Bank Math

PrepBank · পাতা ১১০ / ১৬১ · ১০,৯০১–১১,০০০ / ১৬,১২৪

১০,৯০১.

A gym offers two membership plans: Tk. 15 per week or Tk. 50 per month. How much does a person save in a year by opting for the monthly plan rather than the weekly plan?

ক
90 tk
খ
140 tk
গ
160 tk
ঘ
180 tk

সঠিক উত্তর: ঘ

180 tk

উত্তর

সঠিক উত্তর: ঘ

180 tk

ঘ

ব্যাখ্যা

Question: A gym offers two membership plans: Tk. 15 per week or Tk. 50 per month. How much does a person save in a year by opting for the monthly plan rather than the weekly plan?

Solution:
Annual cost with the weekly plan = 52 × 15 = 780 tk
Annual cost with the monthly plan = 12 × 50 = 600 tk

Savings = 780 - 600 = 180 tk
So, a person saves Tk. 180 in a year by opting for the monthly plan instead of the weekly plan.

১০,৯০২.

What will come at the place of the question mark?
2, 3, 4, 9, 16, 29, ?

ক
45
খ
54
গ
60
ঘ
65

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: What will come at the place of the question mark?
2, 3, 4, 9, 16, 29, ?

Solution:
The sum of any three consecutive terms of the series gives the next term.
so, missing number = 9 + 16 + 29 = 54

১০,৯০৩.

If 3 : 7 :: 12 : x, then x is equal to:

ক
22
খ
23
গ
28
ঘ
27
ঙ
None

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: If 3 : 7 :: 12 : x, then x is equal to:

Solution:
3 : 7 :: 12 : x
⇒ 3/7 = 12/x
⇒ 3x = 84
⇒ x = 28

∴ x = 28

১০,৯০৪.

Find the least number which is exactly divisible by 12, 15, and 20.

ক
40
খ
50
গ
60
ঘ
80

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: Find the least number which is exactly divisible by 12, 15, and 20.

Solution:
Least number = L.C.M. of 12, 15, and 20 = 60
Hence, the required least number = 60

১০,৯০৫.

If a pole 15m high casts a shadow 5√3m long on the ground, then the elevation of the sun is-

ক
ক) 15°
খ
খ) 30°
গ
গ) 45°
ঘ
ঘ) 60°

সঠিক উত্তর: ঘ

ঘ) 60°

উত্তর

সঠিক উত্তর: ঘ

ঘ) 60°

ঘ

ব্যাখ্যা

Question: If a pole 15m high casts a shadow 5√3m long on the ground, then the elevation of the sun is-

Solution:

খুঁটির উচ্চতা AB = 15m
খুঁটির ছায়ার দৈর্ঘ্য BC =5√3m

ΔABC
tanθ = লম্ব/ভূমি
tanθ = AB/BC
tanθ =15/5√3
tanθ =√3
tanθ = tan60°
θ = 60°

১০,৯০৬.

What is the 9^th term of the sequence : - 2, - 4, - 6, ............................ , - 100?

ক
- 16
খ
- 18
গ
- 20
ঘ
22

সঠিক উত্তর: খ

- 18

উত্তর

সঠিক উত্তর: খ

- 18

খ

ব্যাখ্যা

Question: What is the 9^th term of the sequence : - 2, - 4, - 6, ............................ , - 100?

Solution:
Here,
- 4 - (- 2) = - 4 + 2 = - 2
- 6 - (- 4) = - 6 + 4 = - 2
∴ d = - 2
a = - 2
n = 9

∴ The 9^th term of the sequence = a + (n - 1)d
= - 2 + (9 - 1) (- 2)
= - 2 + 8 (- 2)
= - 2 - 16
= - 18

১০,৯০৭.

The sum of the ages of a father and son is 68 years. Four years ago, the father was five times as old as his son. What is the present age of the son?

ক
12 years
খ
14 years
গ
16 years
ঘ
20 years

সঠিক উত্তর: খ

14 years

উত্তর

সঠিক উত্তর: খ

14 years

খ

ব্যাখ্যা

Question: The sum of the ages of a father and son is 68 years. Four years ago, the father was five times as old as his son. What is the present age of the son?

Solution:
ধরি, পুত্রের বর্তমান বয়স = x বছর
তাহলে, পিতার বর্তমান বয়স = (68 - x) বছর

চার বছর আগে,
পুত্রের বয়স ছিল = (x - 4) বছর
পিতার বয়স ছিল = (68 - x) - 4 = (64 - x) বছর

প্রশ্নমতে,
64 - x = 5(x - 4)
⇒ 64 - x = 5x - 20
⇒ 64 + 20 = 5x + x
⇒ 84 = 6x
⇒ x = 84/6
⇒ x = 14

সুতরাং, পুত্রের বর্তমান বয়স হলো 14 বছর।

১০,৯০৮.

The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 5% per annum is Tk 3. The sum is:

ক
650 Tk
খ
900 Tk
গ
1200 Tk
ঘ
1400 Tk
ঙ
1550 Tk

সঠিক উত্তর: গ

1200 Tk

উত্তর

সঠিক উত্তর: গ

1200 Tk

গ

ব্যাখ্যা

Question: The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 5% per annum is Tk 3. The sum is:

Solution:
Let, Sum = x
Here, r = 5% & n = 2

Now, S.I. = (x × 5 × 2)/100
= x/10

And, C.I. = [x{1 + (5/100)}² - x]
= [x{1 + (1/20)}² - x]
=[x(21/20)² - x]
= (441x - 400x)/400
= 41x/400

∴ (41x/400) - (x/10) = 3
⇒ (41x - 40x)/400 = 3
⇒ x = 1200

১০,৯০৯.

A boat takes half time in moving a certain distance downstream than upstream. The ratio of the speed of the boat in still water and that of the current is?

ক
ক) 2 : 1
খ
খ) 3 : 2
গ
গ) 5 : 3
ঘ
ঘ) 3 : 1

সঠিক উত্তর: ঘ

ঘ) 3 : 1

উত্তর

সঠিক উত্তর: ঘ

ঘ) 3 : 1

ঘ

ব্যাখ্যা

Let the speed of boat in still water = x km/hr,
and Speed of current = y km/hr
Rate downstream = (x + y) km/hr, and Rate upstream = (x – y) km/hr
Distance = Speed × Time
∴ (x−y) × 2t = (x+y)×t
⇒ 2x−2y = x+y
⇒ 2x−x = 2y+y
⇒ x = 3y
⇒ x/y = 3/1 = 3:1

১০,৯১০.

A vendor bought 6 oranges for Tk. 10 and sold them at 4 for Tk. 6. Find his loss or gain percent.

ক
8% gain
খ
10% gain
গ
8% loss
ঘ
10% loss

সঠিক উত্তর: ঘ

10% loss

উত্তর

সঠিক উত্তর: ঘ

10% loss

ঘ

ব্যাখ্যা

Question: A vendor bought 6 oranges for Tk. 10 and sold them at 4 for Tk. 6. Find his loss or gain percent.

Solution:
Suppose, number of oranges bought = LCM of 6 and 4 = 12
∴ CP of 12 oranges = (10/6) × 12 = Tk. 20
and SP of 12 oranges = (6/4) × 12 = Tk. 18
∴ Loss = 20 - 18 = 2

∴ Loss% = (2/20) × 100% = 10%

১০,৯১১.

Musa can do 1/4 of a work in 6 days. In how many days will he complete the work?

ক
24 days
খ
12 days
গ
36 days
ঘ
15 days

সঠিক উত্তর: ক

24 days

উত্তর

সঠিক উত্তর: ক

24 days

ক

ব্যাখ্যা

Question: Musa can do 1/4 of a work in 6 days. In how many days will he complete the work?

Solution:
Musa can do 1/4 of a work in 6 days.
∴ He will complete the work in = 6 × 4 = 24 days

∴ Musa will complete the work in 24 days.

১০,৯১২.

Which amount to be received after 3 years at the rate of 7% p.a. of simple interest on a sum of Tk. 2800?

ক
ক) Tk. 3388
খ
খ) Tk. 2288
গ
গ) Tk. 4488
ঘ
ঘ) Tk. 2388

সঠিক উত্তর: ক

ক) Tk. 3388

উত্তর

সঠিক উত্তর: ক

ক) Tk. 3388

ক

ব্যাখ্যা

Question: Which amount to be received after 3 years at the rate of 7% p.a. of simple interest on a sum of Tk. 2800?

Soution:
Given,
Rate of interest, r = 7%
Principal, P = 2800 Tk.
Time, n = 3 years.

∴ Total interest, I = Pnr
= (2800 × 3 × 7)/100
= 588 Tk.

So, amount = Principal + Simple interest
= (2800 + 588) Tk.
= 3388 Tk.

১০,৯১৩.

A man sells two articles at Tk.99 each. He gains 10% on one and loss 10% on the other. Then on overall basis he-

ক
ক) Tk. 1
খ
খ) Tk. 5
গ
গ) Tk. 10
ঘ
ঘ) Tk. 2

সঠিক উত্তর: ঘ

ঘ) Tk. 2

উত্তর

সঠিক উত্তর: ঘ

ঘ) Tk. 2

ঘ

ব্যাখ্যা

Total Selling Price= Tk.(2×99)
= Tk.198
C.P. of first article = Tk. {(100/110) × 99}
= Tk. 90

C.P. of second article = Tk. {(100/90) × 99}
= Tk. 110
Total C.P.= Tk.(90 + 110)
= Tk. 200
∴Loss= Tk.(200−198)= Tk. 2

১০,৯১৪.

Sayed covers 20 miles in 40 minutes. What is his speed in km/hr?

ক
48.3 km/hr
খ
48 km/hr
গ
37.6 km/hr
ঘ
51.2 km/hr

সঠিক উত্তর: ক

48.3 km/hr

উত্তর

সঠিক উত্তর: ক

48.3 km/hr

ক

ব্যাখ্যা

Question: Sayed covers 20 miles in 40 minutes. What is his speed in km/hr?

