ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: Find the average of first 20 consecutive natural numbers.

Solution:
The average of first n consecutive natural numbers is
=(n + 1)/2

Here,
n=20

So, average = (20 + 1)/2
= 21/2
= 10.5

Question: Ten years ago, the sum of ages of a father and his son was 34 years. If the ratio of present ages of the father and son is 7 : 2, find the present age of the son.

Solution:
Let the present age of the father is 7x and present age of son is 2x.

As per question, ten years ago;
(7x - 10) + (2x - 10) = 34
⇒ 7x - 10 + 2x - 10= 34
⇒ 9x  = 34 + 20
⇒ 9x = 54
∴ x = 6

∴ Present age of son = 2 × 6= 12 years

Question: If the average of three consecutive even numbers is 34, find the largest of these numbers.

Solution:
Let the first number is x, then the next two even numbers would be x + 2, x + 4

As per question;
(x + x + 2 + x + 4)/3 = 34
⇒ (3x + 6)/3 = 34
⇒ 3x + 6 = 102
⇒ 3x = 96
∴ x = 32

Largest number would be = 32 + 4 = 36

Question: A man said to his son, "I was one-third of your present age when you were born". If the present age of the man is 72 years, find the present age of the son.

Solution:
Present age of the son be P,
∴ he was born P years ago.
The age of the man was: (72 - P).
His age when the son was born should be equal to 1/3 of P.

∴ (72 - P) = P/3
⇒ 216 - 3P = P
⇒ 4P = 216
⇒ P = 54

Question: The average of Jewel's marks in 6 subjects is 74. If his average in five subjects excluding science is 70, how many marks he obtained in science?

Solution:
Total marks obtained in 6 subjects = 6 × 74 = 444

Total marks in 5 subjects excluding science = 5 × 70 = 350

Therefore, marks obtained in science would be = 444 - 350 = 94

Question: Sarah is 50 years old and Nazrul is 40 years old. How long ago was the ratio of their ages 3 : 2?

Solution:
Let us assume x years ago
At present: Sarah is 50 years and Nazrul is 40 years
x years ago: Sarah’s age = (50 - x) and Nazrul's age = (40 - x)

ATQ,
(50 - x)/(40 - x) = 3/2
⇒ 100 - 2x = 120 - 3x
⇒ x = 20

Therefore, the answer is 20 years.

Question: The average weight of 8 women increases by 2.5 kg when a new woman replaces one of them weighing 65 kg. Find the weight of the new woman.

Solution:
Total weight increased = (8 × 2.5) kg = 20 kg.
So, weight of new woman = (65 + 20) kg = 85 kg.

Question: Twelve years ago, Babu was twice as old as Vuttu. If the ratio of their present ages is 4 : 3 respectively, find the difference between their present ages.

Solution:
Let 12 years ago age of Vuttu was x years and age of Babu was 2x.
So, present age of Vuttu = x + 12
And, present age of Babu = 2x + 12

As per question,
(2x + 12)/(x + 12) = 4/3
⇒ 6x + 36 = 4x + 48
⇒ 2x = 12
∴ x = 6

Present age of Vuttu = 6 + 12 = 18 years
Present age of Babu = 2 × 6 + 12 = 24 years

∴ Required difference between their ages = 24 - 18 = 6 years

Question: The captain of a cricket team of 11 members is 26 years old, and the wicket-keeper is three years older than the captain. If the ages of captain and wicketkeeper are excluded, the average age of the remaining players of the team is one year less than the average age of the whole team. What is the average age of the team?

Solution:
Let the average age of the whole team by x years.
Total age of the whole team 11x years
Age of the captain 26 years
Age of the wiket-keeper 26 + 3 = 29 years

The average age of the remaining players after excluding the ages of captain and wicketkeeper = x - 1
∴ Total age of the players without the ages of captain and wicketkeeper = 9(x - 1)

We can say,
11x - (26 + 29) = 9(x - 1)
⇒ 11x - 55 = 9x - 9
⇒ 11x - 9x = - 9 + 55
⇒ 2x = 46
∴ x = 23 Years.

Question: Ten years ago, Alif was 1/3rd as old as Joy. If Alif is 18 years old now, how old is Joy now?

Solution:
Let,
Age of Joy now x years

ATQ,
(x - 10)/3 = (18 - 10)
⇒ x - 10 = 24
⇒ x = 34

∴ The age of Joy now 34 years

Question: The average monthly income of Rakib and Sunny is Tk. 5050. The average monthly income of Sunny and Rabbi is Tk. 6250 and the average monthly income of Rakib and Rabbi is Tk. 5200. What is the monthly income of Rakib?

Solution:
Rakib + Sunny (total income) = 5050 × 2 = 10100 .............. (i)
Sunny + Rabbi (total income) = 6250 × 2 = 12500 .............. (ii)
Rakib + Rabbi (total income) = 5200 × 2 = 10400 ................. (iii)

Adding (i), (ii) and (iii), we get:
2(Rakib + Sunny + Rabbi) = 10100 + 12500 + 10400
⇒ 2(Rakib + Sunny + Rabbi) = 33000
⇒ Rakib + Sunny + Rabbi  = 16500 ........... (iv)

Subtracting (ii) from (iv), we get
Rakib = 16500 - 12500
∴ Rakib = 4000

∴ Rakib's monthly income = Tk. 4000.

Question: The ratio of the ages of Minu and Meera is 4 : 2. If the sum of their ages is 6 years, find the ratio of their ages after 8 years.

Solution:
Let the age of Minu is 4X and age of Meera 2X.

As per question,
4X + 2X = 6
⇒ 6X = 6
∴ X = 1

∴ Minu's age = 4 × 1 = 4 years
∴ Meera's age = 2 × 1 = 2 years

Ratio of their ages after 8 years;
= (4 + 8) : (2 + 8)
= 12 : 10
= 6 : 5

Question: A museum has an average of 510 visitors on Sunday and 240 on other days. Find the average number of visitors per day in a month of 30 days beginning with a Sunday.

Solution:
Since, the month begins with a Sunday, so there will be 5 Sundays and 25 other days in this month.

Total visitors in Sundays = 5 × 510 = 2550
Total visitors in other days = 25 × 240 = 6000

∴ Total visiotors in the whole month = (2550 + 6000) = 8550

∴ Average number of visitors per day of the month = 8550/30 = 285

Question: Four years ago a man was 6 times as old as his son. After 16 years he will be twice as old as his son. What is the present age of man?

Solution:
Let age of son 4 years ago be = X
So, age of man 4 years ago would be = 6X

As per question after 16 years;
2 × age of son = age of man
∴ 2(X + 4 +16) = (6X + 4 + 16)
⇒ 2X + 40 = 6X + 20
⇒ 2X - 6X = 20 - 40
⇒ - 4X = - 20
∴ X = 5

∴ Present age of man = 6X + 4 = 6 × 5 + 4 = 30 + 4 = 34 years

Question: If the number of quantities in group A is 10 and in group B is 8, and their individual average is 24 and 16 respectively, find the combined average of the two groups.

Solution:
The sum of group A = 10 × 24 = 240
The sum of group B = 8 × 16 = 128

∴ Combined Average of the two groups = (240 + 128)/(10 + 8)
= 368/18
= 20.44