৬,৯০১.
ব্যাখ্যা
Question:
Solution:
PrepBank · বিষয়ভিত্তিক প্রশ্ন
Bank Math
Bank Math
PrepBank · পাতা ৭০ / ১৬১ · ৬,৯০১–৭,০০০ / ১৬,১২৪
৬,৯০২.
An observer 2m tall is 10√3 m away from a tower. The angle of elevation from his eye to the top of the tower is 30°. The height of the tower is:
ব্যাখ্যা
SR = PQ = 2 m
PS = QR = 10√3
tan 30° = TS/PS
1/√3 = TS/10√3
TS = 10√3/√3
= 10
TR = TS + SR
= 10 + 2
= 12 m.
৬,৯০৩.
If dividing P(x) = 5x3 + 6x2 - ax + 6 by x - 2 results the remainder 6 then find the value of a.
ব্যাখ্যা
Question: If dividing P(x) = 5x3 + 6x2 - ax + 6 by x - 2 results the remainder 6 then find the value of a.
Solution:
Dividing P(x) by x - 2 we will get the remainder
∴ P(2) = 5 × 23 + 6 × 22 - a × 2 + 6
= 40 + 24 - 2a + 6
= 70 - 2a
ATQ,
70 - 2a = 6
⇒ 2a = 70 - 6
⇒ 2a = 64
∴ a = 32
Solution:
Dividing P(x) by x - 2 we will get the remainder
∴ P(2) = 5 × 23 + 6 × 22 - a × 2 + 6
= 40 + 24 - 2a + 6
= 70 - 2a
ATQ,
70 - 2a = 6
⇒ 2a = 70 - 6
⇒ 2a = 64
∴ a = 32
৬,৯০৪.
W, X, Y and Z are four different positive integers. When X is divided by Y, the quotient is Z and the remainder is W. If W = X - 7, what is the sum of all possible values of W?
ব্যাখ্যা
Question: W, X, Y and Z are four different positive integers. When X is divided by Y, the quotient is Z and the remainder is W. If W = X - 7, what is the sum of all possible values of W?
Solution:
From the given information, we can write: X = YZ + W
Also given: W = X - 7
X = YZ + W
⇒ X = YZ + X - 7
⇒ 0 = YZ - 7
∴ 7 = YZ
There are only 2 possible cases:
case 1: Y = 1 and Z = 7
case 2: Y = 7 and Z = 1
case 1 yields a CONTRADICTION.
If Y = 1, then we are dividing X by 1, and if we divide by 1, the remainder will always be ZERO.
In other words, if Y = 1, then W = 0 So, we can definitely rule out case 1,
It must be the case that Y = 7 and Z = 1 (case 2)
So, we have: When X is divided by 7, the quotient is 1 and the remainder is W
This tells us that 7 divides into X 1 time
So, the possible values of X are: 7, 8, 9, 10, 11, 12 and 13 (since 7 divides into each value 1 time.
Let's check each case.
If X = 7,
then the remainder (W) is 0.
Doesn't follow the rule.
If X = 8,
then the remainder (W) is 1.
Since Y = W,
Doesn't follow the rule.
If X = 9,
then the remainder (W) is 2.
So, when X (9) is divided by 7 (Y), the quotient (Z) is 1, and the remainder (W) is 2.
Follows the rule.
If X = 10,
then the remainder (W) is 3.
So, when X (10) is divided by 7 (Y), the quotient (Z) is 1, and the remainder (W) is 3.
Follows the rule.
If X = 11,
then the remainder (W) is 4.
So, when X (11) is divided by 7 (Y), the quotient (Z) is 1, and the remainder (W) is 4.
Follows the rule.
If X = 12,
then the remainder (W) is 5.
So, when X (12) is divided by 7 (Y), the quotient (Z) is 1, and the remainder (W) is 5.
Follows the rule.
If X = 13,
then the remainder (W) is 6.
So, when X (13) is divided by 7 (Y), the quotient (Z) is 1, and the remainder (W) is 6.
Follows the rule.
Sum = 2 + 3 + 4 + 5 + 6
= 20
Solution:
From the given information, we can write: X = YZ + W
Also given: W = X - 7
X = YZ + W
⇒ X = YZ + X - 7
⇒ 0 = YZ - 7
∴ 7 = YZ
There are only 2 possible cases:
case 1: Y = 1 and Z = 7
case 2: Y = 7 and Z = 1
case 1 yields a CONTRADICTION.
If Y = 1, then we are dividing X by 1, and if we divide by 1, the remainder will always be ZERO.
In other words, if Y = 1, then W = 0 So, we can definitely rule out case 1,
It must be the case that Y = 7 and Z = 1 (case 2)
So, we have: When X is divided by 7, the quotient is 1 and the remainder is W
This tells us that 7 divides into X 1 time
So, the possible values of X are: 7, 8, 9, 10, 11, 12 and 13 (since 7 divides into each value 1 time.
Let's check each case.
If X = 7,
then the remainder (W) is 0.
Doesn't follow the rule.
If X = 8,
then the remainder (W) is 1.
Since Y = W,
Doesn't follow the rule.
If X = 9,
then the remainder (W) is 2.
So, when X (9) is divided by 7 (Y), the quotient (Z) is 1, and the remainder (W) is 2.
Follows the rule.
If X = 10,
then the remainder (W) is 3.
So, when X (10) is divided by 7 (Y), the quotient (Z) is 1, and the remainder (W) is 3.
Follows the rule.
If X = 11,
then the remainder (W) is 4.
So, when X (11) is divided by 7 (Y), the quotient (Z) is 1, and the remainder (W) is 4.
Follows the rule.
If X = 12,
then the remainder (W) is 5.
So, when X (12) is divided by 7 (Y), the quotient (Z) is 1, and the remainder (W) is 5.
Follows the rule.
If X = 13,
then the remainder (W) is 6.
So, when X (13) is divided by 7 (Y), the quotient (Z) is 1, and the remainder (W) is 6.
Follows the rule.
Sum = 2 + 3 + 4 + 5 + 6
= 20
৬,৯০৫.
The solution to the system x + y = 5, x - y = 1 is
ব্যাখ্যা
Question: The solution to the system x + y = 5, x - y = 1 is-
Solution:
দেওয়া আছে
x + y = 5....................(1)
x - y = 1....................(2)
(1) নং + (2)নং ⇒
x + y + x - y = 5 + 1
⇒ 2x = 6
∴x = 3
(1) নং ⇒
x + y = 5
⇒ 3 + y = 5
⇒ y = 5 - 3
∴ y = 2
নির্ণেয় সমাধান x = 3, y = 2
Solution:
দেওয়া আছে
x + y = 5....................(1)
x - y = 1....................(2)
(1) নং + (2)নং ⇒
x + y + x - y = 5 + 1
⇒ 2x = 6
∴x = 3
(1) নং ⇒
x + y = 5
⇒ 3 + y = 5
⇒ y = 5 - 3
∴ y = 2
নির্ণেয় সমাধান x = 3, y = 2
৬,৯০৬.
How much time will it take for an amount of Tk. 900 to yield Tk. 180 as interest at 5% per annum of simple interest?
ব্যাখ্যা
Question: How much time will it take for an amount of Tk. 900 to yield Tk. 180 as interest at 5% per annum of simple interest?
Solution:
I = Pnr
n = I / pr
= 180 /(900 × 5%)
= 4 years
Solution:
I = Pnr
n = I / pr
= 180 /(900 × 5%)
= 4 years
৬,৯০৭.
Abid, Bulbul, and Kabil are partners in a business. Their shares are in the proposition of (1/3) : (1/4) : (1/5). Abir withdraws half of his capital after 15 months and after another 15 months, a profit of Tk. 4340 is divided. The share of Kabil's is-
ব্যাখ্যা
Question: Abid, Bulbul, and Kabil are partners in a business. Their shares are in the proposition of (1/3) : (1/4) : (1/5). Abir withdraws half of his capital after 15 months and after another 15 months, a profit of Tk. 4340 is divided. The share of Kabil's is -
Solution:
Ratio of initial investments = 1/3 : 1/4 : 1/5
= 20 : 15 : 12
Let their initial investments be 20x, 15x and 12x respectively.
Abid : Bulbul : Kabil = (20x × 15) + (10x × 15): (15x × 30) : (12x × 30)
= 450x : 450x : 360x
= 5 : 5 : 4
Sum of the ratio = 5 + 5 + 4 = 14.
∴ Kabil's share = 4340 × (4/14)
= 1240 Tk.
Solution:
Ratio of initial investments = 1/3 : 1/4 : 1/5
= 20 : 15 : 12
Let their initial investments be 20x, 15x and 12x respectively.
Abid : Bulbul : Kabil = (20x × 15) + (10x × 15): (15x × 30) : (12x × 30)
= 450x : 450x : 360x
= 5 : 5 : 4
Sum of the ratio = 5 + 5 + 4 = 14.
∴ Kabil's share = 4340 × (4/14)
= 1240 Tk.
৬,৯০৮.
Three pipes A, B and C can fill a tank in 10 hours. After working at it together for 3 hours, C is closed and A and B can fill the remaining part in 14 hours. How much time taken by C to fill the tank alone?
ব্যাখ্যা
Three pipes A, B, and C can fill a tank in 8 hours. A, B, and C’s 1 hour work=1/10
A, B and C's 3 hour work= 3/10 Remaining work= 1 – (3/10) = 7/10
The remaining part will be filled by A and B in 14 hours. Then,
⇒ (7/10) × (A + B) = 14
⇒ (A + B)'s whole work= 14 × (10/7)
= 20 hr (A + B)'s 1-hour work
= 1/20
A, B, and C's 1-hour work = 1/10
C's 1 hour work= (A + B + C) – (A + B)
⇒ (1/10) – (1/20)
⇒ 1/20
∴ C can fill the tank in 20 hours.
৬,৯০৯.
If 5√5 × 53 ÷ 5-3/2 =5a + 2 then what is the value of a?
ব্যাখ্যা
Question: If 5√5 × 53 ÷ 5-3/2 =5a + 2 then what is the value of a?
Solution:
Solution:
৬,৯১০.
What is the slope of a line perpendicular to the line whose equation is 20x - 2y = 6?
ব্যাখ্যা
Question: What is the slope of a line perpendicular to the line whose equation is 20x - 2y = 6?
Solution:
সরল রেখার সাধারণ সমীকরণ,
y = mx + c ......(1) (এখানেm = ঢাল)
যদি কোনো রেখার ঢাল হয় m, তবে তার লম্ব (perpendicular) রেখার ঢাল হবে,
m' = - (1/m)
এখন,
20x - 2y = 6
2y = 20x - 6
y = 10x + (-3)
(1) নং এর সাথে তুলনা করে পাই,
m = 10
∴ লম্ব (perpendicular) রেখার ঢাল হবে, m' = - (1/10)
৬,৯১১.