Solution:
We know that,
1 mile = 1.61km
20 miles = (20 × 1.61)km
= 32.2 km

time = 40 minutes = 40/60 = 2/3 hour

speed = 32.2/(2/3) km/hr
= 48.3 km/hr

১০,৯১৫.

A and B enter into a partnership. A invest Tk 5000. At the end of 3 months, he withdraws Tk 500 and at the end of 7 months he withdraws another Tk 900. B gets Tk 800 as his share of the total profit of Tk 1800 at the end of the year. How much did B invest, if B invested along with A at the beginning of the year?

ক
Tk 2400
খ
Tk 3000
গ
Tk 3200
ঘ
Tk 3400

সঠিক উত্তর: ঘ

Tk 3400

উত্তর

সঠিক উত্তর: ঘ

Tk 3400

ঘ

ব্যাখ্যা

Question: A and B enter into a partnership. A invest Tk 5000. At the end of 3 months, he withdraws Tk 500 and at the end of 7 months he withdraws another Tk 900. B gets Tk 800 as his share of the total profit of Tk 1800 at the end of the year. How much did B invest, if B invested along with A at the beginning of the year?

Solution:
A invest 5000 for 3 months, 4500 for 4 months and 3600 for 5 months and gets a interest of 1000

ATQ,
{(5000 × R × 3)/(12 × 100)} + {(4500 × R × 4)/(12 × 100)} + {(3600 × R × 5)/(12 × 100)} = 1000
⇒ {(15000 × R)/(12 × 100)} + {(18000 × R)/(12 × 100)} + {(18000 × R)/(12 × 100)} = 1000
⇒ (15000R/1200) + (18000R/1200) + (18000R/1200) = 1000
⇒ (51000R)/1200 = 1000
⇒ 51000R = 1200000
⇒ R = 1200000/51000
⇒ R=1200/51

For B,
{(P × 1200)/(51 × 1)}/100 = 800
⇒ (P × 1200/51)/100 = 800
⇒ (P × 1200)/51 = 80000
⇒ P × 1200 = 4080000
∴ P = 3400

১০,৯১৬.

3/ 4 part of the tank is full of water. When 30 litres of water is taken out, the tank becomes empty. The capacity of the tank is -

ক
ক) 32 liters
খ
খ) 42 liters
গ
গ) 40 liters
ঘ
ঘ) 38 liters

সঠিক উত্তর: গ

গ) 40 liters

উত্তর

সঠিক উত্তর: গ

গ) 40 liters

গ

ব্যাখ্যা

If a tank has 4x liters of total capacity and it holds 3x liters of water and if 30 liters of water is taken out, the tank becomes empty.
It means 3x liters of water is taken out
3x = 30 liters
x = 10 liters
Capacity of tank
= 4x = 4 × 10 = 40 liters

১০,৯১৭.

A student mistakenly multiplied a number by 7/10 instead of 7/5. Find the percentage error in the result.

ক
5%
খ
50%
গ
10%
ঘ
12%

সঠিক উত্তর: খ

50%

উত্তর

সঠিক উত্তর: খ

50%

খ

ব্যাখ্যা

Question: A student mistakenly multiplied a number by 7/10 instead of 7/5. Find the percentage error in the result.

Solution:
Let
The number is 100.

ATQ,
The actual calculation be: (7/5) × 100 = 140
and error calculation be: (7/10) × 100 = 70

∴ Difference = 140 - 70 = 70

∴ Percentage error = (70/140) × 100 = 50%

১০,৯১৮.

Two numbers are in the ratio 2 : 5. If 16 is added to both the numbers, their ratio becomes 1 : 2. What is the bigger number?

ক
ক) 92
খ
খ) 80
গ
গ) 56
ঘ
ঘ) 78

সঠিক উত্তর: খ

খ) 80

উত্তর

সঠিক উত্তর: খ

খ) 80

খ

ব্যাখ্যা

Let the numbers be 2x, 5x
ATQ,
(2x + 16) / (5x + 16) = 1/2
Or, 4x + 32 = 5x + 16
Or, x = 16
∴ The numbers: 2x = 2 × 16 = 32
And, 5x = 5 × 16 = 80

১০,৯১৯.

Two pipes A and B can fill a tank in 24 hours and 30 hours respectively. If both the pipes are opened simultaneously in the empty tank, how much time will be taken by them to fill it?

ক
13 hr
খ
13 hr 20 min
গ
10 hr 20 min
ঘ
None of the above

সঠিক উত্তর: খ

13 hr 20 min

উত্তর

সঠিক উত্তর: খ

13 hr 20 min

খ

ব্যাখ্যা

Question: Two pipes A and B can fill a tank in 24 hours and 30 hours respectively. If both the pipes are opened simultaneously in the empty tank, how much time will be taken by them to fill it?

Solution:
A's 1 hour work = 1/24
B's 1 hour work = 1/30

In 1 hour (A + B) together can fill = 1/24 + 1/30
= (5 + 4)/120
= 9/120
= 3/40

Total time to fill the tank = 40/3 hr = (40/3) × 60 minutes
= 800 minutes
= 13 hr 20 min

১০,৯২০.

If a : b = 2 : 3 and a : c = 4 : 7, then b : c =?

ক
6 : 5
খ
3 : 7
গ
6 : 7
ঘ
6 : 1

সঠিক উত্তর: গ

6 : 7

উত্তর

সঠিক উত্তর: গ

6 : 7

গ

ব্যাখ্যা

প্রশ্ন: If a : b = 2 : 3 and a : c = 4 : 7, then b : c =?

সমাধান:
a : b = 2 : 3
⇒ a/b = 2/3

a : c = 4 : 7
⇒ a/c = 4/7

(a/b) / (a/c) = (2/3)/(4/7)
⇒ c/b = 7/6
∴ b/c = 6/7
∴ b : c = 6 : 7

১০,৯২১.

To represent a family budget on a circle graph, how many degrees of the circle should be used to represent an item that is 20% of the total budget?

ক
ক) 76°
খ
খ) 72°
গ
গ) 60°
ঘ
ঘ) 20°

সঠিক উত্তর: খ

খ) 72°

উত্তর

সঠিক উত্তর: খ

খ) 72°

খ

ব্যাখ্যা

Question: To represent a family budget on a circle graph, how many degrees of the circle should be used to represent an item that is 20% of the total budget?

Solution:
সম্পূর্ণ বৃত্ত = ৩৬০°

তাহলে যে উপাদান ২০% জায়গা দখল করবে তার উৎপন্ন কোণ = ৩৬০° এর ২০%
= ৩৬০° এর ১/৫
= ৭২°

১০,৯২২.

Find the value of 5(m + 4) - 2(3m - 1) + m.

ক
18
খ
22
গ
15
ঘ
24

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: Find the value of 5(m + 4) - 2(3m - 1) + m.

Solution:
Given that,
5(m + 4) - 2(3m - 1) + m
= 5m + 20 - 6m + 2 + m
= 6m - 6m + 22
= 22

১০,৯২৩.

A reduction of 20% in the price of chocolates enables a man to buy 20 chocolates more for Tk. 40. The price per chocolate before the reduction was

ক
40 paisa
খ
50 paisa
গ
1 taka
ঘ
1 taka 40 paisa

সঠিক উত্তর: খ

50 paisa

উত্তর

সঠিক উত্তর: খ

50 paisa

খ

ব্যাখ্যা

Question: A reduction of 20% in the price of chocolates enables a man to buy 20 chocolates more for Tk. 40. The price per chocolate before the reduction was

Solution:
বর্তমান মূল্য ৮০ টাকা হলে পূর্বমূল্য ১০০ টাকা
বর্তমান মূল্য ১ টাকা হলে পূর্বমূল্য ১০০/৮০ টাকা
বর্তমান মূল্য ৪০ টাকা হলে পূর্বমূল্য ১০০ টাকা (১০০/৮০) × ৪০ টাকা
= ৫০ টাকা

২০ টি চকলেটের দাম (৫০ - ৪০) টাকা = ১০ টাকা
১ টি চকলেটের দাম = ১০/২০ টাকা
= ০.৫ টাকা
= ৫০ পয়সা

১০,৯২৪.

In what ratio, water must be mixed with fruit juice costing Tk. 24 per litre so that the juice would be worth of Tk. 20 per litre?

ক
1 : 4
খ
1 : 5
গ
1 : 6
ঘ
2 : 5
ঙ
None of these

সঠিক উত্তর: খ

1 : 5

উত্তর

সঠিক উত্তর: খ

1 : 5

খ

ব্যাখ্যা

Question: In what ratio, water must be mixed with fruit juice costing Tk. 24 per litre so that the juice would be worth of Tk. 20 per litre?

Solution:
Cost of 1 litre of water = Tk. 0 = cheaper quantity.
Cost of 1 litre of juice = Tk. 24 = dearer quantity.
And, the mean price = m = Tk. 20

Therefore, (Cheaper quantity) : (Dearer quantity) = (d - m) : (m - c) = 4 : 20 = 1 : 5
Hence, the required answer is 1 : 5.

১০,৯২৫.

A worker was hired for 7 days. Each day, he was paid Tk. 10 more than what he was paid for the previous day of work. the total amount he was paid in the first 4 days of work equaled the total amount he was paid in the last 3 days. What was his staring pay?

ক
ক) Tk. 90
খ
খ) Tk. 138
গ
গ) Tk. 150
ঘ
ঘ) Tk. 160

সঠিক উত্তর: ক

ক) Tk. 90

উত্তর

সঠিক উত্তর: ক

ক) Tk. 90

ক

ব্যাখ্যা

Question: A worker was hired for 7 days. Each day, he was paid Tk. 10 more than what he was paid for the previous day of work. the total amount he was paid in the first 4 days of work equaled the total amount he was paid in the last 3 days. What was his staring pay?

Solution:
ধরি,
starting payment ছিলো x টাকা

২য় দিন = x + 10
৩য় দিন = ( x + 20)
৪র্থ দিন = ( x + 30)
৫ম দিন = ( x + 40)
৬ষ্ঠ দিন = ( x + 50)
৭ম দিন = ( x + 60) টাকা

প্রশ্নমতে,
x + (x + 10) + (x + 20) + (x + 30) = (x + 40) + (x + 50) + (x + 60)
4x + 60 = 3x + 150
4x - 3x = 150 - 60
x = 90

১০,৯২৬.

