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পরীক্ষা - ৬

বিষয়: গণিত - ২
টপিক:
Average; Problems on Ages

প্রশ্ন দেখুন অনুশীলন

পেট্রোবাংলা প্রিলি ও লিখিত সমন্বিত প্রস্তুতি [Archived]

পেট্রোবাংলা প্রিলি ও লিখিত সমন্বিত প্রস্তুতি [Archived] · তারিখ অনির্ধারিত · ৩০ প্রশ্ন

১.

Father is aged three times more than his son Rakib. After 8 years, he would be two and a half times of Rakib's age. After further 8 years, how many times would he be of Rakib's age?

ক
2 times
খ
2.5 times
গ
2.75 times
ঘ
3 times
ঙ
None of these

ব্যাখ্যা

Question: Father is aged three times more than his son Rakib. After 8 years, he would be two and a half times of Rakib's age. After further 8 years, how many times would he be of Rakib's age?

Solution:

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

ATQ,
(4x + 8) = (5/2)(x + 8)

⇒ 8x + 16 = 5x + 40
⇒ 3x = 24

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

২.

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

ক
86
খ
85
গ
84
ঘ
83
ঙ
82

ব্যাখ্যা

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

Solution:

The sum of all the observations here is 87 + 84 + 86 + 90 + 82 + 88 + 78 = 595

Number of observations = 7

So, Average = 595/7 = 85

৩.

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?

ক
10 years
খ
8 years
গ
5 years
ঘ
4 years
ঙ
None of these

ব্যাখ্যা

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:

Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then,
x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50

⇒ 5x = 20
∴ x = 4.

∴ Age of the youngest child = x = 4 years.

৪.

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

ক
30
খ
20
গ
60
ঘ
80
ঙ
None of these

ব্যাখ্যা

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:

Average of 4 terms = 20

Hence, the total sum of 4 terms = 80

Let terms be A, B, C, D

So, the sum will be A + B + C + D = 80

Given,
3A = B + C + D
3A + A = A + B + C + D
4A = A + B + C + D

So, 4A = 80,

A = 20

৫.

Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is definitely the difference between R and Q's age?

ক
1 year
খ
2 years
গ
25 years
ঘ
Data inadequate
ঙ
None of these

ব্যাখ্যা

Question: Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is definitely the difference between R and Q's age?

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.

৬.

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-

ক
30 years
খ
25 years
গ
40 years
ঘ
42 years
ঙ
None of these

ব্যাখ্যা

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:

Average of A,B,C is 25

So, sum of their ages =75

Now, the sum of B and C will be 50 (because their average is 25)

So age of A =75 - 50 = 25 years

৭.

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?

ক
32 years
খ
36 years
গ
40 years
ঘ
48 years
ঙ
None of these

ব্যাখ্যা

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:

Let the mother's present age be x years.

Then, the person's present age = 2x/5 years.

ATQ,

(2x/5) + 8 = (1/2)(x + 8)
(2x + 40)/5 = (x + 8)/2
⇒ 2(2x + 40) = 5(x + 8)
⇒ 4x + 80 = 5x + 40
∴ x = 40

৮.

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

ক
increased by 2.5
খ
remains the same
গ
increased by 1
ঘ
increased by 2
ঙ
None of these

ব্যাখ্যা

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

Solution:

The average of 7 consecutive numbers is n implies that the 4th term is equal to n.

Now if we include next two terms then the average of 9 terms will be the 5th term. Now as the terms are consecutive, so the 5th term will be n + 1.

(1 + 2 + 3 + 4 + 5 + 6 + 7)/7 = 28/7 = 4

(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9)/9 = 45/9 = 5

৯.

What is Rasel's present age, if after 20 years his age will be 10 times his age 10 years back?

ক
6.2 years
খ
7.7 years
গ
10 years
ঘ
13.3 years
ঙ
None of these

ব্যাখ্যা

Question: What is Rasel's present age, if after 20 years his age will be 10 times his age 10 years back?

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

১০.

