চিত্রগুলো ত্রিভুজ আকৃতির।
৪, ৭, ৯ চিত্রগুলো চতুর্ভুজ আকৃতির।
১৫,৯৮৩.
At what rate percent per annum will a sum of money double in 4 years?
ব্যাখ্যা
Question: At what rate percent per annum will a sum of money double in 4 years?
Solution:
ধরি, সুদের হার x%
আসল x টাকা
সুদাসল = 2x টাকা
সুদ = 2x - x টাকা
= x টাকা
x = x × r × 4/100
∴ r = 25%
Solution:
ধরি, সুদের হার x%
আসল x টাকা
সুদাসল = 2x টাকা
সুদ = 2x - x টাকা
= x টাকা
x = x × r × 4/100
∴ r = 25%
১৫,৯৮৪.
If a series looks like 3, 4.78, 6.56, 8.34, 10.12, ..........., then which of the following comes next in the sequence?
ব্যাখ্যা
⊗ 3 + 1.78 = 4.78
⊗ 4.78 + 1.78 = 6.56
⊗ 6.56 + 1.78 = 8.34
⊗ 8.34 + 1.78 = 10.12
⊗ 10.12 + 1.78 = 11.9
⊗ 4.78 + 1.78 = 6.56
⊗ 6.56 + 1.78 = 8.34
⊗ 8.34 + 1.78 = 10.12
⊗ 10.12 + 1.78 = 11.9
১৫,৯৮৫.
Find the value of 3(p + 5) - 2(2p - 3) + p
ব্যাখ্যা
Question: Find the value of 3(p + 5) - 2(2p - 3) + p
Solution: Given that,
3(p + 5) - 2(2p - 3) + p
= 3p + 15 - 4p + 6 + p
= (3p - 4p + p) + (15 + 6)
= 0 + 21
= 21
১৫,৯৮৬.
P and Q can do a work in 10 days, Q and R can do it in 15 days, and P and R can do it in 12 days. If all three work together, in how many days can they complete the work?
ব্যাখ্যা
Question: P and Q can do a work in 10 days, Q and R can do it in 15 days, and P and R can do it in 12 days. If all three work together, in how many days can they complete the work?
Solution:
P + Q can do in 1 day = 1/10 part
Q + R can do in 1 day = 1/15 part
P + R can do in 1 day = 1/12 part
∴ 2(P + Q + R) can do in 1 day = ((1/10) + (1/15) + (1/12))
= (6 + 4 + 5)/60
= 15/60
= 1/4 part
∴ P + Q + R can do in 1 day = 1/(4 × 2) part = 1/8 part
∴ Total days needed = 1/(1/8) = 8 days
Solution:
P + Q can do in 1 day = 1/10 part
Q + R can do in 1 day = 1/15 part
P + R can do in 1 day = 1/12 part
∴ 2(P + Q + R) can do in 1 day = ((1/10) + (1/15) + (1/12))
= (6 + 4 + 5)/60
= 15/60
= 1/4 part
∴ P + Q + R can do in 1 day = 1/(4 × 2) part = 1/8 part
∴ Total days needed = 1/(1/8) = 8 days
১৫,৯৮৭.
Sumi and Shila start simultaneously from a place A towards B 120 km apart. Sumi's speed is 4 km/h less than that of Shila. Shila, after reaching B, turns back and meets Sumi at a place 20 km away from B. Find Sumi's speed-
ব্যাখ্যা
Question: Sumi and Shila start simultaneously from a place A towards B 120 km apart. Sumi's speed is 4 km/h less than that of Shila. Shila, after reaching B, turns back and meets Sumi at a place 20 km away from B. Find Sumi's speed-
Question:
Let, the speed of Sumi be = a kmph
Now,
Shila's speed = (a + 4) kmph
∴ Distance covered by Sumi = (120 + 20) = 140 km
∴ Distance covered by Rafiq = (120 - 20) = 100 km.