What is the L.C.M of the numbers 36, 54 and 90?

ক
ক) 18
খ
খ) 120
গ
গ) 356
ঘ
ঘ) 540

সঠিক উত্তর: ঘ

ঘ) 540

উত্তর

সঠিক উত্তর: ঘ

ঘ) 540

ঘ

ব্যাখ্যা

Question: What is the L.C.M of the numbers 36, 54 and 90?

Solution:
36 = 2 × 3 × 2 × 3
54 = 3 × 3 × 3 × 2
90 = 2 × 3 × 3 × 5

∴ the L.C.M of the numbers 36, 54 and 90 is = 2 × 2 × 3 × 3 × 5 × 3
= 540

১০,৯২৭.

The L.C.M of two numbers is 12 times their H.C.F. The sum of H.C.F and L.C.M is 403. If one number is 93, find the other.

ক
128
খ
116
গ
124
ঘ
114

সঠিক উত্তর: গ

124

উত্তর

সঠিক উত্তর: গ

124

গ

ব্যাখ্যা

Question: The L.C.M of two numbers is 12 times their H.C.F. The sum of H.C.F and L.C.M is 403. If one number is 93, find the other.

Solution:
Let, H.C.F of the numbers be x and L.C.M be 12x.

ATQ,
x + 12x = 403
⇒ 13x = 403
⇒ x = 403/13
∴ x = 31

So, H.C.F = 31 and L.C.M = 12 × 31 = 372

Other number = (31 × 372)/93 = 124

১০,৯২৮.

If x= 10 which of the following has the minimum value?

ক
ক) x/2
খ
খ) 2-x
গ
গ) 2/x
ঘ
ঘ) (2-x)(2-x)

সঠিক উত্তর: খ

খ) 2-x

উত্তর

সঠিক উত্তর: খ

খ) 2-x

খ

ব্যাখ্যা

x = 10, প্রদত্ত অপশনগুলোতে বসিয়ে পাই,
x/2 = 10/2 = 5
2 - x = 2 - 10 = -8
2/x = 2/10 = 0.2
(2 -x) (2-x) = (2 - 10) (2 - 10) = (-8)(-8) = 64
অতএব, সর্বনিম্ন মান হচ্ছে 2 - x

১০,৯২৯.

If the area of a small pizza is 49π in², what size pizza box would best fit the small pizza?

ক
ক) 10 in
খ
খ) 12 in
গ
গ) 14 in
ঘ
ঘ) 9 in

সঠিক উত্তর: গ

গ) 14 in

উত্তর

সঠিক উত্তর: গ

গ) 14 in

গ

ব্যাখ্যা

area of a pizza (circle) = πr² = 49π
Or, r²= 49π/π = 49
Or, r = 7
So, the size of the pizza box would be = 2r = 2 × 7 = 14 in

১০,৯৩০.

A vendor purchased 45 dozen bananas for Tk. 250. Out of these 40 bananas were rotten and could not be sold. At what rate per dozen should he sell the remaining bananas to make a profit of 20%?

ক
ক) Tk. 5.5
খ
খ) Tk. 6
গ
গ) Tk. 7.2
ঘ
ঘ) Tk. 9

সঠিক উত্তর: গ

গ) Tk. 7.2

উত্তর

সঠিক উত্তর: গ

গ) Tk. 7.2

গ

ব্যাখ্যা

Question: A vendor purchased 45 dozen bananas for Tk. 250. Out of these 40 bananas were rotten and could not be sold. At what rate per dozen should he sell the remaining bananas to make a profit of 20%?

Solution:
Total bananas = 45 × 12 = 540
Total good bananas = 540 - 40 = 500
Cost price of 540 bananas = Tk. 250

At 20% profit selling price of 500 bananas = 120% of 250 = Tk. 300
∴ Selling price of 1 banana = (300/500) = 3/5
∴ The selling price of 12 bananas = (3/5) × 12 = Tk. 7.2

So, the selling price of 1 dozen bananas is Tk. 7.2

১০,৯৩১.

Each side of a rhombus is 17 cm, and one diagonal measures 30 cm. What is the length of the other diagonal?

ক
12 cm
খ
18 cm
গ
22 cm
ঘ
16 cm

সঠিক উত্তর: ঘ

16 cm

উত্তর

সঠিক উত্তর: ঘ

16 cm

ঘ

ব্যাখ্যা

প্রশ্ন: Each side of a rhombus is 17 cm, and one diagonal measures 30 cm. What is the length of the other diagonal?
(একটি রম্বসের প্রতিটি বাহুর দৈর্ঘ্য ১৭ সে. মি. এবং একটি কর্ণের দৈর্ঘ্য ৩০ সে. মি. হলে রম্বসটির অপর কর্ণের দৈর্ঘ্য কত?)

সমাধান:
রম্বসের প্রতিটি বাহুর দৈর্ঘ্য সমান এবং কর্ণদ্বয় পরস্পরকে সমকোণে সমদ্বখণ্ডিত করে ।

তাহলে, AB = AD = BC = CD = ১৭ সে. মি. এবং কর্ণ AC = ৩০ সে. মি. হলে।

OA = ৩০/২ = ১৫ সে. মি.
AOB সমকোণী ত্রিভুজ হতে -
⇒ AB² = OA² + OB²
⇒ ১৭^২ = ১৫^২ + OB²
⇒ OB² = ১৭^২ - ১৫^২
⇒ OB² = ২৮৯ - ২২৫
⇒ OB² = ৬৪
⇒ OB = √৬৪
∴ OB = ৮

অপর কর্ণ, BD = OD + OB = OB + OB = (৮ + ৮) = ১৬ সে. মি.

১০,৯৩২.

A candidate scoring 25% marks in an examination fails by 10 marks while another candidate who score 50% marks get 15 marks more than the minimum pass marks. What is the minimum pass mark?

ক
35
খ
45
গ
50
ঘ
65
ঙ
100

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: A candidate scoring 25% marks in an examination fails by 10 marks while another candidate who score 50% marks get 15 marks more than the minimum pass marks. What is the minimum pass mark?

Solution:
Let total mark = m

ATQ,
(m × 25%) + 10 = (m × 50%) – 15
⇒ (m/4) + 10 = (m/2) - 15
⇒ (m/2) - (m/4) = 15 + 10
⇒ m/4 = 25
⇒ m = 100

∴ minimum pass mark = (m/4) + 10
= (100/4) + 10
= 25 + 10
= 35

১০,৯৩৩.

What is the correct number in the third circle?

ক
1
খ
2
গ
4
ঘ
6

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: What is the correct number in the third circle?

Solution:
First circle: 56 ÷ 7 = 8 , 63 ÷ 9 = 7 ∴ 8 - 7 = 1
Second circle: 56 ÷ 8 = 7, 42 ÷ 7 = 6 ∴ 7 - 6 = 1

Third circle: 72 ÷ 9 = 8 , 42 ÷ 7 = 6 ∴ 8 - 6 = 2

১০,৯৩৪.

How many '8' will you pass on the way when you count from 1 to 100?

ক
ক) 11
খ
খ) 20
গ
গ) 80
ঘ
ঘ) 70

সঠিক উত্তর: খ

খ) 20

উত্তর

সঠিক উত্তর: খ

খ) 20

খ

ব্যাখ্যা

Question: How many '8' will you pass on the way when you count from 1 to 100?

Solution:
১ -১০ পর্যন্ত ৮ আছে = ১ টি
১১ - ২০ পর্যন্ত ৮ আছে = ১ টি
২১ - ৩০ পর্যন্ত ৮ আছে = ১ টি
৩১ - ৪০ পর্যন্ত ৮ আছে = ১ টি
৪১ - ৫০ পর্যন্ত ৮ আছে = ১ টি
৫১ - ৬০ পর্যন্ত ৮ আছে = ১ টি
৬১ - ৭০ পর্যন্ত ৮ আছে = ১ টি
৭১ - ৮০ পর্যন্ত ৮ আছে = ২ টি
৮১ - ৯০ পর্যন্ত ৮ আছে = ১০ টি
৯১ - ১০০ পর্যন্ত ৮ আছে = ১ টি

∴ মোট ৮ রয়েছে = ২০ টি

১০,৯৩৫.

A train travels 15 miles at a speed of 90 miles per hour. If the total time taken for the train's journey to and from the destination is 35 minutes, what is the speed of the train on its return trip?

ক
30 miles/hour
খ
40 miles/hour
গ
36 miles/hour
ঘ
46 miles/hour

সঠিক উত্তর: গ

36 miles/hour

উত্তর

সঠিক উত্তর: গ

36 miles/hour

গ

ব্যাখ্যা

Question: A train travels 15 miles at a speed of 90 miles per hour. If the total time taken for the train's journey to and from the destination is 35 minutes, what is the speed of the train on its return trip?

Solution:
Time taken to travel 15 miles at 90 miles per hour = 15/90 hours = 1/6 hour = 10 minutes
So, the time taken to return = 35 - 10 minutes = 25 minutes

Distance covered in 25 minutes = 15 miles
Distance covered in 1 minute = 15/25 miles
∴ the speed during the return trip (for 60 minutes) = (15 × 60)/25 = 36 miles per hour

১০,৯৩৬.

The average age of P, Q, R, S and T is 32 years. The average age of P and Q is 28 years, and the average age of R and S is 35 years. What is the age of T?

ক
34 years
খ
30 years
গ
36 years
ঘ
40 years

সঠিক উত্তর: ক

34 years

উত্তর

সঠিক উত্তর: ক

34 years

ক

ব্যাখ্যা

Question: The average age of P, Q, R, S and T is 32 years. The average age of P and Q is 28 years, and the average age of R and S is 35 years. What is the age of T?