Given the equations below, what is the value of mn? 2(m + n) + m = 9; 3m - 3n = 24
ব্যাখ্যা
দেয়া আছে
3m - 3n = 24
3(m - n) = 24
m - n = 8
m = 8 + n ....................(1)
2(m + n) + m = 9
2(8 + n + n) + 8 + n = 9
16 + 4n + 8 + n = 9
5n + 24 = 9
5n = 9 - 24
5n = - 15
n = - 3
(1) নং সমীকরণ হতে পাই
m = 8 + n
m = 8 - 3 = 5
mn = 5(- 3) = - 15
3m - 3n = 24
3(m - n) = 24
m - n = 8
m = 8 + n ....................(1)
2(m + n) + m = 9
2(8 + n + n) + 8 + n = 9
16 + 4n + 8 + n = 9
5n + 24 = 9
5n = 9 - 24
5n = - 15
n = - 3
(1) নং সমীকরণ হতে পাই
m = 8 + n
m = 8 - 3 = 5
mn = 5(- 3) = - 15
৬,৯১২.
A wheel of a car of radius 35 cm is rotating at 500 RPM. What is the speed of the car in km/hr?
ব্যাখ্যা
Question: A wheel of a car of radius 35 cm is rotating at 500 RPM. What is the speed of the car in km/hr?
Solution:
The radius of the wheel measures 35 cm.
In one rotation, the wheel will cover a distance which is equal to the circumference of the wheel.
∴ in one rotation this wheel will cover 2 × π × 35 = 2 × (22/7) × 35 = 220 cm.
In a minute, the distance covered by the wheel = circumference of the wheel × rpm
∴ this wheel will cover a distance of 220 × 500 = 110000 cm in a minute.
In an hour, the wheel will cover a distance of 110000 × 60 = 6600000 cm.
Therefore, the speed of the car = 6600000 cm/hr = 66 km/hr
Solution:
The radius of the wheel measures 35 cm.
In one rotation, the wheel will cover a distance which is equal to the circumference of the wheel.
∴ in one rotation this wheel will cover 2 × π × 35 = 2 × (22/7) × 35 = 220 cm.
In a minute, the distance covered by the wheel = circumference of the wheel × rpm
∴ this wheel will cover a distance of 220 × 500 = 110000 cm in a minute.
In an hour, the wheel will cover a distance of 110000 × 60 = 6600000 cm.
Therefore, the speed of the car = 6600000 cm/hr = 66 km/hr
৬,৯১৩.
The price of rice has fallen by 20%. How much rice can be bought now with the money that was sufficient to buy 10 kg of rice previously?
ব্যাখ্যা
Question: The price of rice has fallen by 20%. How much rice can be bought now with the money that was sufficient to buy 10 kg of rice previously?
Solution:
Let 100Tk is spend on rice initially for 10kg
after 20% fall, the price is needed now is = 100 - (20% of 100)
= 100 - 20
= 80Tk
new price of rice per kg is = 80/10 = 8Tk
at 8Tk per kg, rice can be bought in 100Tk is = 100/8 = 12.5kg
Solution:
Let 100Tk is spend on rice initially for 10kg
after 20% fall, the price is needed now is = 100 - (20% of 100)
= 100 - 20
= 80Tk
new price of rice per kg is = 80/10 = 8Tk
at 8Tk per kg, rice can be bought in 100Tk is = 100/8 = 12.5kg
৬,৯১৪.
One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:
ব্যাখ্যা
Question: One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:
Solution:
Let the slower pipe alone fill the tank in x minutes.
Then, the faster pipe will fill it in x/3 minutes.
∴ (1/x) + (3/x) = 1/36
⇒ 4/x = 1/36
⇒ x = 144 minutes
∴ x = 2 hours 24 minutes
Solution:
Let the slower pipe alone fill the tank in x minutes.
Then, the faster pipe will fill it in x/3 minutes.
∴ (1/x) + (3/x) = 1/36
⇒ 4/x = 1/36
⇒ x = 144 minutes
∴ x = 2 hours 24 minutes
৬,৯১৫.
If the diameter of a circle is 4π, then what is the ratio between radius and Circumference of circle-
ব্যাখ্যা
Question: If the diameter of a circle is 4π, then what is the ratio between radius and Circumference of circle-
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
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
৬,৯১৬.
A train takes 15 seconds to pass a stationary point and covers 20 km in 25 minutes. Find the length of the train.
ব্যাখ্যা
Question: A train takes 15 seconds to pass a stationary point and covers 20 km in 25 minutes. Find the length of the train.
Solution:
Speed = 20km/25min
= (20 × 1000)m/(25 × 60)sec
= (40/3)m/s
∴ Length = Speed × Time to pass point
= (40/3) × 15
= 200 meters
Solution:
Speed = 20km/25min
= (20 × 1000)m/(25 × 60)sec
= (40/3)m/s
∴ Length = Speed × Time to pass point
= (40/3) × 15
= 200 meters
৬,৯১৭.
A container filled liquid containing 4 parts of water and 6 parts of milk. How much of the mixture must be drawn off and filled with water so that the mixture contains half and half water?
ব্যাখ্যা
Question: A container filled liquid containing 4 parts of water and 6 parts of milk. How much of the mixture must be drawn off and filled with water so that the mixture contains half and half water?
Solution:
Let water = 40 liters
and milk is 60 liters.
Let, x amount taken out from the mixture.
Water = 40 - x × (2/5) + x
and milk = 60 - x × (3/5)
ATQ,
Equate both the equation, we get x = 50/3
Now, mixture drawn ff = (50/3) / 100 = 1/6
Solution:
Let water = 40 liters
and milk is 60 liters.
Let, x amount taken out from the mixture.
Water = 40 - x × (2/5) + x
and milk = 60 - x × (3/5)
ATQ,
Equate both the equation, we get x = 50/3
Now, mixture drawn ff = (50/3) / 100 = 1/6
৬,৯১৮.
After being dropped a certain ball always bounces back to 2/5 of the height of its previous bounce. After the first bounce it reaches a height of 125 inches. How high (in inches) will it reach after its fourth bounce?
ব্যাখ্যা
প্রশ্ন: After being dropped a certain ball always bounces back to 2/5 of the height of its previous bounce. After the first bounce it reaches a height of 125 inches. How high (in inches) will it reach after its fourth bounce?
সমাধান:
প্রতি ড্রপে বলটি পূর্ববর্তী উচ্চতার ২/৫ অংশ উঠে।
১ম ড্রপে বলটি উঠে ১২৫ ইঞ্চি
২য় ড্রপে বলটি উঠে {১২৫ × (২/৫)} ইঞ্চি
= ৫০ ইঞ্চি
৩য় ড্রপে বলটি উঠে {৫০ × (২/৫)} ইঞ্চি
= ২০ ইঞ্চি
৪র্থ ড্রপে বলটি উঠে { ২০ × (২/৫)} ইঞ্চি
= ৮ ইঞ্চি
সমাধান:
প্রতি ড্রপে বলটি পূর্ববর্তী উচ্চতার ২/৫ অংশ উঠে।
১ম ড্রপে বলটি উঠে ১২৫ ইঞ্চি
২য় ড্রপে বলটি উঠে {১২৫ × (২/৫)} ইঞ্চি
= ৫০ ইঞ্চি
৩য় ড্রপে বলটি উঠে {৫০ × (২/৫)} ইঞ্চি
= ২০ ইঞ্চি
৪র্থ ড্রপে বলটি উঠে { ২০ × (২/৫)} ইঞ্চি
= ৮ ইঞ্চি
৬,৯১৯.
The area of a rhombus is 198 sq.cm and the length of one of the diagonals is 22 cm. The length of other diagonal is-
ব্যাখ্যা
Question: The area of a rhombus is 198 sq.cm and the length of one of the diagonals is 22 cm. The length of other diagonal is-
Solution:
⇒ We have given area of rhombus = 96cm2 and d1=22cm.
⇒ Area of rhombus = (1/2) × d1×d2
⇒ 198 = (1/2) × 22 × d2.
⇒ 11 × d2 = 198
∴ d2 = 18 cm
Solution:
⇒ We have given area of rhombus = 96cm2 and d1=22cm.
⇒ Area of rhombus = (1/2) × d1×d2
⇒ 198 = (1/2) × 22 × d2.
⇒ 11 × d2 = 198
∴ d2 = 18 cm
৬,৯২০.
5 years ago the ratio of father's age to son's age was 5:1 and 2 years later father's age will be 3 times his son's age. What is the ratio of their present age?
ব্যাখ্যা
মনেকরি,
5 বছর পূর্বে পিতার বয়স = 5x বছর
এবং পুত্রের বয়স =x বছর
∴ বর্তমানে পিতার বয়স = (5x+5) বছর
এবং পুত্রের বয়স = (x + 5) বছর
প্রশ্নমতে, 5x + 5 + 2 = 3 (x + 5 + 2)
⇒ 5x + 7 = 3(x + 7)
⇒ 5x + 7 = 3x + 21
⇒ 2x = 14
⇒ x=7
∴ বর্তমানে পিতার বয়স 5×7+5 = 40 বছর
বর্তমানে পুত্রের বয়স = 7 + 5 = 12 বছর
∴ পিতা ও পুত্র = 40 : 12 =10 : 3
৬,৯২১.
Rene earns Tk. 85 per hour on days other than Sundays and twice that rate on Sundays. Last week she worked a total of 40 hours, including 8 hours on Sunday. What were her earnings for the week?
ব্যাখ্যা
Question: Rene earns Tk. 85 per hour on days other than Sundays and twice that rate on Sundays. Last week she worked a total of 40 hours, including 8 hours on Sunday. What were her earnings for the week?
Solution:
During the week Rene worked a total of 40 - 8 = 32 hours at a rate of Tk. 85 per hour.
On Sunday she worked 8 hours at a rate of Tk. 85 × 2 = Tk. 170 per hour.
Therefore her total earnings for the week were 32 × 85 + 8 × 170 = Tk. 4080
Solution:
During the week Rene worked a total of 40 - 8 = 32 hours at a rate of Tk. 85 per hour.
On Sunday she worked 8 hours at a rate of Tk. 85 × 2 = Tk. 170 per hour.
Therefore her total earnings for the week were 32 × 85 + 8 × 170 = Tk. 4080
৬,৯২২.
The ratio of speed of a motor-boat to that of the current of water is 5 : 1. The boat goes along with the current in 3 hours. It will come back in-
ব্যাখ্যা
Question: The ratio of speed of a motor-boat to that of the current of water is 5 : 1. The boat goes along with the current in 3 hours. It will come back in-
Solution:
Since the ratio 5 : 1 is given.