ATQ,
140/(a + 4) = 100/a
⇒ 140a = 100a + 400
⇒ 140a - 100a = 400
⇒ 40a = 400
⇒ a = 400/40
∴ a = 10 kmph
Question:
Let, the speed of Sumi be = a kmph
Now,
Shila's speed = (a + 4) kmph
∴ Distance covered by Sumi = (120 + 20) = 140 km
∴ Distance covered by Rafiq = (120 - 20) = 100 km.
ATQ,
140/(a + 4) = 100/a
⇒ 140a = 100a + 400
⇒ 140a - 100a = 400
⇒ 40a = 400
⇒ a = 400/40
∴ a = 10 kmph
১৫,৯৮৮.
If x/y = 2/3, then (x - y)/x?
ব্যাখ্যা
Question: If x/y = 2/3, then (x - y)/x?
Solution:
(x - y)/x
= x/x - y/x
= 1- y/x
= 1- 3/2
= (2 - 3)/2
= - 1/2
Solution:
(x - y)/x
= x/x - y/x
= 1- y/x
= 1- 3/2
= (2 - 3)/2
= - 1/2
১৫,৯৮৯.
A can do a piece of work in 10 days; B in 15 days. They work for 5 days. The rest of the work was finished by C in 2 days. If they get Tk. 3000 for the whole work, the daily wages of B and C together is:
ব্যাখ্যা
Question: A can do a piece of work in 10 days; B in 15 days. They work for 5 days. The rest of the work was finished by C in 2 days. If they get Tk. 3000 for the whole work, the daily wages of B and C together is:
Solution:
Part of work done by A= 1/10 × 5 ⇒ 1/2
Part of work done by B = 1/15 × 5 ⇒ 1/3
Part of work done by C = 1 - (1/2 + 1/3)
⇒ 1 - 5/6
⇒ 1/6
∴ (A’s share) : (B’s share) : (C’s share) = 1/2 : 1/3 : 1/6
⇒ 3 : 2 : 1
A’s share = 3/6 × 3000 ⇒Tk. 1500
B’s share = 2/6 × 3000 ⇒Tk. 1000
C’s share = 1/6 × 3000 ⇒Tk. 500
A’s daily wages = 1500/5 ⇒ Tk. 300
B’s daily wages = 1000/5 ⇒ Tk. 200
C’s daily wages = 500/2 ⇒ Tk. 250
Daily wages of Y and Z = (200 + 250) ⇒Tk. 450
The daily wages of B and C together is Tk. 450.
Solution:
Part of work done by A= 1/10 × 5 ⇒ 1/2
Part of work done by B = 1/15 × 5 ⇒ 1/3
Part of work done by C = 1 - (1/2 + 1/3)
⇒ 1 - 5/6
⇒ 1/6
∴ (A’s share) : (B’s share) : (C’s share) = 1/2 : 1/3 : 1/6
⇒ 3 : 2 : 1
A’s share = 3/6 × 3000 ⇒Tk. 1500
B’s share = 2/6 × 3000 ⇒Tk. 1000
C’s share = 1/6 × 3000 ⇒Tk. 500
A’s daily wages = 1500/5 ⇒ Tk. 300
B’s daily wages = 1000/5 ⇒ Tk. 200
C’s daily wages = 500/2 ⇒ Tk. 250
Daily wages of Y and Z = (200 + 250) ⇒Tk. 450
The daily wages of B and C together is Tk. 450.
১৫,৯৯০.
By selling a property for Tk. 45000 a person incurs a loss of 10%. Find the selling price to gain the profit of 15%?
ব্যাখ্যা
Question: By selling a property for Tk. 45000 a person incurs a loss of 10%. Find the selling price to gain the profit of 15%?
Solution:
CP = SP × 100/(100 - L%)
SP = CP × (100 + P%)/100
Here SP → Selling Price, CP → Cost Price, L% → Loss%, P% → Profit%
Calculation:
CP = 45000 × 100/(100 - 10)
⇒ CP = 45000 × (10/9)
= 50000
New Selling price = CP × (100 + 15)/100
⇒ New Selling price = 50000 × (115/100)
= 57500
∴ He should sell the land for Tk. 57500 to gain 15%
Solution:
CP = SP × 100/(100 - L%)
SP = CP × (100 + P%)/100
Here SP → Selling Price, CP → Cost Price, L% → Loss%, P% → Profit%
Calculation:
CP = 45000 × 100/(100 - 10)
⇒ CP = 45000 × (10/9)
= 50000
New Selling price = CP × (100 + 15)/100
⇒ New Selling price = 50000 × (115/100)
= 57500
∴ He should sell the land for Tk. 57500 to gain 15%
১৫,৯৯১.