Solution:
Given that,
There are 5 people P, Q, R, S, T
Average age of all five = 32 years
Total age of all five = 5 × 32 = 160 years

And,
Average age of P and Q = 28 years
So, age of (P + Q) = 2 × 28 = 56 years

Average age of R and S = 35 years
So, age of (R + S) = 2 × 35 = 70 years

∴ Now, total age of (P + Q + R + S) = 56 + 70 = 126 years

Age of T = Total age of all five - Age of (P + Q + R + S)
= 160 - 126
= 34 years

So the age of T is 34 years.

১০,৯৩৭.

Find out the wrong number in the series: 190, 166, 145, 128, 112, 100, 91

ক
100
খ
128
গ
145
ঘ
112

সঠিক উত্তর: খ

128

উত্তর

সঠিক উত্তর: খ

128

খ

ব্যাখ্যা

Question: Find out the wrong number in the series: 190, 166, 145, 128, 112, 100, 91

Solution:
190, 166, 145, 128, 112, 100, 91
এখানে,
190 - 166 = 24
166 - 145 = 21
145 - 128 = 17
128 - 112 = 16
112 - 100 = 12
100 - 91 = 9

প্রতিটি পদের পার্থক্যে 3 করে হ্রাস পাচ্ছে।
কিন্তু, 145 - 128 = 17
128 - 112 = 16
এর পার্থক্য হতে দেখা যায় যে, 3 করে হ্রাস পাচ্ছে না।
128 এর স্থলে 127 হলে ক্রমটি সঠিক থাকে।

তাই, 128 এর স্থরে 127 হবে।
সিরিজের ভুল সংখ্যাটি 128

১০,৯৩৮.

Before anybody could notice, Arif took 1/3 of the chocolates from a box. Later, his three sisters arrived and the remaining chocolates were distributed equally among the four of them. Arif received a total of 48 chocolates. How many did each of her sisters receive?

ক
16
খ
18
গ
21
ঘ
24
ঙ
None of these

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Let,
Total Chocolates = X
First time Arif took = X/3
Rest Amount = X - (X/3) = 2X/3
Amount of Chocolate when it divided equally = (2X/3) × (1/4)
= X/6
ATQ,
x/6 + x/3 = 48
Or, X/2 = 48
Or, X = 96
So, each sister got = 96/6
= 16

১০,৯৩৯.

A brother was 7 years senior to his sister 9 years ago. Their ages together add up to 53 at present. Find the sister’s and brother's current age.

ক
26 years, 38 years
খ
24 years, 36 years
গ
23 years, 30 years
ঘ
22 years, 42 years

সঠিক উত্তর: গ

23 years, 30 years

উত্তর

সঠিক উত্তর: গ

23 years, 30 years

গ

ব্যাখ্যা

Question: A brother was 7 years senior to his sister 9 years ago. Their ages together add up to 53 at present. Find the sister’s and brother's current age.

Solution:
Let the brother's present age be b and the sister's present age be s.

9 years ago:
Brother's age: b - 9
Sister's age: s - 9

Given,
b - 9 = (s - 9) + 7
⇒ b - 9 = s - 2
⇒ b = s + 7

b + s = 53
⇒ b = s + 7
⇒ (s + 7) + s = 53
⇒ 2s + 7 = 53
⇒ 2s = 46
⇒ s = 23

The sister's present age is 23 years.

Brother's present age is 30 years.

১০,৯৪০.

The average of four numbers 13, 27, 35, and X is 25. Find the number X.

ক
ক) 20
খ
খ) 25
গ
গ) 30
ঘ
ঘ) 35
ঙ
ঙ) None of above

সঠিক উত্তর: খ

খ) 25

উত্তর

সঠিক উত্তর: খ

খ) 25

খ

ব্যাখ্যা

Average = (13 + 27 + 35 + X)/4 = 25
Or, X + 75 = 100
So, X = 25

১০,৯৪১.

The sum of the ages of David and Farid is y years. If David is 12 years older than Farid , how many years old will Farid be y years from now, in terms of y?

ক
y - 6
খ
2y - 6
গ
(y/2) - 6
ঘ
(3y/2) - 6
ঙ
(5y/2) - 6

সঠিক উত্তর: ঘ

(3y/2) - 6

উত্তর

সঠিক উত্তর: ঘ

(3y/2) - 6

ঘ

ব্যাখ্যা

Question: The sum of the ages of David and Farid is y years. If David is 12 years older than Farid , how many years old will Farid be y years from now, in terms of y?

Solution:
The sum of the ages of David and Farid is y years: d + f = y;
David is 12 years older than Farid: d = f + 12.

Subtract one from another: f = y - f - 12
⇒ f = (y/2) - 6.

y years from now, Farid will be f + y = (y/2) - 6 + y
= (3y/2) - 6 years old.

১০,৯৪২.

Two numbers are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is

ক
ক) 27
খ
খ) 33
গ
গ) 49
ঘ
ঘ) 55

সঠিক উত্তর: খ

খ) 33

উত্তর

সঠিক উত্তর: খ

খ) 33

খ

ব্যাখ্যা

ধরি,
ক্ষুদ্রতর সংখ্যাটি 3x এবং বৃহত্তর সংখ্যাটি 5x
প্রশ্নমতে, (3x - 9)/(5x - 9) = 12/23
⇒ 69x - 207 = 60x - 108
⇒ 69x - 60x = 207 - 108
⇒ 9x = 99
⇒ x = 11
অতএব, ক্ষুদ্রতর সংখ্যাটি = 3 × 11 = 33

১০,৯৪৩.

Akash multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation?

ক
50%
খ
57%
গ
64%
ঘ
68%

সঠিক উত্তর: গ

64%

উত্তর

সঠিক উত্তর: গ

64%

গ

ব্যাখ্যা

Question: Akash multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation?

Solution:
Let the number be x

Error = (5x/3) - (3x/5)
= (25x - 9x)/15
= 16x/15

% Error ={(16x/15) × (3/5x) × 100}% = 64%

১০,৯৪৪.

Mizan took a loan of Tk. 1500 with simple interest for as many years as the rate of interest. If he paid Tk. 540 as interest at the end of the loan period, what was the rate of interest?

ক
3%
খ
9%
গ
5%
ঘ
8%
ঙ
6%.

সঠিক উত্তর: ঙ

6%.

উত্তর

সঠিক উত্তর: ঙ

6%.

ঙ

ব্যাখ্যা

Simple interest is the same as the rate of interest.
Hence,
Rate of interest = R% and Time = R years

S.I. = (P × R × R)/100
⇒ 540 = (1500 × R²)/100
⇒ 15R²= 540
⇒ R² = 36
⇒ R = 6 %

Rate of Interest = 6%.

১০,৯৪৫.

Four girls are sitting on a bench to be photographed. Seema is to the left of Rani. Mary is to the right of Rani. Rita is between Rani and Mary. Who would be second from the left in the photograph?

ক
ক) Rani
খ
খ) Seema
গ
গ) Mary
ঘ
ঘ) Rita

সঠিক উত্তর: ক

ক) Rani

উত্তর

সঠিক উত্তর: ক

ক) Rani

ক

ব্যাখ্যা

Question: Four girls are sitting on a bench to be photographed. Seema is to the left of Rani. Mary is to the right of Rani. Rita is between Rani and Mary. Who would be second from the left in the photograph?

Solution:
Seema is to the left of Rani.
Seema ⇔ Rani

Mary is to the right of Rani.
Rani ⇔ Mary

Rita is between Rani and Mary.
Rani ⇔ Rita ⇔ Mary

∴ Seema ⇔ Rani ⇔ Rita ⇔ Mary.

Rani would be second from the left in the photograph.

১০,৯৪৬.

The ratio of male students to female students in a class is 13 to 19. If there are 224 people in the class, including one teacher, one administrator and thirty evaluations. How many people in the class are male students?

ক
ক) 78
খ
খ) 80
গ
গ) 91
ঘ
ঘ) 114

সঠিক উত্তর: ক

ক) 78

উত্তর

সঠিক উত্তর: ক

ক) 78

ক

ব্যাখ্যা

দেওয়া আছে,
মোট লোক সংখ্যা = 224
1 জন শিক্ষক, 1 জন প্রশাসক ও 30 জন মূল্যায়নকারী বাদ দিলে অবশিষ্ট লোক সংখ্যা
= 224 - (1 + 1 + 30)
= 224 - 32
= 192 জন
এই 192 জনের মধ্যে ছাত্র : ছাত্রী = 13:19
∴ ছাত্র সংখ্যা = 13/(13+19) × 192
= (13/32) × 192
= 78 জন

১০,৯৪৭.

How many kgs of sugar costing Tk 12 per kg must be mixed with 35 kg of sugar costing Tk 8 per kg so that may be a gain of 15% by selling the mixture at Tk 12.65 per kg?

ক
100 kg
খ
85 kg
গ
90 kg
ঘ
105 kg

সঠিক উত্তর: ঘ

105 kg

উত্তর

সঠিক উত্তর: ঘ

105 kg

ঘ

ব্যাখ্যা

Question: How many kgs of sugar costing Tk 12 per kg must be mixed with 35 kg of sugar costing Tk 8 per kg so that may be a gain of 15% by selling the mixture at Tk 12.65 per kg?

Solution:
Let, the sugar of Tk 12 per kg is = x kg

ATQ,
115% of (8 × 35 + 12 × x) = 12.65(35 + x)
⇒ (115/100) × (280 + 12x) = 442.75 + 12.65x
⇒ 322 + 13.8x = 442.75 + 12.65x
⇒ 1.15x = 120.75
⇒ x = 105

১০,৯৪৮.

A school has only four classes having 10, 20, 30 and 40 students respectively with pass percentage of 20%, 30%, 60% and 100% respectively. Find the pass percentage of the entire school.

ক
ক) 56%
খ
খ) 76%
গ
গ) 34%
ঘ
ঘ) 66%

সঠিক উত্তর: ঘ

ঘ) 66%

উত্তর

সঠিক উত্তর: ঘ

ঘ) 66%

ঘ

ব্যাখ্যা

Pass Candidates of first class
= 20% of 10
= 2

Pass Candidates of second class
= 30% of 20
= 6

Pass Candidates of third class
= 60% of 30
= 18

Pass Candidates of fourth class
= 100% of 40
= 40

Total Pass Candidate
= 2 + 6 + 18 + 40
= 66

Total no of Student
= 10 + 20 + 30 + 40
= 100

Pass %
= (66/100) × 100
= 66%

১০,৯৪৯.