Let the speed of boat in still water = 5 km/hr and speed of stream = 1 km/hr
Now,
Downstream speed = 5 + 1 = 6 km/hr
Upstream speed = 5 - 1 = 4 km/hr
∴ Distance = Downstream speed × downstream time = 6 × 3 = 18km
∴ Upstream time = Distance/upstream speed = 18/4 = 4.5 hours
Solution:
Since the ratio 5 : 1 is given.
Let the speed of boat in still water = 5 km/hr and speed of stream = 1 km/hr
Now,
Downstream speed = 5 + 1 = 6 km/hr
Upstream speed = 5 - 1 = 4 km/hr
∴ Distance = Downstream speed × downstream time = 6 × 3 = 18km
∴ Upstream time = Distance/upstream speed = 18/4 = 4.5 hours
৬,৯২৩.
What is the 4th term of the sequence: sin(nπ/6)
ব্যাখ্যা
Question: What is the 4th term of the sequence: sin(nπ/6)
Solution:
এখানে,
sin(nπ/6) এর চতুর্থ পদ = {sin(4 × π)/6}
= {sin(4 × 180°)/6}
= sin120°
= sin(90° + 30°)
= cos30°
= √3/2
Solution:
এখানে,
sin(nπ/6) এর চতুর্থ পদ = {sin(4 × π)/6}
= {sin(4 × 180°)/6}
= sin120°
= sin(90° + 30°)
= cos30°
= √3/2
৬,৯২৪.
A sum of money lent out at simple interest amounts to Tk. 720 after 2 years and Tk. 1020 after a further period of 5 years. Find the principal?
ব্যাখ্যা
Question: A sum of money lent out at simple interest amounts to Tk. 720 after 2 years and Tk. 1020 after a further period of 5 years. Find the principal?
Solution:
According to the question,
Principal + Simple interest for 2 years = Tk. 720 ------------- (1)
Principal + Simple interest for 7 years = Tk. 1020 ------------ (2)
Subtracting equation (1) from (2)
Principal + Simple interest for 7 years = Tk. 1020
Principal + Simple interest for 2 years = Tk. 720
--------------------------------------------------------
∴ Simple interest for 5 years = Tk. 300
⇒ Simple interest for 1 years = Tk. 300/5
⇒ Simple interest for 1 year = Tk. 60
⇒ Simple interest for 2 years = Tk. (60 × 2)
∴ Simple interest for 2 years = = Tk. 120
∴ Principal amount = (Amount after 2 years - 2 years Simple interest)
⇒ Principal amount = Tk. (720 - 120)
∴ Principal amount = Tk. 600
Solution:
According to the question,
Principal + Simple interest for 2 years = Tk. 720 ------------- (1)
Principal + Simple interest for 7 years = Tk. 1020 ------------ (2)
Subtracting equation (1) from (2)
Principal + Simple interest for 7 years = Tk. 1020
Principal + Simple interest for 2 years = Tk. 720
--------------------------------------------------------
∴ Simple interest for 5 years = Tk. 300
⇒ Simple interest for 1 years = Tk. 300/5
⇒ Simple interest for 1 year = Tk. 60
⇒ Simple interest for 2 years = Tk. (60 × 2)
∴ Simple interest for 2 years = = Tk. 120
∴ Principal amount = (Amount after 2 years - 2 years Simple interest)
⇒ Principal amount = Tk. (720 - 120)
∴ Principal amount = Tk. 600
৬,৯২৫.
Which year is not a leap year?
ব্যাখ্যা
Question: Which year is not a leap year?
Solution:
A leap year is divisible by 4.
Here,
1996 ÷ 4 = 499, divisible by 4 , so leap year.
1994 ÷ 4 = 498.5, not divisible by 4 , not a leap year.
2000 ÷ 4 = 500, divisible by 4 , so leap year.
2004 ÷ 4 = 501, divisible by 4, so leap year.
1988 ÷ 4 = 497, divisible by 4, so leap year.
৬,৯২৬.
A rhombus is a quadrilateral -
ব্যাখ্যা
Question: A rhombus is a quadrilateral -
Solution:
রম্বস
- যে চতুর্ভুজের চারটি বাহু সমান ও সমান্তরাল কিন্তু কর্ণ দুইটি অসমান তথা কোণগুলো সমকোণ নয় তাকে রম্বস বলে।
- সামান্তরিকের সন্নিহিত বাহুদ্বয় সমান হলে তখন তা রম্বস হয়ে
- রম্বসের কর্ণদ্বয় পরস্পরকে সমকোণে সমদ্বিখণ্ডিত করে।
- রম্বসের বিপরীত কোণগুলো পরস্পর সমান।
- রম্বসের কর্ণদ্বয়ের অন্তর্ভুক্ত কোণ 90°
৬,৯২৭.
After selling a saree for Tk. 3360 a shopkeeper suffers a loss of 16%. If he wants to earn 15% profit after giving the discount of 8%, what will be the marked price of the saree?
ব্যাখ্যা
Question: After selling a saree for Tk. 3360 a shopkeeper suffers a loss of 16%. If he wants to earn 15% profit after giving the discount of 8%, what will be the marked price of the saree?
Solution:
After selling a saree for Tk. 3360 a shopkeeper suffers a loss of 16%.
Selling price Tk. 84 when Cost price = Tk. 100
∴ Selling price Tk. 3360 when Cost price = Tk. (100 × 3360)/84
= Tk. 4000
15% profit,
Cost price Tk. 100 then Selling price = Tk. 115
∴ Cost price Tk. 4000 then Selling price = Tk. (115 × 4000)/100
= Tk. 4600
discount 8%,
Selling price Tk. 92 When Marked price = Tk. 100
∴ Selling price Tk. 4600 When Marked price = Tk. (100 × 4600)/92
= Tk. 5000
Solution:
After selling a saree for Tk. 3360 a shopkeeper suffers a loss of 16%.
Selling price Tk. 84 when Cost price = Tk. 100
∴ Selling price Tk. 3360 when Cost price = Tk. (100 × 3360)/84
= Tk. 4000
15% profit,
Cost price Tk. 100 then Selling price = Tk. 115
∴ Cost price Tk. 4000 then Selling price = Tk. (115 × 4000)/100
= Tk. 4600
discount 8%,
Selling price Tk. 92 When Marked price = Tk. 100
∴ Selling price Tk. 4600 When Marked price = Tk. (100 × 4600)/92
= Tk. 5000
৬,৯২৮.
If two times X is equal to three times of Y and also equal to four times of Z, then X : Y : Z is -
ব্যাখ্যা
Question: If two times X is equal to three times of Y and also equal to four times of Z, then X : Y : Z is -
Solution:
2X = 3Y
Or, Y = 2X/3
and 2X = 4Z
Or, Z = X/2
Hence, X : Y : Z = X : 2X/3 : X/2
= 1 : 2/3 : 1/2
= 6 : 4 : 3
Solution:
2X = 3Y
Or, Y = 2X/3
and 2X = 4Z
Or, Z = X/2
Hence, X : Y : Z = X : 2X/3 : X/2
= 1 : 2/3 : 1/2
= 6 : 4 : 3
৬,৯২৯.
A farmer travelled a distance of 61 km in 9 hours. He travelled partly on foot 4 km/hr and partly on bicycle at 9 km/hr. The distance travelled on foot is:
ব্যাখ্যা
Question: A farmer travelled a distance of 61 km in 9 hours. He travelled partly on foot 4 km/hr and partly on bicycle at 9 km/hr. The distance travelled on foot is:
Solution:
Let the distance travelled on foot be x km
Then,
distance travelled on bicycle = (61 - x) km
So,
x/4 + (61 - x)/9 = 9
⇒ 9x + 4(61 - x) = 9
⇒ 9x + 244 - 4x = 9 × 36
⇒ 5x = 324 - 244
⇒ 5x = 80
⇒ x = 80/5
∴ x = 16 km.
∴ The distance travelled on foot is 16 km.
Solution:
Let the distance travelled on foot be x km
Then,
distance travelled on bicycle = (61 - x) km
So,
x/4 + (61 - x)/9 = 9
⇒ 9x + 4(61 - x) = 9
⇒ 9x + 244 - 4x = 9 × 36
⇒ 5x = 324 - 244
⇒ 5x = 80
⇒ x = 80/5
∴ x = 16 km.
∴ The distance travelled on foot is 16 km.
৬,৯৩০.
If sinθ = 5/13 , then secθ = ?
ব্যাখ্যা
Question: If sinθ = 5/13 , then secθ = ?
Solution:
এখানে,
sinθ = 5/13
∴ লম্ব = 5, অতিভুজ = 13
∴ ভূমি = √(132 - 52) = 12
∴ secθ = অতিভূজ/ভূমি
= 13/12
৬,৯৩১.
a + b = √7, a - b = √5. Find the value of 17ab(a2 + b2) = ?
ব্যাখ্যা
Question: a + b = √7, a - b = √5. Find the value of 17ab(a2 + b2) = ?
Solution:
Given,
a + b = √7
a - b = √5
ATQ,
17ab(a2 + b2)
= (17/8) × 8ab(a2 + b2)
= (17/8) × 4ab × 2(a2 + b2)
= (17/8) × {(a + b)2- (a - b)2)} {(a + b)2+(a - b)2)}
= (17/8) × {(√7)2- (√5)2)} {(√7)2+(√5)2)}
= (17/8) × (7 - 5) × (7 + 5)
= (17/8) × 2 × 12
= (17/8) × 24
= 17 × 3
= 51
৬,৯৩২.
A tank is 30% full with water. If 18 liters of water is added the tank becomes 3/4 full. What is the capacity of the tank?
ব্যাখ্যা
Question: A tank is 30% full with water. If 18 liters of water is added the tank becomes 3/4 full. What is the capacity of the tank?
Solution:
Let, Capacity of the tank is x Liters.
ATQ,
30% of x + 18 = (3/4) × x
⇒ (30x/100) + 18 = 3x/4
⇒ (3x/10) + 18 = 3x/4
⇒ (3x/4) - (3x/10) = 18
⇒ (15x - 6x)/20 = 18
⇒ 9x = 18 × 20
⇒ 9x = 360
∴ x = 40
∴ The capacity of tank is 40 Liters.
Solution:
Let, Capacity of the tank is x Liters.
ATQ,
30% of x + 18 = (3/4) × x
⇒ (30x/100) + 18 = 3x/4
⇒ (3x/10) + 18 = 3x/4
⇒ (3x/4) - (3x/10) = 18
⇒ (15x - 6x)/20 = 18
⇒ 9x = 18 × 20
⇒ 9x = 360
∴ x = 40
∴ The capacity of tank is 40 Liters.
৬,৯৩৩.
Rana earns 30% more than Mina. Tina earns 60% more than Mina. How much % is the wages earned by Tina more than that earned by Rana?