A sum of money at compound interest doubles itself in 15 years. It will become four times of itself in-
ব্যাখ্যা
Question: A sum of money at compound interest doubles itself in 15 years. It will become four times of itself in-
Solution:
let the sum P
2P = P (1 + r)15
⇒ (1 + r)15 = 2
let, sum will 4 times in n years
4P = P(1 + r)n
⇒ 4 = (1 + r)n
⇒ 22 = (1 + r)n
⇒ ((1 + r)15)2 = (1 + r)n
⇒ (1 + r)30 = (1 + r)n
∴ n = 30 years
Solution:
let the sum P
2P = P (1 + r)15
⇒ (1 + r)15 = 2
let, sum will 4 times in n years
4P = P(1 + r)n
⇒ 4 = (1 + r)n
⇒ 22 = (1 + r)n
⇒ ((1 + r)15)2 = (1 + r)n
⇒ (1 + r)30 = (1 + r)n
∴ n = 30 years
১৫,৯৯২.
Ashik buys a field of agricultural land for Tk. 3,60,000. He sells one-third at a loss of 20% and two-fifths at a gain of 25%. At what price must he sell the remaining field so as to make an overall profit of 10%?
ব্যাখ্যা
Question: Ashik buys a field of agricultural land for Tk. 3,60,000. He sells one-third at a loss of 20% and two-fifths at a gain of 25%. At what price must he sell the remaining field so as to make an overall profit of 10%?
Solution:
Selling price of total agricultural field at a profit at 10% = 3,60,000 + 10% of 3,60,000
= 3,60,000 + 36000
= 396000
Selling price of 1/3 agricultural field at a loss of 20% = (3,60,000/3) × (80/100)
= 120000 × (80/100)
= 96000
Selling price of 2/5 agricultural field at a profit of 25% = {(2 × 3,60,000)/5} × (125/100)
= 144000 × (125/100)
= 180000
Sell price of the remaining field = {396000 - (96000 + 180000)}
= 120000 tk
১৫,৯৯৩.
Rahim performs 6/15 of the total journey by rail 8/20 by bus and the remaining 12 km on foot, his total journey is:
ব্যাখ্যা
Question: Rahim 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
⇒ (24x + 24x + 720)/60 = x
⇒ 24x + 24x + 720 = 60x
⇒ 60x - 48x = 720
⇒ 12x = 720
∴ x = 60
∴ Total journey = 60 km.
Solution:
Let, the total journey be x km.
ATQ,
∴ (6x/15) + (8x/20) + 12 = x
⇒ (24x + 24x + 720)/60 = x
⇒ 24x + 24x + 720 = 60x
⇒ 60x - 48x = 720
⇒ 12x = 720
∴ x = 60
∴ Total journey = 60 km.
১৫,৯৯৪.
REF, SGH, TIJ, ____, VMN
ব্যাখ্যা
Question: REF, SGH, TIJ, ____, VMN.
Solution:
There are two alphabetical series here.
The first series is with the first letters only: R, S, T, U, V.
The second series involves the remaining letters: , EF, GH, IJ, KL, MN.
∴ Answer will be = UKL
Solution:
There are two alphabetical series here.
The first series is with the first letters only: R, S, T, U, V.
The second series involves the remaining letters: , EF, GH, IJ, KL, MN.
∴ Answer will be = UKL
১৫,৯৯৫.