(.1 × .01 × .002)/(.2 × .02 × .002) = ?

ক
0.0001
খ
0.25
গ
.50
ঘ
0.625

সঠিক উত্তর: খ

0.25

উত্তর

সঠিক উত্তর: খ

0.25

খ

ব্যাখ্যা

Question (.1 × .01 × .002)/(.2 × .02 × .002) = ?

Solution:
(.1 × .01 × .002)/(.2 × .02 × .002)
= 0.000002/0.000008
= 2/8
= 1/4
= 0.25

১০,৯৫০.

Let N be the smallest positive integer that is divisible by both 18 and 24. How many distinct prime factors does N have?

ক
2
খ
3
গ
5
ঘ
6

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: Let N be the smallest positive integer that is divisible by both 18 and 24. How many distinct prime factors does N have?

Solution:
এখানে, N হলো 18 এবং 24 দ্বারা বিভাজ্য ক্ষুদ্রতম সংখ্যা।
সুতরাং, N হবে 18 এবং 24 এর ল.সা.গু।

এখন, 18 = 2 × 3 × 3 = 2¹ × 3²
এবং 24 = 2 × 2 × 2 × 3 = 2³ × 3¹

LCM(18, 24) = 2³ × 3² = 8 × 9 = 72
অতএব, N = 72

72 এর মৌলিক উৎপাদক = 2³ × 3²

স্বতন্ত্র মৌলিক উৎপাদকগুলি হলো 2 এবং 3।

∴ N এর স্বতন্ত্র মৌলিক উৎপাদকের সংখ্যা হলো 2টি।

১০,৯৫১.

A bag contains 45 marbles, 15 of which are red. If one marble is picked at random, what is the probability that it is not red?

ক
1/3
খ
3/4
গ
2/3
ঘ
2/15

সঠিক উত্তর: গ

2/3

উত্তর

সঠিক উত্তর: গ

2/3

গ

ব্যাখ্যা

Question: A bag contains 45 marbles, 15 of which are red. If one marble is picked at random, what is the probability that it is not red?

Solution:
Given that,
Total marbles = 45
Red marbles = 15
∴ Non-red marbles = 45 - 15 = 30

∴ Probability of picking a non-red marble = Number of non-red marbles/Total marbles
= 30/45
= 2/3

১০,৯৫২.

The average weight of 47 balls is 4 g. If the weight of the bag (in which the balls are kept) be included; the calculated average weight per ball increases by 0.3 g. What is the weight of the bag?

ক
14.1 g
খ
16.1 g
গ
18.1 g
ঘ
30 g

সঠিক উত্তর: ক

14.1 g

উত্তর

সঠিক উত্তর: ক

14.1 g

ক

ব্যাখ্যা

Question: The average weight of 47 balls is 4 g. If the weight of the bag (in which the balls are kept) be included; the calculated average weight per ball increases by 0.3 g. What is the weight of the bag?

Solution:

Total increased weight

= 0.3 × 47

= 14.1 g

১০,৯৫৩.

A car covers a distance of 15 km in 15 minutes. If its speed is decreased by 10 km/h, then the time taken by it to cover the distance of 20 km will be-

ক
26 minutes
খ
30 minutes
গ
24 minutes
ঘ
20 minutes

সঠিক উত্তর: গ

24 minutes

উত্তর

সঠিক উত্তর: গ

24 minutes

গ

ব্যাখ্যা

Question: A car covers a distance of 15 km in 15 minutes. If its speed is decreased by 10 km/h, then the time taken by it to cover the distance of 20 km will be-

Solution:
Given,
15 minutes covers 15 km
∴ 1 minutes = 15/15 km
= 1 km
∴ 60 minutes or 1 hours = (1 × 60) km
= 60 km

If its speed is decreased by 10 km/h
Then new speed = (60 - 10) km
= 50 km/h

∴ 1 km cover in (60 ÷ 50) minutes
= 6/5 minutes
∴ 20 km cover in = (6/5 × 20) minutes
= 24 minutes

১০,৯৫৪.

Courier charges for packages to a certain destination are Tk. 95 for the first 300 grams and Tk 10 for each additional 100 grams or part thereof. What could be the weight in grams of a package for which the charge is Tk. 165?

ক
900 grams
খ
1000 grams
গ
1150 grams
ঘ
1190 grams
ঙ
1200 grams

সঠিক উত্তর: খ

1000 grams

উত্তর

সঠিক উত্তর: খ

1000 grams

খ

ব্যাখ্যা

Question: Courier charges for packages to a certain destination are Tk. 95 for the first 300 grams and Tk 10 for each additional 100 grams or part thereof. What could be the weight in grams of a package for which the charge is Tk. 165?

Solution:
Let
the additional is 100x grams
Additional 100 grams requires Tk.10
∴ Additional 100x grams requires Tk. (10 × 100x)/100 = Tk. 10x

ATQ,
95 + 10x = 165
⇒ 10x = 70
∴ x = 7

∴ The additional weight = 100 × 7 = 700 grams
∴ Total weight will be = 700 + 300 = 1000 grams

১০,৯৫৫.

Jashim and Imran start walking from A to B at 5 and 3 km per hour respectively. Jashim reaches B and starts back for A. How far from B will he meet Imran if the distance between A and B is 32 km?

ক
ক) 6
খ
খ) 8
গ
গ) 9
ঘ
ঘ) 12

সঠিক উত্তর: খ

খ) 8

উত্তর

সঠিক উত্তর: খ

খ) 8

খ

ব্যাখ্যা

Question: Jashim and Imran start walking from A to B at 5 and 3 km per hour respectively. Jashim reaches B and starts back for A. How far from B will he meet Imran if the distance between A and B is 32 km?

Solution:
A থেকে B এর দূরত্ব = 32 কি.মি
Jashim এবং Imran B থেকে x কি.মি দূরে পরস্পর সাক্ষাৎ করে।

প্রশ্নমতে
(32 + x)/5 = (32 - x)/3 [তাদের ভ্রমণের সময় সমান]
⇒ 3x + 96 = 160 - 5x
⇒ 3x + 5x = 160 - 96
⇒ 8x = 64
⇒ x = 64/8
x = 8 কি.মি

১০,৯৫৬.

The value of √(10 + √(25 + √(108 + √(154 + √225)))) is:

ক
ক) 6
খ
খ) 2
গ
গ) 4
ঘ
ঘ) 8

সঠিক উত্তর: গ

গ) 4

উত্তর

সঠিক উত্তর: গ

গ) 4

গ

ব্যাখ্যা

√(10 + √(25 + √(108 + √(154 + √225))))
= √(10 + √(25 + √(108 + √(154 + 15))))
= √(10 + √(25 + √(108 + √169)))
= √(10 + √(25 + √(108 + 13)))
= √(10 + √(25 + √121))
= √(10 + √(25 + 11))
= √(10 + √36)
= √(10 + 6)
= √16
= 4

১০,৯৫৭.

A sum becomes 4 times at simple interest in 10 years. What is the rate of interest?

ক
ক) 10%
খ
খ) 20%
গ
গ) 30%
ঘ
ঘ) 40%
ঙ
ঙ) 50%

সঠিক উত্তর: গ

গ) 30%

উত্তর

সঠিক উত্তর: গ

গ) 30%

গ

ব্যাখ্যা

Here, the sum becomes 4 times that means 100, becomes 400.
Rate of such question is given by
R = interest/time = 300/10 = 30%

১০,৯৫৮.

5 workers can complete work in 21 days. In how many days, 15 workers can complete the work?

ক
ক) 4 days
খ
খ) 5 days
গ
গ) 6 days
ঘ
ঘ) 7 days

সঠিক উত্তর: ঘ

ঘ) 7 days

উত্তর

সঠিক উত্তর: ঘ

ঘ) 7 days

ঘ

ব্যাখ্যা

Question: 5 workers can complete work in 21 days. In how many days, 15 workers can complete the work?

Solution:
5 workers can complete work in 21 days
1 workers can complete work in 5 × 21 days
= 105 days
15 workers can complete work in 105/15 days
= 7 days

১০,৯৫৯.

To do a certain work, B would take time thrice as long as A and C together and C twice as long as A and B together. The three men together complete the work in 10 days. The time taken by A to complete the work separately is-

ক
18 days
খ
24 days
গ
26 days
ঘ
32 days

সঠিক উত্তর: খ

24 days

উত্তর

সঠিক উত্তর: খ

24 days

খ

ব্যাখ্যা

Question: To do a certain work, B would take time thrice as long as A and C together and C twice as long as A and B together. The three men together complete the work in 10 days. The time taken by A to complete the work separately is-

Solution:
If B does the work in = 3x days
(A + C) will do the same work in x days.

If C does that work in = 2y days
(A + B) will do it in y days.

∴ (1/x) + (1/3x) = 1/10
⇒ 4/3x = 1/10
⇒ 3x = 40
⇒ x = 40/3
Again,
(1/y) + (1/2y) = 1/10
⇒ 3/2y = 1/10
⇒ 2y = 30
⇒ y = 15

Now, (A + B + C)’s 1 day’s work = 1/10
⇒ (1/A) + (1/40) + (1/30) = 1/10
⇒ 1/A = (1/10) − (1/40) − (1/30)
⇒ 1/A = (12 - 3 - 4)/120
⇒ 1/A = 5/120
⇒ 1/A = 1/24

∴ A alone will complete the work in 24 days.

১০,৯৬০.

A student multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation?

ক
54%
খ
34%
গ
44%
ঘ
64%

সঠিক উত্তর: ঘ

64%

উত্তর

সঠিক উত্তর: ঘ

64%

ঘ

ব্যাখ্যা

Question: A student multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation?

Solution:
Let, the number be x.
Then, error = (5/3)x - (3/5)x
= (25x - 9x)/15
= 16x/15

Error% = {(16x/15) × (3/5x) × 100}%
= 64%

১০,৯৬১.