ব্যাখ্যা
Question: Rana earns 30% more than Mina. Tina earns 60% more than Mina. How much % is the wages earned by Tina more than that earned by Rana?
Solution:
Let's assume Mina's wage is 100 tk.
Rana's wage = 100 + (30% of 100) =130 tk
Tina's wage = 100 + (60% of 100) = 160 tk
Percentage difference = (Difference in wages/Rana's wage) × 100
= {(Tina's wage - Rana's wage)/Rana's wage} × 100
= {(160 - 130)/130} × 100
= 23.08%
Therefore, the wages earned by Tina is 23.08% more than the wages earned by Rana.
Solution:
Let's assume Mina's wage is 100 tk.
Rana's wage = 100 + (30% of 100) =130 tk
Tina's wage = 100 + (60% of 100) = 160 tk
Percentage difference = (Difference in wages/Rana's wage) × 100
= {(Tina's wage - Rana's wage)/Rana's wage} × 100
= {(160 - 130)/130} × 100
= 23.08%
Therefore, the wages earned by Tina is 23.08% more than the wages earned by Rana.
৬,৯৩৪.
2, 4, 12, 48, 240, (....)
ব্যাখ্যা
Go on multiplying the given numbers by 2, 3, 4, 5, 6. So, the correct next number is 1440.
৬,৯৩৫.
The next term of the series: 25, 49, 81, ____ is
ব্যাখ্যা
Question: The next term of the series: 25, 49, 81, ____ is
Solution:
Given: 25, 49, 81, ____
The series is: 52, 72, 92, 112
So, the next term is 112 = 121
৬,৯৩৬.
10, 4, 16, 26; what is the median of the numbers shown?
ব্যাখ্যা
Question: 10, 4, 16, 26; what is the median of the numbers shown?
Solution:
সংখ্যাগুলোকে উর্ধ্বক্রমে সাজিয়ে পাই, 4, 10, 16, 26
∴ মধ্যক = (10 + 16)/2
= 26/2
= 13
Solution:
সংখ্যাগুলোকে উর্ধ্বক্রমে সাজিয়ে পাই, 4, 10, 16, 26
∴ মধ্যক = (10 + 16)/2
= 26/2
= 13
৬,৯৩৭.
একটি পার্টিতে মহিলা ও পুরুষের অনুপাত ৩ : ২। যদি আরও ২০ জন পুরুষ পার্টিতে যোগ দেয় তাহলে অনুপাতটি উল্টে যাবে। পার্টিতে কতজন মহিলা ছিল?
ব্যাখ্যা
প্রশ্ন: একটি পার্টিতে মহিলা ও পুরুষের অনুপাত ৩ : ২। যদি আরও ২০ জন পুরুষ পার্টিতে যোগ দেয় তাহলে অনুপাতটি উল্টে যাবে। পার্টিতে কতজন মহিলা ছিল?
সমাধান:
ধরি,
পার্টিতে মহিলা ও পুরুষের সংখ্যা যথাক্রমে ৩ক এবং ২ক।
প্রশ্নমতে,
৩ক/(২ক + ২০) = ২/৩
⇒ ৯ক = ৪ক + ৪০
⇒ ৫ক = ৪০
∴ ক = ৮
অতএব, মহিলার সংখ্যা ছিল = (৩ × ৮) = ২৪ জন
সমাধান:
ধরি,
পার্টিতে মহিলা ও পুরুষের সংখ্যা যথাক্রমে ৩ক এবং ২ক।
প্রশ্নমতে,
৩ক/(২ক + ২০) = ২/৩
⇒ ৯ক = ৪ক + ৪০
⇒ ৫ক = ৪০
∴ ক = ৮
অতএব, মহিলার সংখ্যা ছিল = (৩ × ৮) = ২৪ জন
৬,৯৩৮.
A car dealership has 40 cars on the lot, 30% of which are silver. If the dealership receives a new shipment of 80 cars, 40% of which are not silver, what percent of the total number of cars are silver?
ব্যাখ্যা
Question: A car dealership has 40 cars on the lot, 30% of which are silver. If the dealership receives a new shipment of 80 cars, 40% of which are not silver, what percent of the total number of cars are silver?
Solution:
old silver car = 30% of 40 = 12
new silver car = (100 - 40)% of 80
= 60% of 80
= 48
% silver car = {(12 + 48)/ (40 + 80)} × 100%
=(60/120)× 100%
= 1/2 × 100%
= 50%
Solution:
old silver car = 30% of 40 = 12
new silver car = (100 - 40)% of 80
= 60% of 80
= 48
% silver car = {(12 + 48)/ (40 + 80)} × 100%
=(60/120)× 100%
= 1/2 × 100%
= 50%
৬,৯৩৯.
One-third of Anas' investment in National Savings Certificate is equal to one-half of his investment in FDR. If he has Tk. 150000 as total investment. how much he invested in FDR?
ব্যাখ্যা
Question: One-third of Anas' investment in National Savings Certificate is equal to one-half of his investment in FDR. If he has Tk. 150000 as total investment. how much he invested in FDR?
Solution:
Let,
Investment in National Savings Certificate be Tk. x
Investment in FDR be Tk.(150000 - x)
ATQ,
x/3 = (1/2)(150000 - x)
⇒ x/3 = 75000 - x/2
⇒ (x/3) + (x/2) = 75000
⇒ (2x + 3x)/6= 75000
⇒ 5x/6 = 75000
⇒ x = (75000 × 6)/5
∴ x = 90000
∴ Investment in FDR is Tk.(150000 - 90000) = Tk. 60000
Solution:
Let,
Investment in National Savings Certificate be Tk. x
Investment in FDR be Tk.(150000 - x)
ATQ,
x/3 = (1/2)(150000 - x)
⇒ x/3 = 75000 - x/2
⇒ (x/3) + (x/2) = 75000
⇒ (2x + 3x)/6= 75000
⇒ 5x/6 = 75000
⇒ x = (75000 × 6)/5
∴ x = 90000
∴ Investment in FDR is Tk.(150000 - 90000) = Tk. 60000
৬,৯৪০.
Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill the cistern. How much time will be taken by A to fill the cistern separately?
ব্যাখ্যা
Let the cistern be filled by pipe A alone in x hours.
Then, pipe B will fill it in (x + 6) hours
∴ 1/ x + 1/ x+6 = 1/ 4
⇒ x+6+x/ x(x+6) = 1/ 4
⇒ x² − 2x−24 = 0
⇒ (x−6)(x+4) = 0
⇒ x = 6 [neglecting the negative value of x].
৬,৯৪১.
দুইটি ট্রেন দুটি স্টেশন থেকে একসাথে যাত্রা শুরু করে পরস্পরের দিকে রওনা দেয়। স্টেশন দুটি ২০০ কিমি দূরে অবস্থিত। তারা একে অপরকে একটি স্টেশন থেকে ১১০ কিমি দূরত্বে অতিক্রম করে। ট্রেন দুইটির গতিবেগের অনুপাত কত?
ব্যাখ্যা
প্রশ্ন: দুইটি ট্রেন দুটি স্টেশন থেকে একসাথে যাত্রা শুরু করে পরস্পরের দিকে রওনা দেয়। স্টেশন দুটি ২০০ কিমি দূরে অবস্থিত। তারা একে অপরকে একটি স্টেশন থেকে ১১০ কিমি দূরত্বে অতিক্রম করে। ট্রেন দুইটির গতিবেগের অনুপাত কত?
সমাধান:
ধরি,
প্রথম ট্রেনের গতিবেগ = ক কিমি/ঘণ্টা
দ্বিতীয় ট্রেনের গতিবেগ = খ কিমি/ঘণ্টা
প্রথম ট্রেন অতিক্রম করে = ১১০ কিমি
দ্বিতীয় ট্রেন অতিক্রম করে = ২০০ - ১১০ = ৯০ কিমি
যেহেতু উভয় ট্রেন একসাথে শুরু করে এবং একই সময়ে একে অপরকে অতিক্রম করে, অতএব তাদের সময় সমান।
সময় = দূরত্ব/গতি
তাহলে,
১১০/ক = ৯০/খ
⇒ ক/খ = ১১০/৯০
⇒ ক : খ = ১১০ : ৯০
⇒ ক : খ = ১১ : ৯
∴ ট্রেন দুইটির গতির অনুপাত ১১ : ৯
৬,৯৪২.
A line of length 1.5 metres was measured as 1.55 metres by mistake. What will be the value of the error percent?
ব্যাখ্যা
Question: A line of length 1.5 metres was measured as 1.55 metres by mistake. What will be the value of the error percent?
Solution:
Percentage error = 1.55 - 1.50 = 0.05
∴ Percentage error % = (0.05/1.50) × 100
= (5/150) × 100
= 10/3
= 3.33%
Solution:
Percentage error = 1.55 - 1.50 = 0.05
∴ Percentage error % = (0.05/1.50) × 100
= (5/150) × 100
= 10/3
= 3.33%
৬,৯৪৩.
In a certain zoo, the ratio of tigers to lions to snakes in stock is 3 : 5 : 7. If there are 48 lions and snakes total in stock, how many tigers are there?
ব্যাখ্যা
Question: In a certain zoo, the ratio of tigers to lions to snakes in stock is 3 : 5 : 7. If there are 48 lions and snakes total in stock, how many tigers are there?
Solution:
5x + 7x = 48
⇒ 12x = 48
⇒ x = 48/12 = 4
number of tigers = 3x
= 3 × 4
= 12
Solution:
5x + 7x = 48
⇒ 12x = 48
⇒ x = 48/12 = 4
number of tigers = 3x
= 3 × 4
= 12
৬,৯৪৪.
The ratio between Karim's age and Rahim's age is 10 : 11. What is the age of Rahim in percentage of Karim's age ?
ব্যাখ্যা
Question: The ratio between Karim's age and Rahim's age is 10 : 11. What is the age of Rahim in percentage of Karim's age ?
Solution:
Given that,
The ratio of Karim's age to Rahim's age = 10 : 11
Let, Karim's age = 10x
and Rahim's age = 11x
Now, we find Rahim's age as a percentage of Karim's age,
∴ Percentage = (Rahim’s age/Karim’s age) × 100
= (11x/10x) × 100
= 110
So, Rahim's age is 110% of Karim's age.
Solution:
Given that,
The ratio of Karim's age to Rahim's age = 10 : 11
Let, Karim's age = 10x
and Rahim's age = 11x
Now, we find Rahim's age as a percentage of Karim's age,
∴ Percentage = (Rahim’s age/Karim’s age) × 100
= (11x/10x) × 100
= 110
So, Rahim's age is 110% of Karim's age.
৬,৯৪৫.
The sample space of three coins tossed together is:
ব্যাখ্যা
Number of coins tossed = 3
∴ Sample space of three coins tossed = 23 = 8
∴ Sample space of three coins tossed = 23 = 8
৬,৯৪৬.