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-

ক
75
খ
100
গ
72
ঘ
77.5
ঙ
79.5

ব্যাখ্যা

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:

Total score for 9 innings is 75 × 9 = 675

Total score after 10th innings = 675 + 100 = 775

So, average = 775/10 = 77.5

১১.

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.

ক
32.5 years
খ
27.5 years
গ
25 years
ঘ
24.9 years
ঙ
None of these

ব্যাখ্যা

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:

Let age of Romi be y

Nisha is 15 years elder than Romi = (y + 15). So Nisha's age 5 years ago = (y + 15 - 5).

Romi's age before 5 years = (y - 5)

5 years ago, Nisha is 3 times as old as Romi

(y + 15 - 5) = 3 (y - 5)

⇒ (y + 10) = (3y - 15)

⇒ 2y = 25
⇒ y = 12.5

Romi's age = 12.5 years

Nisha's age = (y + 15) = (12.5 + 15) = 27.5 years.

১২.

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)?

ক
115
খ
80
গ
90
ঘ
85
ঙ
None of these

ব্যাখ্যা

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:

As men and women are equal so , there are 4 women and 4 men so, total consumption will be 72 × 4 = 288(by men) and 50 × 4 = 200(by women)

Total consumption = 488.

But after including Akhi the average consumption for 9 people is given to be 67.
So the total consumption will be 67 × 9 = 603.
So, Neetu’s consumption will be = 603 - 488 = 115

১৩.

One year ago, the ratio of Hemal and Pavel ages was 2 : 3 respectively. After five years from now, this ratio becomes 4 : 5. How old is Pavel now?

ক
5 years
খ
25 years
গ
10 years
ঘ
15 years
ঙ
None of these

ব্যাখ্যা

Question: One year ago, the ratio of Hemal and Pavel ages was 2 : 3 respectively. After five years from now, this ratio becomes 4 : 5. How old is Pavel now?

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

১৪.

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?

ক
50
খ
20
গ
40
ঘ
60
ঙ
None of these

ব্যাখ্যা

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:

Total tariff = 30000

So, for odd dates (5th , 7th , and so on) = 1000

And for even dates (6th , 8th and so on ) = 2000

So, the average amount of money for 2 days is Tk. 1500.

So, total amount paid = 30000

So, number of days he stayed in the hotel = 30000/1500 = 20.

১৫.

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

ক
36 years
খ
23 years
গ
29 years
ঘ
Cannot be determined
ঙ
None of these

ব্যাখ্যা

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:

Let Rohan's age be x years.

Then,
Didar's age = (x - 9) years.

(x - 9)/x = 4/5

⇒ 5x - 45 = 4x
∴ x = 45
Hence, Didar's age = (x - 9) = 45 - 9 = 36 years.

১৬.

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

ক
56
খ
- 20
গ
- 40
ঘ
- 50
ঙ
None of these

ব্যাখ্যা

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:

Sum of all the terms = 250

Sum of first four terms = 45 + 42 + 119 + 84 = 290

So, the 5th term should be 250 - 290 = - 40.

১৭.

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.

ক
1 : 3
খ
3 : 1
গ
4 : 3
ঘ
3 : 4
ঙ
None of these

ব্যাখ্যা

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:

Currently, the ratio of their ages is 5 : 3. Suppose, their ages are: 5x and 3x.

Sara’s age 4 years ago = 5x - 4

Vaishali’s age after 4 years = 3x + 4

Ratio of Sara’s age 4 years ago and Vaishali's age after 4 years is 1 : 1

Therefore,

(5x - 4)/(3x + 4) = 1/1
⇒ 5x - 4 = 3x + 4

⇒ 2x = 8
∴ x = 4

We are required to find the ratio between Sara’s age 4 years hence and Vaishali’s age 4 years ago.

Sara's age: (5x + 4)

Vaishali's age: (3x - 4)

Putting the value of x, we get:

(5x + 4)/(3x - 4) = 24/8 = 3/1 = 3 : 1

১৮.

If the average number of 8 terms is given to be 40 and the average of first 6 terms is given to be 35. What is the average of the remaining 2 terms?