The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 5 years hence?

ক
ক) 50
খ
খ) 60
গ
গ) 70
ঘ
ঘ) 80

সঠিক উত্তর: গ

গ) 70

উত্তর

সঠিক উত্তর: গ

গ) 70

গ

ব্যাখ্যা

According to the question,
A + B = 60,
A = 2B
2B + B = 60
⇒ B = 20 then A = 40.

5 years,
their ages will be 45 and 25.
Sum of their ages = 45 + 25
= 70.

১০,৯৬২.

(√8–√4–√2) equales:

ক
ক) 2−√2
খ
খ) √2–2
গ
গ) 2
ঘ
ঘ) -2

সঠিক উত্তর: খ

খ) √2–2

উত্তর

সঠিক উত্তর: খ

খ) √2–2

খ

ব্যাখ্যা

(√8–√4–√2)
=2√2–2−√2
=2√2–√2–2
=√2–2

১০,৯৬৩.

How many poles can be erected along fence of 200 feet at equal distance of 20 feet?

ক
ক) 10
খ
খ) 11
গ
গ) 12
ঘ
ঘ) 14

সঠিক উত্তর: খ

খ) 11

উত্তর

সঠিক উত্তর: খ

খ) 11

খ

ব্যাখ্যা

Question: How many poles can be erected along fence of 200 feet at equal distance of 20 feet?

Solution:
প্রথম ২০ ফুট এর জন্য খুঁটি লাগবে ২ টি
বাকি ১৮০ ফুট এর জন্য খুঁটি লাগবে = ১৮০/২০ = ৯ টি

∴ মোট খুঁটি লাগবে = ৯ + ২ = ১১ টি

১০,৯৬৪.

A circle touches all four sides of a quadrilateral PQRS. If PQ = 11 cm. QR = 12 cm and PS = 8 cm. Then what is the length of RS?

ক
3
খ
6
গ
9
ঘ
12

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: A circle touches all four sides of a quadrilateral PQRS. If PQ = 11 cm. QR = 12 cm and PS = 8 cm. Then what is the length of RS?

Solution:

If a circle touches all four sides of quadrilateral PQRS then,
PQ+ RS = SP+ RQ

So,
11 + RS = 8+ 12
⇒ RS = 20 - 11
⇒ RS = 9

১০,৯৬৫.

ক
9
খ
0
গ
3
ঘ
7

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question:

Solution:

১০,৯৬৬.

Which of the following is a rational number?

ক
ক) √3 × √9
খ
খ) √2 × √4
গ
গ) √2 × √8
ঘ
ঘ) √2 × √9

সঠিক উত্তর: গ

গ) √2 × √8

উত্তর

সঠিক উত্তর: গ

গ) √2 × √8

গ

ব্যাখ্যা

Question: Which of the following is a rational number?

Solution:
We know,
Rational number × Irrational number = Irrational Number.
Here,
√3 × √9 = √3 × 3 = 3√3 is a irrational number.
√2 × √4 = 2√2 is a irrational number.
√2 × √8 = √16 = 4 is a rational number.
√2 × √9 = √2 × 3 = 3√2 is a irrational number.

১০,৯৬৭.

The ratio of the salary of A, B and C is 7 : 5 : 3. If C gets Tk. 222 less than what B gets, then what is the salary of A?

ক
ক) Tk. 770
খ
খ) Tk. 777
গ
গ) Tk. 780
ঘ
ঘ) Tk. 788

সঠিক উত্তর: খ

খ) Tk. 777

উত্তর

সঠিক উত্তর: খ

খ) Tk. 777

খ

ব্যাখ্যা

Question: The ratio of the salary of A, B and C is 7 : 5 : 3. If C gets Tk. 222 less than what B gets, then what is the salary of A?

Solution:
Let,
A gets 7x
B gets 5x
C gets 3x

ATQ,
3x = 5x - 222
⇒ 5x - 3x = 222
⇒ 2x = 222
∴ x = 111

∴ The salary of A is 7 × 111 = 777 Tk.

১০,৯৬৮.

A, B and C enter into a partnership with capitals in the ratio 5:6:8. At the end of the business term, they received the profit in the ratio 5:3:12. Find the ratio of time for which they contributed their capitals?

ক
ক) 2 : 1 : 3
খ
খ) 1 : 2 : 3
গ
গ) 2 : 3 : 1
ঘ
ঘ) 3 : 2 : 1

সঠিক উত্তর: ক

ক) 2 : 1 : 3

উত্তর

সঠিক উত্তর: ক

ক) 2 : 1 : 3

ক

ব্যাখ্যা

Profit= Time×Capital invested
Time= Profit/ Capital invested
Required ratio of time
=5/5:3/6:12/8
=1:1/2:3/2
=2:1:3

১০,৯৬৯.

If 5 men and 2 boys working together can do four times as much work per hour as a man and a boy together, Working capacities of a man and a boy are in the ratio:

ক
ক) 3 : 1
খ
খ) 2 : 1
গ
গ) 4 : 1
ঘ
ঘ) 6 : 1

সঠিক উত্তর: খ

খ) 2 : 1

উত্তর

সঠিক উত্তর: খ

খ) 2 : 1

খ

ব্যাখ্যা

Qustion: If 5 men and 2 boys working together can do four times as much work per hour as a man and a boy together, Working capacities of a man and a boy are in the ratio:

Solution:
Let
1 man 1 day work = x
1 boy 1 day work = y

Now
5x + 2y = 4(x + y)
5x + 2y = 4x + 4y
5x - 4x = 4y - 2y
x = 2y
x/y = 2/1
x : y = 2 : 1

১০,৯৭০.

An agent allows a rebate of 4% to an investor while the bank pays an interest of 14% on the investment. What is the actual rate of interest earned by the investor on his investment?

ক
18.75%
খ
18%
গ
17.75%
ঘ
16%

সঠিক উত্তর: ক

18.75%

উত্তর

সঠিক উত্তর: ক

18.75%

ক

ব্যাখ্যা

Let the investor invests Tk. 100

Rebate given = 4%

So, the actual investment = 100 - 4
= 96

The bank pays interest of 14% on the investment which is Tk. 100 without rebate and Tk. 96 with rebate.
Therefore required rate of interest = (114 - 96)/96 × 100
= 18.75%

১০,৯৭১.

A short distance athlete has taken 60 seconds to cover 100 meters. If he makes 30 steps in 9 seconds, how many steps has he taken in that time?

ক
ক) 130
খ
খ) 170
গ
গ) 173
ঘ
ঘ) None of these

সঠিক উত্তর: ঘ

ঘ) None of these

উত্তর

সঠিক উত্তর: ঘ

ঘ) None of these

ঘ

ব্যাখ্যা

In 9 sec the athlete makes 30 steps
∴ In 60 sec the athlete will make = (30×60)/9 = 200 steps

১০,৯৭২.

Three numbers are in the ratio 4 : 5 : 6 and their average is 25. The largest number is:

ক
30
খ
42
গ
32
ঘ
36

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question; Three numbers are in the ratio 4 : 5 : 6 and their average is 25. The largest number is:

Solution:
Let the three numbers be 4x, 5x and 6x

According to the question,
(4x + 5x + 6x) /3 = 25
⇒ 15x = 25 × 3
⇒ 15x = 75
⇒ x = 75/15 =5

largest number = 6x = 6 × 5 = 30

১০,৯৭৩.

A sells an article to B at gain of 25% B sells it to C at a gain of 20% and C sells it to D at a gain 10%. If D pays Tk. 330 for it, how much did it cost to A?

ক
Tk. 180
খ
Tk. 200
গ
Tk. 225
ঘ
Tk. 250

সঠিক উত্তর: খ

Tk. 200

উত্তর

সঠিক উত্তর: খ

Tk. 200

খ

ব্যাখ্যা

Question: A sells an article to B at gain of 25% B sells it to C at a gain of 20% and C sells it to D at a gain 10%. If D pays Tk. 330 for it, how much did it cost to A?

Solution:
Let,
Cost Price for A was = 100

Then, CP for B = (100 + 25% of 100) = 125
CP for C = (125 + 20% of 125) = 150
CP for D = (150 + 10% of 150 ) = 165

But, D pay Tk. 660. Then it must be equal to,
165 = 330
1 = 330/165
∴ 100 = {330 × (100/165)} = 200

So, CP for A = Tk. 200

১০,৯৭৪.

If 'a' is an odd number and 'b' is an even number, which one of the following must be an even number?

ক
a² + b²
খ
ab + 1
গ
a + b
ঘ
(a + b)² + 1

সঠিক উত্তর: ঘ

(a + b)² + 1

উত্তর

সঠিক উত্তর: ঘ

(a + b)² + 1

ঘ

ব্যাখ্যা

Question: If 'a' is an odd number and 'b' is an even number, which one of the following must be an even number?

Solution:
Suppose, a = 1 and b = 2

a + b = 1 + 2 = 3
ab + 1 = 1 × 2 + 1 = 3
a² + b²= 1² + 2² = 5
(a + b)² + 1 = (1 + 2)² + 1 = 10

১০,৯৭৫.

An item sells for 250 taka and includes a 25% profit. How much did it originally cost?

ক
Tk. 200
খ
Tk. 180
গ
Tk. 220
ঘ
Tk. 160

সঠিক উত্তর: ক

Tk. 200

উত্তর

সঠিক উত্তর: ক

Tk. 200

ক

ব্যাখ্যা

Question: An item sells for 250 taka and includes a 25% profit. How much did it originally cost?

Solution:
ধরি,
ক্রয়মূল্য = 100 টাকা
∴ 25% লাভে বিক্রয়মূল্য = 100 + (100 এর 25%) = 100 + 25 = 125 টাকা

দেওয়া আছে,
বিক্রয়মূল্য = 250 টাকা

এখন,
বিক্রয়মূল্য 125 টাকা হলে ক্রয়মূল্য = 100 টাকা
∴ বিক্রয়মূল্য 1 টাকা হলে ক্রয়মূল্য = 100/125 টাকা
∴ বিক্রয়মুল্য 250 টাকা হলে ক্রয়মূল্য = (100 × 250)/125 = 200 টাকা

১০,৯৭৬.