The side of an equilateral triangle is 2m. What is the area of the triangle?
ব্যাখ্যা
Question: The side of an equilateral triangle is 2m. What is the area of the triangle?
Solution:
Area = (√3/4)22
= (√3/4)× 4 m2
= √3 m2
Solution:
Area = (√3/4)22
= (√3/4)× 4 m2
= √3 m2
৬,৯৪৭.
150 liters of a mixture contains 20% water. What amount of additional water should be added such that the water content be raised to 25%?
ব্যাখ্যা
Question: 150 liters of a mixture contains 20% water. What amount of additional water should be added such that the water content be raised to 25%?
Solution:
water in the mixture = 20% of 150 = 30 liters
Let, x liters of water were added to the mixture to make water 25% of the new mixture.
ATQ,
30 + x = 25% of (150 + x)
⇒ 30 + x = (1/4) × (150 + x)
⇒ 120 + 4x = 150 + x
⇒ 3x = 30
⇒ x = 10
Solution:
water in the mixture = 20% of 150 = 30 liters
Let, x liters of water were added to the mixture to make water 25% of the new mixture.
ATQ,
30 + x = 25% of (150 + x)
⇒ 30 + x = (1/4) × (150 + x)
⇒ 120 + 4x = 150 + x
⇒ 3x = 30
⇒ x = 10
৬,৯৪৮.
100kg of solution A is mixed with 60kg of solution B. If solution A has tin and copper in the ratio 1 : 4 and solution B has lead and tin in the ratio 3 : 2, then what is the amount of tin in the new solution?
ব্যাখ্যা
Question: 100kg of solution A is mixed with 60kg of solution B. If solution A has tin and copper in the ratio 1 : 4 and solution B has lead and tin in the ratio 3 : 2, then what is the amount of tin in the new solution?
Solution:
A এর মিশ্রণে টিনের পরিমাণ = (100 এর 1/(1 + 4)} কেজি
= 20 কেজি
B এর মিশ্রণে টিনের পরিমাণ =(60 এর 2/(3 + 2)} কেজি
= 24 কেজি
A এবং B এর মিশ্রণে মোট টিনের পরিমাণ = (20 + 24)কেজি
= 44 কেজি
Solution:
A এর মিশ্রণে টিনের পরিমাণ = (100 এর 1/(1 + 4)} কেজি
= 20 কেজি
B এর মিশ্রণে টিনের পরিমাণ =(60 এর 2/(3 + 2)} কেজি
= 24 কেজি
A এবং B এর মিশ্রণে মোট টিনের পরিমাণ = (20 + 24)কেজি
= 44 কেজি
৬,৯৪৯.
A batsman scored 100 runs which include 6 boundaries and 6 sixes. What percent of his total score did he make by running between the wickets?
ব্যাখ্যা
Question: A batsman scored 100 runs which include 6 boundaries and 6 sixes. What percent of his total score did he make by running between the wickets?
Solution:
Total score of batsman = 100 runs
runs from boundaries = 6 × 4 = 24
runs from sixes =6 × 6 = 36
∴ Total runs from boundaries and sixes = 24 + 36
= 60 runs
Total runs by the batsman = 100 - 60 = 40 runs
percentage of his score made by running between wickets = (40/100) × 100 = 40%
Solution:
Total score of batsman = 100 runs
runs from boundaries = 6 × 4 = 24
runs from sixes =6 × 6 = 36
∴ Total runs from boundaries and sixes = 24 + 36
= 60 runs
Total runs by the batsman = 100 - 60 = 40 runs
percentage of his score made by running between wickets = (40/100) × 100 = 40%
৬,৯৫০.
If (x + 7)2 = 81, which of the following can be the value of (x - 5)?
ব্যাখ্যা
Question: If (x + 7)2 = 81, which of the following can be the value of (x - 5)?
Solution:
Given that,
(x + 7)2 = 81
⇒ x + 7 = ± √81
x + 7 = ± 9
So there are two possible solutions.
Case 1: (Positive value)
x + 7 = 9
⇒ x = 9 - 7
⇒ x = 2
Case 2: (Negative value)
⇒ x + 7 = - 9
⇒ x = - 9 - 7
∴ x = - 16
So x = 2, - 16
Now, x - 5 = 2 - 5 = - 3 ; [x = 2]
৬,৯৫১.
The difference between discount of 35% and two successive discount of 20% on a certain bill was 22, the amount of the bill is = ?
ব্যাখ্যা
Question: The difference between discount of 35% and two successive discount of 20% on a certain bill was 22, the amount of the bill is = ?
Solution:
st discount = 35%
Single equivalent discount of 20% each
= [20 + 20 - {(20 × 20)/100}]%
= 36%
Difference = 36% - 35%
= 1%
Let the amount of the bill Tk. x
∴ (1/100) × x = 22
⇒ x/100 = 22
∴ x = 2200
Solution:
st discount = 35%
Single equivalent discount of 20% each
= [20 + 20 - {(20 × 20)/100}]%
= 36%
Difference = 36% - 35%
= 1%
Let the amount of the bill Tk. x
∴ (1/100) × x = 22
⇒ x/100 = 22
∴ x = 2200
৬,৯৫২.
If the list price of a shirt is Tk. 800, and a Tk. 160 discount is offered on the shirt, then what is the discount percentage?
ব্যাখ্যা
Question: If the list price of a shirt is Tk. 800, and a Tk. 160 discount is offered on the shirt, then what is the discount percentage?
Solution:
Discount % = (Discount/marked Price) × 100
Marked Price = Tk. 800
Discount = Tk. 160
Discount (%) = (160/800) ×100%
= 20%
∴ Therefore, the discount percentage is calculated as 20%.
Solution:
Discount % = (Discount/marked Price) × 100
Marked Price = Tk. 800
Discount = Tk. 160
Discount (%) = (160/800) ×100%
= 20%
∴ Therefore, the discount percentage is calculated as 20%.
৬,৯৫৩.
If k is an integer and k = 462/n, then which of the following could be the value of n?
ব্যাখ্যা
Question: If k is an integer and k = 462/n, then which of the following could be the value of n?
Solution:
462/4 = 115.5, not an integer
462/5 = 92.4, not an integer
462/9 = 51.33, not an integer
462/22 = 21, which is an integer.
Solution:
462/4 = 115.5, not an integer
462/5 = 92.4, not an integer
462/9 = 51.33, not an integer
462/22 = 21, which is an integer.
৬,৯৫৪.
A car owner buys petrol at Tk.17, TK. 19 and TK. 20 per liter for three consecutive years. Compute the average cost per liter. If he spends Tk. 6460 per year.
ব্যাখ্যা
Question: A car owner buys petrol at Tk.17, TK. 19 and TK. 20 per liter for three consecutive years. Compute the average cost per liter. If he spends Tk. 6460 per year.
Solution:
Total quantity of petrol consumed in 3 years
= (6460/17 + 6460/19 + 6460/20) litres
= (380 + 340 + 323) litres
= 1043 litres
Total amount spent
= Tk. (3 × 6460)
= Tk. 19380
∴ Average cost
= Tk. (19380/1043)
= Tk. 18.58
Solution:
Total quantity of petrol consumed in 3 years
= (6460/17 + 6460/19 + 6460/20) litres
= (380 + 340 + 323) litres
= 1043 litres
Total amount spent
= Tk. (3 × 6460)
= Tk. 19380
∴ Average cost
= Tk. (19380/1043)
= Tk. 18.58
৬,৯৫৫.
If the daily wages of a man is double to that of a woman, how many men should work for 25 days to earn Rs.14400? Given that wages for 40 women for 30 days are Rs.21600.
ব্যাখ্যা
Wages of 1 woman for 1 day = 21600/(40 × 30)
Wages of 1 man for 1 day = (21600 × 2)/(40 × 30)
Wages of 1 man for 25 days = (21600 × 2 × 25)/(40 × 30)
Number of men = 14400/{(21600 × 2 × 25)/(40 × 30)}
= 144/{(216 × 50)/(40 × 30)}
= 144/9
= 16.
৬,৯৫৬.
Anis's and Bulbul's shares in a business are in the ratio of 5 : 3. If Anis has invested Tk. 70000 for 12 months, for what period Bulbul has invested Tk. 60000?
ব্যাখ্যা
Question: Anis's and Bulbul's shares in a business are in the ratio of 5 : 3. If Anis has invested Tk. 70000 for 12 months, for what period Bulbul has invested Tk. 60000?
Solution:
Let,
Bulbul has invested for x months
Anis : Bulbul = (70000 × 12) : (60000 × x) = 5 : 3
⇒ 84 : 6x = 5 : 3
⇒ 14 : x = 5 : 3
⇒ 14/x = 5/3
⇒ 5x = 42
⇒ x = 42/5
∴ x = 8.4
Solution:
Let,
Bulbul has invested for x months
Anis : Bulbul = (70000 × 12) : (60000 × x) = 5 : 3
⇒ 84 : 6x = 5 : 3
⇒ 14 : x = 5 : 3
⇒ 14/x = 5/3
⇒ 5x = 42
⇒ x = 42/5
∴ x = 8.4
৬,৯৫৭.
What percent of 1/2 is 12/16?
ব্যাখ্যা
Question: What percent of 1/2 is 12/16?
Solution:
Percentage = (3/4)/(1/2) × 100
= (3/4) × (2/1) × 100
= (3/2) × 100
= 150%
Therefore, 12/16 is 150% of 1/2.
৬,৯৫৮.
x + y = x - y হলে, y এর মান নিচের কোনটি?
ব্যাখ্যা
প্রশ্ন: x + y = x - y হলে, y এর মান নিচের কোনটি?
সমাধান:
দেওয়া আছে,
x + y = x - y
⇒ y = - y
⇒ y + y = 0
⇒ 2y = 0
∴ y = 0
৬,৯৫৯.
A ball and a bat costs 110 taka. The bat costs 100 taka more than the ball. How much does the ball cost?
ব্যাখ্যা
প্রশ্ন: একটি ব্যাট ও বলের মূল্য একত্রে ১১০ টাকা। ব্যাটের দাম বলের থেকে ১০০ টাকা বেশি হলে, বলের দাম কত?
সমাধান:
ধরি,
বলের দাম = p টাকা
∴ ব্যাটের দাম = p + 100
প্রশ্নমতে,
p + p + 100 = 110
2p = 10
p = 5
∴ বলের দাম = 5 টাকা
সমাধান:
ধরি,
বলের দাম = p টাকা
∴ ব্যাটের দাম = p + 100
প্রশ্নমতে,
p + p + 100 = 110
2p = 10
p = 5
∴ বলের দাম = 5 টাকা
৬,৯৬০.