ক
30
খ
55
গ
40
ঘ
42
ঙ
None of these

ব্যাখ্যা

Question: If the average number of 8 terms is given to be 40 and the average of first 6 terms is given to be 35. What is the average of the remaining 2 terms?

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

১৯.

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?

ক
11 years
খ
13 years
গ
15 years
ঘ
Cannot be Determined
ঙ
None of the above

ব্যাখ্যা

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:

Let the age of Iqbal be x

Let the age of Shikhar be y

Let the age of Charu be z

Then, according to question,

(x + y) - (y + z) = 12

⇒ x + y - y - z = 12

⇒ x - z = 12

Thus, Charu is 12 years younger than Iqbal

২০.

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

ক
33.5
খ
33
গ
35
ঘ
34
ঙ
36.5

ব্যাখ্যা

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

২১.

Arif is 2 years older than Belal who is twice as old as Chandni. If the total of the ages of Arif, Belal and Chandni be 27, then how old is Belal?

ক
10 years
খ
11 years
গ
12 years
ঘ
13 years
ঙ
15 years

ব্যাখ্যা

Question: Arif is 2 years older than Belal who is twice as old as Chandni. If the total of the ages of Arif, Belal and Chandni be 27, then how old is Belal?

Solution:

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

২২.

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

ক
23
খ
22
গ
24
ঘ
21
ঙ
25

ব্যাখ্যা

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

২৩.

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.

ক
25.7 years
খ
28 years
গ
29.3 years
ঘ
36 years
ঙ
None of these

ব্যাখ্যা

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:

Present age of the son be P, he was born P years ago.

The age of the man was: (48 - P).

His age when the son was born should be equal to 1/3 of P.

(48 - P) =P/3
⇒ 144 - 3P = P
⇒ 4P = 144
∴ P = 36

২৪.

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

ক
63
খ
33
গ
27
ঘ
25
ঙ
None of these

ব্যাখ্যা

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

২৫.

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)

ক
40, 50
খ
18, 25
গ
40, 60
ঘ
20, 25
ঙ
None of these

ব্যাখ্যা

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:

Their present ages be 4x and 5x.

5 years ago, the ratio of their ages was 7 : 9, then
(4x - 5) : (5x - 5) = 7 : 9

⇒ 36x - 45 = 35x - 35
⇒ x = 45 - 35
∴ x = 10.

Their present ages are: 40, 50.

২৬.

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

ক
17.19
খ
19.17
গ
23.17
ঘ
21.17
ঙ
None of these

ব্যাখ্যা

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

২৭.

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

ক
20 years
খ
30 years
গ
40 years
ঘ
25 years
ঙ
None of these

ব্যাখ্যা

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

Solution:

Here, we have to calculate How many years ago the ratio of their ages was 3 : 2.
Let us assume x years ago

At present:
Sazan is 50 years and Nazmul is 40 years

x years ago:
Sazan’s age = (50 - x) and
Nazmul's age = (40 - x)

Given, the ratio of their ages was 3 : 2

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

∴ x = 20

Therefore, the answer is 20 years.

২৮.

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

ক
16
খ
18
গ
14
ঘ
24
ঙ
12

ব্যাখ্যা

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

২৯.

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.

ক
11 : 7
খ
9 : 5
গ
7 : 4
ঘ
7 : 3
ঙ
None of these

ব্যাখ্যা

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:

10 years ago, age of mother was three times the age of her son. Say, the age of son was x and mother's age was 3x.

At present:
Mother's age is (3x + 10) and
son’s age is (x + 10)

After ten years:
Mother's age will be (3x + 10) +10 and
son’s age will be (x + 10) + 10.
Given that, mother’s age is twice that of son after ten years.

(3x + 10) +10 = 2 [(x + 10) + 10]

⇒ (3x + 20) = 2[x + 20]
⇒ 3x + 20 = 2x + 40

∴ x = 20

∴ (3x + 10) : (x + 10) = 70 : 30 = 7 : 3.

৩০.

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.

ক
56 kg
খ
60 kg
গ
58 kg
ঘ
52 kg
ঙ
54 kg

ব্যাখ্যা

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.