The product of two numbers is 72 and the sum of their squares is 145. The sum of the numbers is:

ক
7
খ
8
গ
13
ঘ
17

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

ব্যাখ্যা

Question: The product of two numbers is 72 and the sum of their squares is 145. The sum of the numbers is:

Solution:
let the two numbers be x, y

xy = 72
x² + y² = 145
⇒ (x + y)² - 2 × 72 = 145
⇒ (x + y)² = 289
∴ x + y = 17

১০,৯৭৭.

Let x : y = a/b : - b/a, If (x - y) = (a/b + b/a) then x is equal to -

ক
ক) (a - b)/a
খ
খ) (a + b)/a
গ
গ) (a + b)/b
ঘ
ঘ) None of these

সঠিক উত্তর: ঘ

ঘ) None of these

উত্তর

সঠিক উত্তর: ঘ

ঘ) None of these

ঘ

ব্যাখ্যা

Question: Let x : y = a/b : - b/a, If (x - y) = (a/b + b/a) then x is equal to -

Solution:
Given,
⇒ x/y =(a/b)/(-b/a)
⇒ x/y = - a²/b²
⇒ y =(−b²/a²)x

Now,
x - y = a/b + b/a
⇒ x + (b²/a²)x = (a²+ b²)/ab
⇒ x(a²+ b²)/a² = (a²+b²)/ab
⇒ x = a²/ab
⇒ x = a/b

১০,৯৭৮.

The capital stock of a company is Tk. 500000 and is divided into 5000 shares of common stock. If the company pays a dividend of Tk. 64000, what amount will Rakib receive for his 50 shares?

ক
Tk. 700
খ
Tk. 640
গ
Tk. 680
ঘ
None of these

সঠিক উত্তর: খ

Tk. 640

উত্তর

সঠিক উত্তর: খ

Tk. 640

খ

ব্যাখ্যা

Question: The capital stock of a company is Tk. 500000 and is divided into 5000 shares of common stock. If the company pays a dividend of Tk. 64000, what amount will Rakib receive for his 50 shares?

Solution:
5000 shares income Tk. 64000
1 share incomes Tk. 64000/5000
50 shares income Tk. (64000 × 50)/5000
= Tk. 640

১০,৯৭৯.

equals how many eighteenths?

ক
12
খ
14
গ
18
ঘ
15

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

ব্যাখ্যা

Question: equals how many eighteenths?

Solution:
1/2 + 1/3
= 5/6

now,
( 5/6 ) ÷ ( 1/18 )
= 15

১০,৯৮০.

The radii of two cylinders are in the ratio of 2 : 3 and their heights are in the ratio of 5 : 3. The ratio of their volume is-

ক
4 : 9
খ
9 : 4
গ
20 : 27
ঘ
20 : 25

সঠিক উত্তর: গ

20 : 27

উত্তর

সঠিক উত্তর: গ

20 : 27

গ

ব্যাখ্যা

Question: The radii of two cylinders are in the ratio of 2 : 3 and their heights are in the ratio of 5 : 3. The ratio of their volume is-

Solution:
Let the radius of both cylinders be 2x and 3x.
Let the height of both cylinders be 5y and 3y.

Ratio of the volume of two cylinders = {π × (2x)² × (5y)}/{π × (3x)² × (3y)}
= (4x² × 5)/(9x² × 3)
= 20/27

∴ Ratio = 20 : 27

১০,৯৮১.

66 cubic centimeters of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:

ক
64 m
খ
82 m
গ
74 m
ঘ
84 m

সঠিক উত্তর: ঘ

84 m

উত্তর

সঠিক উত্তর: ঘ

84 m

ঘ

ব্যাখ্যা

Question: 66 cubic centimeters of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:

Solution:
Let, the length of the wire be h
Radius = 1/2 mm = 1/20 cm

ATQ,
πr²h = 66
⇒ (22/7) × (1/20)² × h = 66
⇒ h = (66 × 7 × 20 × 20)/22
⇒ h = 8400 cm
⇒ h = 8400/100 m
∴ h = 84 m

১০,৯৮২.

In what ratio a mixture of 30% alcohol strength be mixed with that of 50% alcohol strength so as to get a mixture of 45% alcohol strength?

ক
1 : 2
খ
1 : 3
গ
1 : 5
ঘ
1 : 4

সঠিক উত্তর: খ

1 : 3

উত্তর

সঠিক উত্তর: খ

1 : 3

খ

ব্যাখ্যা

Question: In what ratio a mixture of 30% alcohol strength be mixed with that of 50% alcohol strength so as to get a mixture of 45% alcohol strength?

Solution:
Let, X contains 30% alcohol strength and
Y contains 50% alcohol strength

According to the question,
(30% of X) + (50% of Y) = 45% of (X + Y)
⇒ 30X + 50Y = 45X + 45Y
⇒ 15X = 5Y
⇒ X : Y = 1 : 3

১০,৯৮৩.

In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?

ক
5/7
খ
1/7
গ
1/2
ঘ
1/5
ঙ
2/7

সঠিক উত্তর: ঙ

2/7

উত্তর

সঠিক উত্তর: ঙ

2/7

ঙ

ব্যাখ্যা

Question: In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?

Solution:
Total number of outcomes possible, n(S) = 10 + 25 = 35
Total number of prizes, n(E) = 10

∴ P(E) = n(E)/n(S) =10/35 =2/7

১০,৯৮৪.

31, 29, 24, 22, 17, ... What number should come next?

ক
1
খ
12
গ
15
ঘ
11

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: 31, 29, 24, 22, 17, ... What number should come next?

Solution:
31 - 29 = 2
29 - 24 = 5
24 - 22 = 2
22 - 17 = 5
17 - 15 = 2

next number is 15

১০,৯৮৫.

In how many ways can 5 people from a group of 8 people be seated around a circular table?

ক
120
খ
672
গ
872
ঘ
1344

সঠিক উত্তর: ঘ

1344

উত্তর

সঠিক উত্তর: ঘ

1344

ঘ

ব্যাখ্যা

Question: In how many ways can 5 people from a group of 8 people be seated around a circular table?

Solution:
প্রথমে,
৮ জনের মধ্যে থেকে ৫ জন বেছে নেওয়ার উপায় = ⁸C₅
= 8!/{5!(8 - 5)!}
= 8!/(5! × 3!)
= 56

এবং,
এই ৫ জনকে বৃত্তাকার টেবিলে বসানোর উপায় = (5 - 1)!
= 4!
= 24

∴ মোট উপায় = 56 × 24
= 1344

১০,৯৮৬.

The speed of a boat in still water is 10 km/hr. If it can travel 26 km downstream and 14 km upstream at the same time, the speed of the stream is-

ক
5 km/hr
খ
2.5 km/hr
গ
6 km/hr
ঘ
3 km/hr

সঠিক উত্তর: ঘ

3 km/hr

উত্তর

সঠিক উত্তর: ঘ

3 km/hr

ঘ

ব্যাখ্যা

Question: The speed of a boat in still water is 10 km/hr. If it can travel 26 km downstream and 14 km upstream at the same time, the speed of the stream is-

Solution:
Let the speed of the stream be x km/hr
Then speed downstream = (10 + x) km/hr
Speed upstream = (10 − x)km/hr

∴26/(10 + x) = 14/(10 − x)
⇒ 260 − 26x = 140 + 14x
⇒ 40x = 120
⇒ x = 3 km/hr

১০,৯৮৭.

In a 600-meter race, C starts 60 meters ahead of D, yet D defeats C by a margin of 30 meters. What distance did C cover when D reached the finish line?

ক
480 meters
খ
520 meters
গ
510 meters
ঘ
500 meters

সঠিক উত্তর: গ

510 meters

উত্তর

সঠিক উত্তর: গ

510 meters

গ

ব্যাখ্যা

Question: In a 600 meter race, C starts 60 meters ahead of D, yet D defeats C by a margin of 30 meters. What distance did C cover when D reached the finish line?

Solution:
In a 600 meter race,
C starts 60 meters ahead.
so C needs to cover = 600 - 60 = 540 meters
D covers the full distance = 600 meters

D defeats C by 30 meters

∴ When D finishes,
C’s distance = 540 - 30 = 510 meters.

১০,৯৮৮.

The length of a rectangular plot is 10 meters less than three times its breadth. If the cost of fencing the plot at Tk 50 per meter is Tk 15000, what is the length of the plot in meters?

ক
100 meters
খ
110 meters
গ
90 meters
ঘ
120 meters

সঠিক উত্তর: খ

110 meters

উত্তর

সঠিক উত্তর: খ

110 meters

খ

ব্যাখ্যা

Question: The length of a rectangular plot is 10 meters less than three times its breadth. If the cost of fencing the plot at Tk 50 per meter is Tk 15000, what is the length of the plot in meters?

Solution:
Let the breadth of the plot be x meters.
Then, the length of the plot is 3x - 10 meters.

Perimeter of the rectangle = 2 × (Length + breadth)
= 2 × (x + 3x - 10 )
= 2 × (4x - 10 )
= 8x - 20

Given,
Cost of fencing per meter = Tk 50
Total cost = Tk 15000

So, Perimeter × 50 = 15000
⇒ (8x - 20) × 50 = 15000
⇒ 8x - 20 = 15000/50
⇒ 8x = 300 + 20
⇒ 8x = 320
∴ x = 40

∴ Breadth = 40 meters.
and length = 3x - 10 = 3 × 40 - 10 = 110 meters.

১০,৯৮৯.

Alcohol and water in two vessels A and B are in the ratio 5 : 3 and 5 : 4 respectively. In what ratio, the liquid of both the vessels be mixed to obtain a new mixture in vessel C in the ratio 7 : 5?