The angle of elevation of the sun, when the height of a tower is √3 times the length of its shadow, is-
ব্যাখ্যা
Question: The angle of elevation of the sun, when the height of a tower is √3 times the length of its shadow, is-
Solution:
Let, ∠ACB = θ
Then, AB/AC = √3
⇒ tan θ = √3 = tan60°
∴ θ = 60°
৬,৯৬১.
Two pipes can fill a tank in 36 and 40 minutes respectively, and a waste pipe can empty 3.5 gallons per minutes. All three pipes working together can fill the tank in 30 minutes. The capacity of the tank is-
ব্যাখ্যা
Question: Two pipes can fill a tank in 36 and 40 minutes respectively, and a waste pipe can empty 3.5 gallons per minutes. All three pipes working together can fill the tank in 30 minutes. The capacity of the tank is-
Solution:
Work done by the waste pipe in 1 minute = (1/30) - [(1/36) + (1/40)]
= (12 - 10 - 9)/360
= - (7/360) [Negative sign means emptying]
∴Volume of (7/360) part = 3.5 gallons
Volume of whole tank = (360 × 3.5)/7 gallons
= 180 gallons
৬,৯৬২.
A 180 liter mixture of milk and water contains 20% water. How much milk, in liters must be added to the mixture will contain water and milk in the ratio of 1 : 7
ব্যাখ্যা
Question: A 180 liter mixture of milk and water contains 20% water. How much milk, in liters must be added to the mixture will contain water and milk in the ratio of 1 : 7?
Solution:
Water in the mixtue = 180 × (20/100) liter
= 36 liter
Milk in the mixture = 180 - 36 liter
= 144
Let,
X liter milk must be added
ATQ,
36/(144 + X) = 1/7
⇒ 144 + X = 252
⇒ X = 252 - 144
∴ X = 108 liter
Solution:
Water in the mixtue = 180 × (20/100) liter
= 36 liter
Milk in the mixture = 180 - 36 liter
= 144
Let,
X liter milk must be added
ATQ,
36/(144 + X) = 1/7
⇒ 144 + X = 252
⇒ X = 252 - 144
∴ X = 108 liter
৬,৯৬৩.
The sum and difference of the L.C.M and H.C.F of two numbers are 592 and 518 respectively. If the sum of the numbers be 296, find the product of the numbers.
ব্যাখ্যা
The sum and difference of the L.C.M and H.C.F of two numbers are 592 and 518 respectively. If the sum of the numbers be 296, find the product of the numbers.
সমাধান:
Given That,
LCM + HCF = 592 .................(1)
LCM - HCF = 518 .....................(2)
From (1) + (2), we get
2LCM = 1110
∴ LCM = 555
Now,
LCM + HCF = 592
⇒ HCF = 592 - LCM
⇒ HCF = 592 - 555
∴ HCF = 37
We know that,
Product of two numbers = LCM × HCF
= 555 × 37
= 20535
সমাধান:
Given That,
LCM + HCF = 592 .................(1)
LCM - HCF = 518 .....................(2)
From (1) + (2), we get
2LCM = 1110
∴ LCM = 555
Now,
LCM + HCF = 592
⇒ HCF = 592 - LCM
⇒ HCF = 592 - 555
∴ HCF = 37
We know that,
Product of two numbers = LCM × HCF
= 555 × 37
= 20535
৬,৯৬৪.
The diagonals of a rhombus are 72 cm and 30 cm respectively. What is its perimeter?
ব্যাখ্যা
In Rhombus
Let,
a = length of each side
b = base
h = height
d1,d2 are diagonals
Then Perimeter = 4a
= 2√(d12 + d22)
Perimeter = 2√(722 + 302)
= 156 cm.
৬,৯৬৫.
A boy rides his bicycle 10 km at an average speed of 12 km/hr and travel 12 km at an average speed of 10 km/hr. His average speed for the entire trip is approximately :
ব্যাখ্যা
Average speed= Total distance/Total time
Average speed= (10+12)/(10/12)+(12/10)
Average speed= 10.8 km/hr
৬,৯৬৬.
A shopkeeper takes 10% profit on his goods. He lost 20% of his goods during a theft. What is his loss percent?
ব্যাখ্যা
Question: A shopkeeper takes 10% profit on his goods. He lost 20% of his goods during a theft. What is his loss percent?
Solution:
20% of goods are lost in a theft
Loss = 100 - 88 = 12
Solution:
Let the number of goods be 100, and
C.P. of each item be Tk. 1
∴ Total C.P. = Tk. 100
Profit% on each item = 10%
20% of goods are lost in a theft
Number of goods left = 80
Now,
S.P. of 1 item = [(100 + 10)/100] × 1 = Tk. 1.10
S.P. of 1 item = [(100 + 10)/100] × 1 = Tk. 1.10
S.P. of 80 items = 80 × 1.10 = Tk. 88
Loss = 100 - 88 = 12
Loss% = (12/100) × 100% = 12%
Thus, the shopkeeper bears 12% loss.
৬,৯৬৭.
If One-third of one-fourth of a number is 15, then three-tenth of that number is:
ব্যাখ্যা
Question: If One-third of one-fourth of a number is 15, then three-tenth of that number is:
Solution:
Let,
the number is 'x'
then ,
(1/3) × (1/4) × x = 15
⇒ x/12 = 15
⇒ x = 180
Now,
(3/10) × x = (3/10) × 180 = 18 × 3 = 54.
∴ three-tenths of that number is 54.
Solution:
Let,
the number is 'x'
then ,
(1/3) × (1/4) × x = 15
⇒ x/12 = 15
⇒ x = 180
Now,
(3/10) × x = (3/10) × 180 = 18 × 3 = 54.
∴ three-tenths of that number is 54.
৬,৯৬৮.
A train 360 metre long runs with a speed of 45 km/hr. What time will it take to pass a platform 140 metre long?
ব্যাখ্যা
Speed = 45 km/hr = 45 × 5/18
= 25/2 m/s
Distance travelled = Length of the train + Length of the platform
= 360 + 140
= 500 metre.
Time taken to cross the platform = 500/(25/2)
= 40 seconds
= 25/2 m/s
Distance travelled = Length of the train + Length of the platform
= 360 + 140
= 500 metre.
Time taken to cross the platform = 500/(25/2)
= 40 seconds
৬,৯৬৯.
If nCr = 7 and nPr = 840, then r! =?
ব্যাখ্যা
Question: If nCr = 7 and nPr = 840, then r! =?
Solution:
We know,
r! × nCr = nPr
⇒ r! × 7 = 840
⇒ r! = 120
⇒ r! = 5 × 4 × 3 × 2 × 1
∴ r! = 5!
৬,৯৭০.
A rectangular floor that measures 8 meters by 10 meters is to be covered with carpet that each measure 2 meters by 2 meters. If the carpet cost Tk. 12 a piece, what is the total cost to cover the floor?
ব্যাখ্যা
Area of the floor = 8 × 10 = 80 m2
Area of each carpet = 2 × 2 = 4 m2
Required number of carpet = 80/4 = 20
one carpet costs Tk. 12
20 carpet costs Tk. 12 × 20 = Tk. 240
Area of each carpet = 2 × 2 = 4 m2
Required number of carpet = 80/4 = 20
one carpet costs Tk. 12
20 carpet costs Tk. 12 × 20 = Tk. 240
৬,৯৭১.
ব্যাখ্যা
Question:
Solution:
Solution:
৬,৯৭২.
A, B, and C invest 63000, 56000, and 84000 respectively to start a business. After one year, the profit is distributed in the ratio of their investments. If C's share of profit is Tk. 54000, find the total profit earned.
ব্যাখ্যা
Question: A, B, and C invest 63000, 56000, and 84000 respectively to start a business. After one year, the profit is distributed in the ratio of their investments. If C's share of profit is Tk. 54000, find the total profit earned.
Solution:
Let the total profit = x
The ratio of investment = 63000 : 56000 : 84000
= 63 : 56 : 84
= 9 : 8 : 12
Now, sum of the ratios = 29
C's share = (12/29) × x = 54000
⇒ x = (54000 × 29)/12
x = 130500
Hence, the total profit = 130500
Solution:
Let the total profit = x
The ratio of investment = 63000 : 56000 : 84000
= 63 : 56 : 84
= 9 : 8 : 12
Now, sum of the ratios = 29
C's share = (12/29) × x = 54000
⇒ x = (54000 × 29)/12
x = 130500
Hence, the total profit = 130500
৬,৯৭৩.
|3x - 15| = 18. What is the product of all possible values of x?
ব্যাখ্যা
Given,
|3x - 15| = 18
Solve the absolute value equation for both cases.
3x - 15 = 18
⇒ 3x = 15 + 18 = 33
∴ x = 11
or, 3x - 15 = - 18
⇒ 3x = - 18 + 15 = -3
∴ x = -1
The product of all possible values of x is = 11 × (-1) = -11
|3x - 15| = 18
Solve the absolute value equation for both cases.
3x - 15 = 18
⇒ 3x = 15 + 18 = 33
∴ x = 11
or, 3x - 15 = - 18
⇒ 3x = - 18 + 15 = -3
∴ x = -1
The product of all possible values of x is = 11 × (-1) = -11
৬,৯৭৪.
If each side of the square is increased by 20%, what will be the ratio between the new area and the original area of the square?
ব্যাখ্যা
Question: If each side of the square is increased by 20%, what will be the ratio between the new area and the original area of the square?
Solution:
Let,
The side of original square is x
∴ The area of original square is x2
The side of new square is x + 20% of x = x + (x/5) = 6x/5
∴ The area of new square is (36x2)/25
∴ The ratio between the new area and the original area of the square = (36x2)/25 : x2
= 36/25 : 1
= 36 : 25
Solution:
Let,
The side of original square is x
∴ The area of original square is x2
The side of new square is x + 20% of x = x + (x/5) = 6x/5
∴ The area of new square is (36x2)/25
∴ The ratio between the new area and the original area of the square = (36x2)/25 : x2
= 36/25 : 1
= 36 : 25
৬,৯৭৫.
A man can row at 5 kmph in still water. If the velocity of current is 1 km/hr and it takes him 1 hour to row to place and come back, how is the place?
ব্যাখ্যা
Speed downstream =(5 + 1)kmph=6kmph
Speed upstream =(5 - 1)kmph=4kmph
Let the required distance be x km.
x/6 + x/4 = 1
2x+ 3x = 12
5x = 12
x = 12/5
x = 2.4
Speed upstream =(5 - 1)kmph=4kmph
Let the required distance be x km.
x/6 + x/4 = 1
2x+ 3x = 12
5x = 12
x = 12/5
x = 2.4
৬,৯৭৬.
An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?
ব্যাখ্যা
Question: An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?