A trader buys a chair for Tk. 500 and sells it for Tk. 612 at a credit of 6 months. Reckoning money worth 4% per annum, his gain percent is-
ব্যাখ্যা
Question: A trader buys a chair for Tk. 500 and sells it for Tk. 612 at a credit of 6 months. Reckoning money worth 4% per annum, his gain percent is-
Solution:
Money worth in 12 months = 4%
So, money worth in 6 months = (4 × 6)/12 = 2%
So, for 500 Tk. money worth = 2% of 500 = Tk. 10
Total cost of the chair = 500 + 10 = Tk. 510
Total profit = 612 - 510 = Tk. 102
∴ Profit = (102 × 100)/510 = 20%
Solution:
Money worth in 12 months = 4%
So, money worth in 6 months = (4 × 6)/12 = 2%
So, for 500 Tk. money worth = 2% of 500 = Tk. 10
Total cost of the chair = 500 + 10 = Tk. 510
Total profit = 612 - 510 = Tk. 102
∴ Profit = (102 × 100)/510 = 20%
১৫,৯৯৬.
Two trains each 500 meter long, are running in opposite directions on parallel tracks. If their speeds are 45 km/hr and 30 km/hr respectively, the time taken by the slower train to pass the driver of the faster one is -
ব্যাখ্যা
Relative speed = (45 + 30) km/hr.
= 75 km/hr.
= 75 × (5/18) km/hr.
= (125/6) m/s.
We are calculating the time taken by the slower train to pass the driver of the faster one.
Hence, distance = length of the slower train = 500 meter.
Time = 500/(125/6)
= 500 × (6/125)
= 24 seconds.
১৫,৯৯৭.
- 5x - [4y - {9x - (3y - 7x)}] simplifies to
ব্যাখ্যা
Question: - 5x - [4y - {9x - (3y - 7x)}] simplifies to
Solution:
- 5x - [4y - {9x - (3y - 7x)}]
= - 5x - [4y - {9x - 3y + 7x}]
= - 5x - [4y - 9x + 3y - 7x]
= - 5x - [7y - 16x]
= - 5x - 7y + 16x
= 11x - 7y
১৫,৯৯৮.
The difference between compound interest and simple interest on a sum for 2 years at 8% is Tk 768. The sum is -
ব্যাখ্যা
Question: The difference between compound interest and simple interest on a sum for 2 years at 8% is Tk 768. The sum is -
Solution:
Let the sum be p
Then, Compound Interest = p(1+ 8/100)2 - p
= p(108/100)2 - p
= p(27/25)2 - p
= 729p/625 - p
= 104p/625
Again, Simple Interest = p × 2 × (8/100) = 4p/25
ATQ,
104p/625 - 4p/25 = 768
⇒ 4p/625 = 768
⇒ p = (768 × 625)/4
⇒ p = 120000
Solution:
Let the sum be p
Then, Compound Interest = p(1+ 8/100)2 - p
= p(108/100)2 - p
= p(27/25)2 - p
= 729p/625 - p
= 104p/625
Again, Simple Interest = p × 2 × (8/100) = 4p/25
ATQ,
104p/625 - 4p/25 = 768
⇒ 4p/625 = 768
⇒ p = (768 × 625)/4
⇒ p = 120000
১৫,৯৯৯.
Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to stamps?
ব্যাখ্যা
Question : Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps?
Solution:
US : Indian = 5 : 2 = 25 : 10
Indian : British = 5 : 1 = 10 : 2
US : British = 25 : 2
Solution:
US : Indian = 5 : 2 = 25 : 10
Indian : British = 5 : 1 = 10 : 2
US : British = 25 : 2
১৬,০০০.
In a class of 92 students, 40 are taking English, 24 are taking Arabic and 10 are taking both courses. How many students are not enrolled in either course?
ব্যাখ্যা
Question: In a class of 92 students, 40 are taking English, 24 are taking Arabic and 10 are taking both courses. How many students are not enrolled in either course?
Solution:
Total students = 92
Students taking English n(E) = 40
Students taking Arabic n(A) = 24
Students taking both English and Arabic = 10
We know,
n(E ∪ A) = n(E) + n(A) - n(E ∩ A)
n(E ∪ A) = 40 + 24 - 10 = 54
∴ Not enrolled = Total students - n(E ∪ A) = 92 - 54 = 38