ক
ক) 2 : 3
খ
খ) 3 : 2
গ
গ) 3 : 5
ঘ
ঘ) 2 : 5
ঙ
ঙ) 2 : 1

সঠিক উত্তর: ক

ক) 2 : 3

উত্তর

সঠিক উত্তর: ক

ক) 2 : 3

ক

ব্যাখ্যা

According to the question,
Alcohol : Water -
Vessel A - 4 : 3
Vessel B - 2 : 3
Now using alligation,

১০,৯৯০.

A train running at a speed of 72 km/hr crosses a platform double its length in 1 minute. What is the length of the platform in metres?

ক
600 metres
খ
800 metres
গ
700 metres
ঘ
680 metres

সঠিক উত্তর: খ

800 metres

উত্তর

সঠিক উত্তর: খ

800 metres

খ

ব্যাখ্যা

Question: A train running at a speed of 72 km/hr crosses a platform double its length in 1 minute. What is the length of the platform in metres?

Solution:
Speed of the train = 72 km/h
The platform is double the length of the train
Time to cross the platform = 1 minute = 60 seconds

∴ Speed = (72 × 1000)/(60 × 60) = 20 m/s

Let, the length of the train is x
Then, the length of the platform = 2x

∴ Total distance to cross the platform = x + 2x = 3x

We know,
Distance = Speed × Time
⇒ 3x = 20 × 60 =1200
⇒ 3x = 1200
⇒ x = 1200/3
∴ x = 400

So, length of the platform = 2x = 2 × 400 = 800 metres.

১০,৯৯১.

A triangle has a perimeter 13. The two shorter side, have integer lengths equal to x and x + 1. Which of the following could be the length of the other side.

ক
2
খ
6
গ
8
ঘ
None

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: A triangle has a perimeter 13. The two shorter side, have integer lengths equal to x and x + 1. Which of the following could be the length of the other side.

Solution:
The shorter sides have integer lengths equal to x and x + 1
Let the longest side be 'a'
∴ a + x + (x + 1) = 13
⇒ a + 2x = 12 .......(1)

We know that the sum of the lengths of the shorter sides has to be more than the length of the longer one
Looking at the options, we can't have 8 or 10 as values for 'a'

Similarly, we can't have 2 as values for 'a' as it wouldn't be the longest side then.

So, the correct length of other side is 6

১০,৯৯২.

The top of a 15 metre high tower makes an angle of elevation of 60° with the bottom of an electric pole and angle of elevation of 30° with the top of the pole. What is the height of the electric pole?

ক
5 metre
খ
8 metre
গ
10 metre
ঘ
12 metre

সঠিক উত্তর: গ

10 metre

উত্তর

সঠিক উত্তর: গ

10 metre

গ

ব্যাখ্যা

Question: The top of a 15 metre high tower makes an angle of elevation of 60° with the bottom of an electric pole and angle of elevation of 30° with the top of the pole. What is the height of the electric pole?

Solution:

Let,
AB be the tower and CD be the electric pole
Then ∠ACB = 60°, ∠EDB = 30° and AB = 15 m
Let,
CD = h.
Then BE = (AB – AE)
= (AB - CD) =
(15 - h)

We have
AB/AC = tan 60° = √3
⇒ AC = AB/√3 = 15/√3

And,
BE/DE = tan30° = 1/√3
⇒ DE = (BE × √3) = √3 (15 - h) [DE = AC = 15/√3]
⇒ 15/√3 = √3 (15 - h)
⇒ 3(15 - h) = 15
⇒ 3h = 45 - 15
⇒ 3h = 30
∴ h = 10 m

১০,৯৯৩.

January 2, 2007 was Tuesday. What will be the day on January 2, 2008?

ক
Monday
খ
Tuesday
গ
Wednesday
ঘ
Thursday

সঠিক উত্তর: গ

Wednesday

উত্তর

সঠিক উত্তর: গ

Wednesday

গ

ব্যাখ্যা

Question: January 2, 2007 was Tuesday. What will be the day on January 2, 2008?

Solution:
January 2, 2007 was Tuesday
∴ January 1, 2007 was Monday

2007 is not a leap year so the last day of the year is as same as first day.
∴ December 31, 2007 will be Monday.

January 1, 2008 will be Tuesday
January 2, 2008 will be Wednesday.

১০,৯৯৪.

In June a baseball team that played 60 games had won 30% of its games played. After a phenomenal winning streak this team raised its average to 50%. How many games must the team have won in a row to attain this average?

ক
ক) 30
খ
খ) 45
গ
গ) 20
ঘ
ঘ) 24

সঠিক উত্তর: ঘ

ঘ) 24

উত্তর

সঠিক উত্তর: ঘ

ঘ) 24

ঘ

ব্যাখ্যা

Let, Additional match = x
Now,
(30% of 60) + x = 50% of (60+x)
⇒ 18 + x = 30 + 0.5x
⇒ 0.5x = 12
⇒ x = 24

১০,৯৯৫.

A man purchases two clocks A and B at a total cost of Tk. 650. He sells A with a 20% profit and B at a loss of 25% and gets the same selling price for both clocks. What are the purchasing prices of A and B respectively?

ক
225, 425
খ
275, 375
গ
300, 350
ঘ
250, 400

সঠিক উত্তর: ঘ

250, 400

উত্তর

সঠিক উত্তর: ঘ

250, 400

ঘ

ব্যাখ্যা

Question: A man purchases two clocks A and B at a total cost of Tk. 650. He sells A with a 20% profit and B at a loss of 25% and gets the same selling price for both clocks. What are the purchasing prices of A and B respectively?

Solution:
Let
selling price for both clocks is x taka

Purchasing price of A is = x/1.2 taka
Purchasing price of B is = x/0.75 taka

Now
(x/1.2) + (x/0.75 ) = 650
⇒ (100x/120) + (100x/75) = 650
⇒ x/120 + x/75 = 650/100
⇒ x (5 + 8)/600 = 650/100
⇒ x = (650 × 600)/ (100 × 13)
= 300 Taka

Purchasing price of A is = x/1.2 taka = 300/1.2 taka = 250 taka
Purchasing price of B is = x/0.75 taka = 300/0.75 = 400 taka

১০,৯৯৬.

The marked price of a watch was Tk. 1500. A customer bought it for Tk. 1080 after getting two successive discounts. The first discount was 20%. What was the second discount rate?

ক
10%
খ
12%
গ
15%
ঘ
20%

সঠিক উত্তর: ক

10%

উত্তর

সঠিক উত্তর: ক

10%

ক

ব্যাখ্যা

Question: The marked price of a watch was Tk. 1500. A customer bought it for Tk. 1080 after getting two successive discounts. The first discount was 20%. What was the second discount rate?

Solution:
Price after first discount (20%),
= 1500 - (20% of 1500)
= 1500 - (1500 × 0.20)
= 1500 - 300
= Tk. 1200

Amount of second discount
= 1200 − 1080
= Tk. 120

∴ Second discount rate
= (Second discount amount/Price after first discount) × 100
= (120/1200) × 100
= 0.10 × 100
= 10%

∴ The second discount rate is 10%.

১০,৯৯৭.

Two positive numbers are in the ratio 3 : 2. The product of their HCF and LCM is 3456. Find the sum of both the numbers.

ক
186
খ
120
গ
144
ঘ
None of the above

সঠিক উত্তর: খ

120

উত্তর

সঠিক উত্তর: খ

120

খ

ব্যাখ্যা

Question: Two positive numbers are in the ratio 3 : 2. The product of their HCF and LCM is 3456. Find the sum of both the numbers.

Solution:
Let two numbers are 3a and 2a.

HCF × LCM = 1st no. × 2nd no.
⇒ 3456 = 3a × 2a
⇒ 3456 = 6a²
⇒ a² = 576
∴ a = 24

∴ Sum of both the numbers = 3a + 2a = 5a = 5 × 24 = 120

১০,৯৯৮.

A man travels from his home to the office at 4km/hr and reaches his office 20 min late. If the Speed had been 6 km/hr he would have reached 10 min early. Find the distance from his home to office?

ক
ক) 8 km
খ
খ) 12 km
গ
গ) 9 km
ঘ
ঘ) 6 km

সঠিক উত্তর: ঘ

ঘ) 6 km

উত্তর

সঠিক উত্তর: ঘ

ঘ) 6 km

ঘ

ব্যাখ্যা

Let,
The distance between home and office =d
Suppose he reaches the office on Time,
the Time taken = a minutes
Case 1: When he reaches office 20 minutes late,
Time taken = a + 20
Case 2: When he reaches office 10 minutes early,
Time taken = a - 10
As the distance traveled is the same,
The ratio of Speed in case 1 to the Speed in case 2 will be the inverse of the Time taken in both cases.
Ratio of Speed in both cases = 4:6
= 2:3
Ratio of Time in both cases = 3:2
Therefore,
(a + 20)/(a -10)= 3/2
⇒ 2a + 40 = 3a -30
⇒ 3a - 2a = 40 + 30
⇒ a = 70 minutes.
Taking case 1,
4= d/(90/60)
⇒ d= 360/60
= 6 km.

১০,৯৯৯.

In a right angled triangle, two sides are of the same length. Which of the options is one of the angles of that triangle?

ক
ক) 30°
খ
খ) 40°
গ
গ) 45°
ঘ
ঘ) 50°

সঠিক উত্তর: গ

গ) 45°

উত্তর

সঠিক উত্তর: গ

গ) 45°

গ

ব্যাখ্যা

প্রশ্ন: In a right angled triangle, two sides are of the same length. Which of the options is one of the angles of that triangle?

সমাধান:
If two sides of the right angled triangle are equal, it is a right angled isosceles triangle. So, the angles of the triangle are 45°, 45° and 90°

১১,০০০.

(a% of b) + (b% of a) is equal to:

ক
a% of b
খ
2% of ab
গ
2% of 100ab
ঘ
100% of ab

সঠিক উত্তর: খ

2% of ab

উত্তর

সঠিক উত্তর: খ

2% of ab

খ

ব্যাখ্যা

Question: (a% of b) + (b% of a) is equal to:

Solution:
According to question
(a% of b) + (b% of a)
= b × (a/100) + a × (b/100)
= (ab/100) + (ab/100)
= 2ab/100
= 2% of ab