Solution:
Time between 8 o'clock to 2 o'clock = 6 hours
Hour hand rotate in 12 hours 360°
∴ Hour hand rotate in 6 hours (360° × 6)/12
= 180°
Solution:
Time between 8 o'clock to 2 o'clock = 6 hours
Hour hand rotate in 12 hours 360°
∴ Hour hand rotate in 6 hours (360° × 6)/12
= 180°
৬,৯৭৭.
A sum of money amounts to Tk. 5200 in 5 years and to Tk. 5680 in 7 years at simple interest. The rate of interest per annum is?
ব্যাখ্যা
Question: A sum of money amounts to Tk. 5200 in 5 years and to Tk. 5680 in 7 years at simple interest. The rate of interest per annum is?
Solution:
Simple interest for 2 years = (5680 - 5200) Tk.
= Tk. 480
∴ Simple Interest for 2 years = Tk. 480
∴ Simple Interest for 5 years = Tk. (480 × 5/2)
= Tk. 1200
∴ Principal = 5200 - 1200 = Tk. 4000.
We know,
I = Pnr
⇒ r = I/Pn
⇒ r = (1200 × 100)/(4000 × 5)
∴ r = 6%
Solution:
Simple interest for 2 years = (5680 - 5200) Tk.
= Tk. 480
∴ Simple Interest for 2 years = Tk. 480
∴ Simple Interest for 5 years = Tk. (480 × 5/2)
= Tk. 1200
∴ Principal = 5200 - 1200 = Tk. 4000.
We know,
I = Pnr
⇒ r = I/Pn
⇒ r = (1200 × 100)/(4000 × 5)
∴ r = 6%
৬,৯৭৮.
In the first 20 over's of a cricket game, the run rate was only 3.5. What should be the run rate in remaining 30 over's to reach the target of 289 runs?
ব্যাখ্যা
The run rate in remaining 30 over's to reach the target of 289 runs = {289 - (20×3.5)}/30 = 7.3
৬,৯৭৯.
What will come at the place of question mark?
7, 18, 51, 150, ?
7, 18, 51, 150, ?
ব্যাখ্যা
Question: What will come at the place of question mark? 7, 18, 51, 150, ?
Solution:
1st term: 7
2nd term: 18 = 7 × 3 - 3
3rd term: 51 = 18 × 3 - 3
4th term: 150 = 51 × 3 - 3
5th term: 447 = 150 × 3 - 3
৬,৯৮০.
The ratio of the ages of two boys is 5 : 6. After two years the ratio will be 7 : 8. The ratio of their age after 12 years will be = ?
ব্যাখ্যা
Question: The ratio of the ages of two boys is 5 : 6. After two years the ratio will be 7 : 8. The ratio of their age after 12 years will be = ?
Solution:
Ratio of ages of Boys A and B
Present age 5x : 6x
∴ After two years their ages are (5x + 2) and (6x + 2).
According to the question,
(5x + 2) : (6x + 2) = 7 : 8
⇒ 40x + 16 = 42x + 14
⇒ 2x = 2
∴ x = 1
∴ Present age A = 5 × 1 = 5
∴ Present age B = 6 × 1 = 6
After 12 years A = 5 + 12 = 17
After 12 years B = 6 + 12 = 18
∴ A/B = 17/18
Solution:
Ratio of ages of Boys A and B
Present age 5x : 6x
∴ After two years their ages are (5x + 2) and (6x + 2).
According to the question,
(5x + 2) : (6x + 2) = 7 : 8
⇒ 40x + 16 = 42x + 14
⇒ 2x = 2
∴ x = 1
∴ Present age A = 5 × 1 = 5
∴ Present age B = 6 × 1 = 6
After 12 years A = 5 + 12 = 17
After 12 years B = 6 + 12 = 18
∴ A/B = 17/18
৬,৯৮১.
Two numbers are 30% and 20% less than a third number respectively. The ratio of first two numbers is-
ব্যাখ্যা
Question: Two numbers are 30% and 20% less than a third number respectively. The ratio of first two numbers is-
Solution:
Given that,
Two numbers are 30% and 20% less than a third number respectively.
Solution:
Given that,
Two numbers are 30% and 20% less than a third number respectively.
Let the third number be 100.
Now,
First number = 100 - 30% of 100
= 100 - 30
∴ First number = 70
And
Second number = 100 - 20% of 100
= 100 - 20
∴ Second number = 80
∴ Ratio of the first two numbers = First number/Second number
= 70/80
= 7/8
∴ The ratio of the first two numbers is 7 : 8.
৬,৯৮২.
The angles of elevation of the top of a tower from the top and bottom of a tree of height 15 m are 30° and 60° respectively. Find the height of the tower?
ব্যাখ্যা
Question: The angles of elevation of the top of a tower from the top and bottom of a tree of height 15 m are 30° and 60° respectively. Find the height of the tower?
Solution:
Let the CE be h meter.
Height of tree be AD = 15m
BE is the height of tower = BC + CE = 15 + h
AB = CD, let it is = X m
From ΔCDE,
tan30° = EC/CD
⇒ 1/√3 = h/X
∴ X = √3h ..........(1)
From ΔABE,
tan60° = EB/AB
⇒ √3 = (h + 15)/X
∴ X = (h + 15)/√3 ..............(2)
From (1) and (2) we get,
√3h = (h + 15)/√3
⇒ 3h = h + 15
⇒ 2h = 15
∴ h = 7.5
∴ Height of tower = 15 + 7.5 = 22.5 m
Solution:
Let the CE be h meter.
Height of tree be AD = 15m
BE is the height of tower = BC + CE = 15 + h
AB = CD, let it is = X m
From ΔCDE,
tan30° = EC/CD
⇒ 1/√3 = h/X
∴ X = √3h ..........(1)
From ΔABE,
tan60° = EB/AB
⇒ √3 = (h + 15)/X
∴ X = (h + 15)/√3 ..............(2)
From (1) and (2) we get,
√3h = (h + 15)/√3
⇒ 3h = h + 15
⇒ 2h = 15
∴ h = 7.5
∴ Height of tower = 15 + 7.5 = 22.5 m
৬,৯৮৩.
A boat's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The boat's speed against the current is-
ব্যাখ্যা
Question: A boat's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The boat's speed against the current is-
Solution:
ধরি,
নৌকার বেগ x km/hr
স্রোতের বেগ y = 2.5 km/hr
স্রোতের অনুকূলে বেগ x + y = 15 km/hr
∴ x + y = 15
⇒ x = 15 - 2.5
∴ x = 12.5
∴ স্রোতের প্রতিকূলে বেগ x - y = 12.5 - 2.5 = 10 km/hr
Solution:
ধরি,
নৌকার বেগ x km/hr
স্রোতের বেগ y = 2.5 km/hr
স্রোতের অনুকূলে বেগ x + y = 15 km/hr
∴ x + y = 15
⇒ x = 15 - 2.5
∴ x = 12.5
∴ স্রোতের প্রতিকূলে বেগ x - y = 12.5 - 2.5 = 10 km/hr
৬,৯৮৪.
If 45 students can consume a stock of food in 2 months, then for how many days the same stock of food will last for 27 students?
ব্যাখ্যা
Question: If 45 students can consume a stock of food in 2 months, then for how many days the same stock of food will last for 27 students?
Solution:
According to the first condition, students consume food in 2 months, i.e. in 60 days.
So this ratio would be 45 : 60
According to the second condition, the same amount of food is consumed by 27 students in x days.
So that ratio would be 27 : x.
By Inverse Proportion,
45 × 60 = 27 × x
⇒ x = (45 × 60) / 27
∴ x = 100
Solution:
According to the first condition, students consume food in 2 months, i.e. in 60 days.
So this ratio would be 45 : 60
According to the second condition, the same amount of food is consumed by 27 students in x days.
So that ratio would be 27 : x.
By Inverse Proportion,
45 × 60 = 27 × x
⇒ x = (45 × 60) / 27
∴ x = 100
৬,৯৮৫.
Club A has 20 members and club B has 28. If a total of 42 people belong to the two clubs, how many people belong to both clubs?
ব্যাখ্যা
Total Number = Club A + Club B - both club (van Diagram)
or, 42 = 20 + 28 - both
or, both = 6.
৬,৯৮৬.
Which of these is NOT a correct way to find 75% of 35?
ব্যাখ্যা
75% of 35 = (75/100) × 35.
75% কে লেখা যায় = (75/100) = .75 = 3/4
৬,৯৮৭.
The present age of a man is three times the age of his son. After 5 years, the sum of their ages will be 70. What is the son’s current age?
ব্যাখ্যা
Question: The present age of a man is three times the age of his son. After 5 years, the sum of their ages will be 70. What is the son’s current age?
Solution:
Let, son's current age = x
Then, man’s age = 3x
After 5 years, Son’s age = x + 5 and Man’s age = 3x + 5
ATQ,
⇒ x + 5 + 3x + 5 = 70
⇒ 4x + 10 = 70
⇒ 4x = 60
∴ x = 15
So , son’s current age is 15 years.
Solution:
Let, son's current age = x
Then, man’s age = 3x
After 5 years, Son’s age = x + 5 and Man’s age = 3x + 5
ATQ,
⇒ x + 5 + 3x + 5 = 70
⇒ 4x + 10 = 70
⇒ 4x = 60
∴ x = 15
So , son’s current age is 15 years.
৬,৯৮৮.
What is the angle between the hour and minute hands of a clock when it is 8: 20?
ব্যাখ্যা
Question: What is the angle between the hour and minute hands of a clock when it is 8: 20?
Solution:
We know, the angle between the hour and minute hands is,
Angle = |11M - 60H|/2
= |(11 × 20) - (60 × 8)|/2
= |220 - 480|/2
= |- 260|/2
= 260/2
= 130°
∴ The angle between the hour and minute hands at 8: 20 is 130°.
৬,৯৮৯.
Find the simple interest on BDT 12000 at 8% per annum for 6 months.
ব্যাখ্যা
Question: Find the simple interest on BDT 12000 at 8% per annum for 6 months.
Solution:
Principal, P = 12000 Taka
Time, n = 6 months = 6/12 = 1/2 years
Rate of interest, r = 8% = 8/100
Simple Interest, I = P × n × r
= 12000 × (1/2) × (8/100)
= (12000 × 1 × 8)/(2 × 100)
= 96000/200
= 480
∴ The simple interest is Tk. 480.
৬,৯৯০.
A ladder rests against a wall that is perpendicular to the ground. If the bottom of the ladder is 4m away from the bottom of the wall, while the top of the ladder is at a height of 3m. What is the length of the ladder?
ব্যাখ্যা
Length of the ladder = √(32 + 42) = 5m
৬,৯৯১.
ব্যাখ্যা
Question:
Solution:
Solution:
৬,৯৯২.
The angle of elevation of an aeroplane from a point A on the ground is 60°. After a straight flight of the plane for 30 seconds, the angle of elevation becomes 30°. If the palne flies at a constant height of 3600√3 metre, what is the speed of plane?
