পেট্রোবাংলা প্রিলি ও লিখিত সমন্বিত প্রস্তুতি [Archived]

Let Rakib's present age be x years.
Then, father's present age =(x + 3x) years = 4x years.

⇒ 8x + 16 = 5x + 40
⇒ 3x = 24

∴ x = 8.
Hence, required ratio = (4x + 16)/(x + 16) = 48/24 = 2.

 

Question: Find the average of numbers 87, 84, 86, 90, 82, 88, 78.

Solution:

Question: The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?

Solution:

Question: The average of 4 terms is 20 and the 1st term is 1/3 of the remaining terms. What will be the first number?

Solution:

The difference of age between R and Q = The difference of age between Q and T.

Sum of age of R and T is 50
∴ (R + T) = 50.

R - Q = ?

 

ATQ,

R - Q = Q - T

∴ R + T = 2Q

Now given that, (R + T) = 50

50 = 2Q
∴ Q = 25.

 

Question is (R - Q) = ?

Here we know the value(age) of Q (25), but we don't know the age of R.

∴ (R - Q) cannot be determined.

Question: The average age of A, B and C was 25 years and that of B and C was 25 years. A’s present age is-

Solution:

Question: A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present?

Solution:

Question: The average of 7 consecutive numbers is n. If the next two numbers are included, the average will-

Solution:

Let Rasel's present age be x

Rasel's  age before 10 years = x - 10)

Rasel's  age after 20 years = (x + 20)

We are given that,
Rasel's age after 20 years (x + 20) is 10 times his age 10 years back (x - 10)

Therefore,
(x + 20) = 10(x - 10)

⇒ x + 20 = 10x - 100

⇒ 9x = 120
∴ x = 13.3 years

Question: For 9 innings, Tanveer has an average of 75 runs. In the tenth inning, he scores 100 runs, thus increasing his average. His new average is-

Solution:

Question: Nisha is 15 years elder to Romi. If 5 years ago, Nisha was 3 times as old as Romi, then find Nisha’s present age.

Question:

Question: In a family of 8, the men eat on average 72 kg of food and women eat on an average 50 kg of food. The men and women are equal in number. A hungry woman named Akhi joined the family for dinner and the average consumption became 67. How much did Akhi eat (in kgs)?

Solution:

We are given that age ratio of Hemal : Pavel = 2: 3

Hemal’s age = 2x and Pavel’s age = 3x

One year ago, their age was 2x and 3x.

Hence at present,
Hemal's age = 2x +1 and
Pavel's age = 3x +1

After 5 years,
Hemal’s age = (2x +1) + 5 = (2x + 6)

Pavel's age = (3x +1) + 5 = (3x + 6)

After 5 years, this ratio becomes 4 : 5.
Therefore,

(2x + 6)/(3x + 6) = 4/5

⇒ 10x + 30 = 12x + 24
⇒ 2x = 6
∴ x = 3

Pavel's present age = (3x + 1) = (3 × 3 + 1) = 10 years

Question: In a hotel, the tariff for every odd dates is Tk. 1000 and for even dates is Tk. 2000. If the man paid total of Tk. 30000 in all. For how many days did he stay in the hotel given that the first day is 5th date of the month?

Solution:

Question: Didar is younger to Rohan by 9 years. If their ages are in the respective ratio of 4 : 5, how old is Didar?

Solution:

Question: The average of 5 terms is 50. If the first 4 terms are 45, 42, 119, and 84, what will be the last term?

Solution:

Question: The ratio of Sara’s age 4 years ago and Vaishali’s age after 4 years is 1 : 1. Presently, the ratio of their ages is 5 : 3. Find the ratio between Sara’s age 4 years hence and Vaishali’s age 4 years ago.

Solution:

Sum of all the 8 terms = 320

The sum of first 6 terms = 210

Now , the sum of remaining terms = 320 - 210 = 110

So , the average of 2 terms would be = 110/2 = 55

Question: If the total ages of Iqbal and Shikhar is 12 years more than the total age of Shikhar and Charu. Charu is how many years younger than Iqbal?

Solution:

Question: What is the average of natural numbers from 1 to 67?

 

Solution:
Given, natural numbers 1 to 67.

Average of n natural numbers = (n + 1)/2

Here, n = 67

Average = (67 + 1)/2 = 68/2 = 34

Let the present age of Chandni be x

So, Belal’s present age = 2x

And Arif’s present age = 2 + 2x

According to the question,

x + 2x + 2 + 2x = 27

⇒ 5x + 2 = 27

⇒ 5x = 25

⇒ x = 5

So, Belal’s age = 2 × 5 = 10 years

Question: The average of 7 consecutive numbers is 20. What is the largest of these numbers?

 

Solution:
Let the 7 consecutive numbers be x, x + 1, x + 2, x + 3, x + 4, x + 5 and x + 6,

 

As per the given condition;

[x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6)]/7 = 20

⇒ 7x + 21 = 140

⇒ 7x = 119

⇒ x =17

∴ The largest number = x + 6 = 17 + 6 = 23

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 48 years, find the present age of the son.

Solution:

Question: The average of 10 numbers is 23. If each number is increased by 4, what will the new average be?

 

Solution:
Given,

Average of 10 numbers = 23

⇒ Sum/Total numbers = 23

⇒ Sum/10 = 23

∴ Sum of the 10 numbers = 230

If each number is increased by 4, the total increase = 4 × 10 = 40

New sum = 230 + 40 = 270

Therefore, the new average = 270/10 = 27

Question: The ratio of the present ages of Pranto and Qureshi is 4 : 5. Five years ago, the ratio of their ages was 7 : 9. Find their present ages? (In years)

Solution:

Question: The average of 50 numbers is 20. If two numbers 37 and 43 are discarded, find the average of the remaining numbers.

 

Solution:
Given,

Average of 50 numbers = 20

Sum of 50 numbers = 20 × 50 = 1000

Sum of discarded numbers = 37 + 43 = 80

Sum of remaining numbers = 1000 - 80 = 920

Now, total remaining numbers = 50 - 2 = 48

 

Average of remaining numbers = 920/48 = 19.17

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

Solution:

Question: What is the average of the first six multiples of 4?

 

Solution:
First six multiples of 4 is 4, 8, 12, 16, 20, 24

Average = (4 + 8 + 12 + 16 + 20 + 24)/6

= 84/6

= 14

Question: Ten years ago, the age of mother was three times the age of her son. After ten years, mother’s age will be twice that of his son. Find the ratio of their present ages.

Solution:

Question: The average weight of a group of seven boys is 56 kg. The individual weights (in kg) of six of them are 52, 57, 55, 60, 59 and 55. Find the weight of the seventh boy.

 

Solution:
Average weight of 7 boys = 56 kg.

Total weight of 7 boys = (56 × 7) kg = 392 kg.

 

Total weight of 6 boys = (52 + 57 + 55 + 60 + 59 + 55) kg

= 338 kg.

 

Weight of the 7th boy = (total weight of 7 boys) - (total weight of 6 boys)

= (392 - 338) kg

= 54 kg.

 

Therefore, the weight of the seventh boy is 54 kg.