ব্যাখ্যা
Question: The angle of elevation of an aeroplane from a point A on the ground is 60°. After a straight flight of the plane for 30 seconds, the angle of elevation becomes 30°. If the palne flies at a constant height of 3600√3 metre, what is the speed of plane?
Solution:
P and Q = Positions of plane
∠PAB = 60°, ∠QAB = 30°, PB = 3600√3 metre
In ∆ABP, tan 60° = BP/AB
⇒ √3 = 3600√3/AB
⇒ AB = 3600 metre
In ∆ACQ, tan 30° = CQ/AC
⇒ 1/√3 = 3600√3/AC
⇒ AC = 3600 × 3 = 10800 metre
∴ PQ = BC = AC – AB = 10800 – 3600 = 7200 metre
This distance is covered in 30 seconds.
∴ Speed of plane = 7200/30 = 240 m/sec
Solution:
P and Q = Positions of plane
∠PAB = 60°, ∠QAB = 30°, PB = 3600√3 metre
In ∆ABP, tan 60° = BP/AB
⇒ √3 = 3600√3/AB
⇒ AB = 3600 metre
In ∆ACQ, tan 30° = CQ/AC
⇒ 1/√3 = 3600√3/AC
⇒ AC = 3600 × 3 = 10800 metre
∴ PQ = BC = AC – AB = 10800 – 3600 = 7200 metre
This distance is covered in 30 seconds.
∴ Speed of plane = 7200/30 = 240 m/sec
৬,৯৯৩.
Three pipes A, B and C are connected to a tank. Out of the three, A and B are the inlet pipes and C is the outlet pipe. If opened separately, A fills the tank in 10 hours and B fills the tank in 30 hours. If all three are opened simultaneously, it takes 30 minutes extra than if only A and B are opened. How much time does it take to empty the tank if only C is opened?
ব্যাখ্যা
Question: Three pipes A, B and C are connected to a tank. Out of the three, A and B are the inlet pipes and C is the outlet pipe. If opened separately, A fills the tank in 10 hours and B fills the tank in 30 hours. If all three are opened simultaneously, it takes 30 minutes extra than if only A and B are opened. How much time does it take to empty the tank if only C is opened?
Solution:
Let the capacity of tank be LCM (10, 30) = 30 units
Efficiency of pipe A = 30/10 = 3 units/hour
Efficiency of pipe B = 30/30 = 1 units/hour
Combined efficiency of pipes A and B = 4 units/hour
Therefore, time taken to completely fill the tank if only A and B are opened = 30/4 = 7 hours 30 minutes
Time taken to completely fill the tank if all pipes are opened = 7 hours 30 minutes + 30 minutes = 8 hours
Combined efficiency of all pipes = 30/8 = 3.75 units/hour
Now, efficiency of pipe C = Combined efficiency of all three pipes - Combined efficiency of pipes A and B
Therefore, efficiency of pipe C = 4 - 3.75 = 0.25 units/hour
Thus, time taken to empty the tank if only C is opened = 30/0.25 = 120 hours.
Solution:
Let the capacity of tank be LCM (10, 30) = 30 units
Efficiency of pipe A = 30/10 = 3 units/hour
Efficiency of pipe B = 30/30 = 1 units/hour
Combined efficiency of pipes A and B = 4 units/hour
Therefore, time taken to completely fill the tank if only A and B are opened = 30/4 = 7 hours 30 minutes
Time taken to completely fill the tank if all pipes are opened = 7 hours 30 minutes + 30 minutes = 8 hours
Combined efficiency of all pipes = 30/8 = 3.75 units/hour
Now, efficiency of pipe C = Combined efficiency of all three pipes - Combined efficiency of pipes A and B
Therefore, efficiency of pipe C = 4 - 3.75 = 0.25 units/hour
Thus, time taken to empty the tank if only C is opened = 30/0.25 = 120 hours.
৬,৯৯৪.
In how many different ways can the letters of the word 'BANKING' be arranged so that the vowels always come together?
ব্যাখ্যা
Question: In how many different ways can the letters of the word 'BANKING' be arranged so that the vowels always come together?
Solution:
In the word 'BANKING' we treat the two vowels 'A' and 'I' as one letter.
Thus, we have BNKNG(AI)
This has 6 letters of which N occurs 2 times and the rest are different.
As we know that number of ways of arranging n letters out of which r are of same type = n!/r!
Number of ways of arranging these letters = 6!/2! = 360
Now 2 vowels (A,l) can be arranged in 2! = 2 ways
∴ Required number of ways = 360 × 2 = 720
Solution:
In the word 'BANKING' we treat the two vowels 'A' and 'I' as one letter.
Thus, we have BNKNG(AI)
This has 6 letters of which N occurs 2 times and the rest are different.
As we know that number of ways of arranging n letters out of which r are of same type = n!/r!
Number of ways of arranging these letters = 6!/2! = 360
Now 2 vowels (A,l) can be arranged in 2! = 2 ways
∴ Required number of ways = 360 × 2 = 720
৬,৯৯৫.
The length of the bridge, which a train 150 meters long and travelling at 45 km/h can cross in 30 seconds, is-
ব্যাখ্যা
Question: The length of the bridge, which a train 150 metres long and travelling at 45 km/h can cross in 30 seconds, is-
Solution:
Given,
Speed = 45 km/hr
= 45 × (5/18) m/sec
=25/2 m/sec
Time = 30 sec
Let, the length of bridge = x metres
Now
(150 + x)/30 = 25/2
⇒ 300 + 2x = 750
⇒ 2x = 750 - 300
⇒ 2x = 450
⇒ x = 450/2
∴ x = 225
Solution:
Given,
Speed = 45 km/hr
= 45 × (5/18) m/sec
=25/2 m/sec
Time = 30 sec
Let, the length of bridge = x metres
Now
(150 + x)/30 = 25/2
⇒ 300 + 2x = 750
⇒ 2x = 750 - 300
⇒ 2x = 450
⇒ x = 450/2
∴ x = 225
৬,৯৯৬.
If k is a positive integer, what is the smallest possible value of k such that 1080 × k is the square of an integer?
ব্যাখ্যা
Question: If k is a positive integer, what is the smallest possible value of k such that 1080 × k is the square of an integer?
Solution:
আমরা জানি, একটি সংখ্যা পূর্ণবর্গ হতে হলে এর মৌলিক গুণনীয়কের ঘাতসমূহ জোড় সংখ্যা হতে হবে।
1080 = 2 × 2 × 2 × 3 × 3 × 3 × 5
= 23 × 33 × 5
1080k = 23 × 33 × 5 × k
এখন,
এখন k এর মান 2 × 3 × 5 = 30 হলে, 1080k একটি পূর্ণবর্গ সংখ্যা হবে।
1080 × 30 = (23 × 33 × 5) × (2 × 3 × 5)
= 24 × 34 × 52
যেহেতু এই গুণফলের সব মৌলিক উৎপাদকের ঘাত জোড়, তাই এটি একটি পূর্ণবর্গ সংখ্যা।
সুতরাং, k = 30 হলে 1080 × k পূর্ণবর্গ সংখ্যা হয়।
৬,৯৯৭.
A sum of money amounts to Tk. 5200 in 5 years and to Tk. 5680 in 7 years at simple interest. The rate of interest per annum is?
ব্যাখ্যা
Question: A sum of money amounts to Tk. 5200 in 5 years and to Tk. 5680 in 7 years at simple interest. The rate of interest per annum is?
Solution:
Simple interest for 2 years = (5680 - 5200) Tk.
= Tk. 480
∴ Simple Interest for 2 years = Tk. 480
∴ Simple Interest for 5 years = Tk. (480 × 5/2)
= Tk. 1200
∴ Principal = 5200 - 1200 = Tk. 4000.
We know,
I = Pnr
⇒ r = I/Pn
⇒ r = (1200 × 100)/(4000 × 5)
∴ r = 6%
Solution:
Simple interest for 2 years = (5680 - 5200) Tk.
= Tk. 480
∴ Simple Interest for 2 years = Tk. 480
∴ Simple Interest for 5 years = Tk. (480 × 5/2)
= Tk. 1200
∴ Principal = 5200 - 1200 = Tk. 4000.
We know,
I = Pnr
⇒ r = I/Pn
⇒ r = (1200 × 100)/(4000 × 5)
∴ r = 6%
৬,৯৯৮.
In how many ways can 10 examination papers be arranged so that the best and the worst papers never come together?
ব্যাখ্যা
Number of ways in which 10 paper can arranged is 10! Ways.
The best and the worst papers come together, we get 2 papers as 1 paper,
So we have only 9 papers.
These 9 papers can be arranged in 9! ways.
2 papers can be arranged themselves in 2! ways.
The best and the worst paper do not come together, in this case number of arrangement
= 10! - 9! × 2!
= 9!(10 - 2)
= 8 × 9!
The best and the worst papers come together, we get 2 papers as 1 paper,
So we have only 9 papers.
These 9 papers can be arranged in 9! ways.
2 papers can be arranged themselves in 2! ways.
The best and the worst paper do not come together, in this case number of arrangement
= 10! - 9! × 2!
= 9!(10 - 2)
= 8 × 9!
৬,৯৯৯.
The average age of all the students of a class in 18 years. The average age of the boys of the class is 20 years and that of the girls is 15 years. If the number of girls in the class is 20, then find the number of boys in the class.
ব্যাখ্যা
Question: The average age of all the students of a class in 18 years. The average age of the boys of the class is 20 years and that of the girls is 15 years. If the number of girls in the class is 20, then find the number of boys in the class.
Solution:
Let,
the number of boys in the class be x.
Then, 18 × (x + 20) = 20x + (15 × 20)
⇒ 18x + 360 = 20x + 300
⇒ 20x + 300 = 18x + 360
⇒ 20x -18x = 360 -300
⇒ 2x = 60
⇒ x = 30
∴ The number of boys in the class is 30.
৭,০০০.
A mixture contains milk and water in the ratio 7 : 3 cost Tk. 500. Then 2 litters of water were added. What is the profit percentage?
ব্যাখ্যা
Question: A mixture contains milk and water in the ratio 7 : 3 cost Tk. 500. Then 2 litters of water were added. What is the profit percentage?
Solution:
Let
Milk = 7 liters
Water = 3 liters
Original mixture quantity = 10 liters
Cost of original mixture = 500 Taka
Cost per liter = 500 / 10 = 50 Taka
Water added = 2 liters
New total water = 3 + 2 = 5 liters
Milk remains = 7 liters
Total mixture = 7 + 5 = 12 liters
Total Selling Price = 12 × 50 = 600 Taka
Profit = SP - CP = 600 - 500 = 100
Profit % = (100/500) × 100 = 20%
∴ Profit percent = 20%