Problems on Ages

PrepBank · পাতা ৩ / ৭ · ২০১–৩০০ / ৬০৭

২০১.

Himel is two years older than rasel, who is twice as old as rajib. If the total of the ages of himel, rasel, and rajib is 72, how old is himel?

ক
38 years
খ
28 years
গ
30 years
ঘ
32 years

ব্যাখ্যা

প্রশ্ন: Himel is two years older than rasel, who is twice as old as rajib. If the total of the ages of himel, rasel, and rajib is 72, how old is himel?

সমাধান:

Let,

Rajib's age be = a years

Then, rasel's age = 2a years

Himel's age = (2a + 2) years

ATQ,
(2a + 2) + 2a + a = 72

⇒ 5a = 70

∴ a = 14

Hence, himel's age = (2 × 14) + 2 = 30 years.

২০২.

The present age of Mr. Salman is three times the age of his son. Six years hence , the ratio of their ages will be 5 : 2. What is the present age of Mr. Salman?

ক
54 years
খ
60 years
গ
48 years
ঘ
63 years

ব্যাখ্যা

Question: The present age of Mr. Salman is three times the age of his son. Six years hence , the ratio of their ages will be 5 : 2. What is the present age of Mr. Salman?

Solution:
Let the son's age be x years ,
Then Mr. Salman's age = 3x years
Then,
∴ (3x + 6)/(x + 6) = 5/2
⇒2(3x + 6) = 5(x + 6)
⇒ 6x + 12 = 5x + 30
⇒ 6x - 5x = 30 - 12
⇒ x = 18

∴ Present age of Mr. Salman = 3x years
= (3 × 18) years
= 54 years

২০৩.

The total age of A and B is 15 years more than the total age of B and C . C is how many years younger than A?

ক
30 years
খ
8 years
গ
15 years
ঘ
None of these

ব্যাখ্যা

Question: The total age of A and B is 15 years more than the total age of B and C . C is how many years younger than A?

Solution:
The given condition is,
⇒ A + B = (B + C) + 15
⇒ A + B = B + C + 15
⇒ A + B - B - C = 15
⇒ A - C = 15
⇒ C = A − 15

∴ C is 15 years younger than A.

২০৪.

Fuad, Rubel and Pavel are cousins. Fuad’s age is one-third of Rubel and Pavel is five years elder than Rubel. If the sum of the age of the cousins is 40, find the ages of Fuad.

ক
15 years
খ
35 years
গ
25 years
ঘ
10 years
ঙ
5 years

ব্যাখ্যা

Question: Fuad, Rubel and Pavel are cousins. Fuad’s age is one-third of Rubel and Pavel is five years elder than Rubel. If the sum of the age of the cousins is 40, find the ages of Fuad.

Solution:
Let,
Rubel’s age = x
Fuad’s age = x/3
Pavel’s age = x + 5

ATQ,
Fuad + Rubel + Pavel = 40
(x/3) + x + (x + 5) = 40
⇒ (x/3) + 2x + 5 = 40
⇒ (x + 6x)/3 = 40 - 5
⇒ 7x/3 = 35
⇒ x = (35 × 3)/7 = 15
∴ x = 15 years

∴ Fuad age is = 15 × (1/3) = 5 years.

২০৫.

The average of 4 consecutive numbers is 5.5 . The largest of these numbers is:

ক
5
খ
6
গ
7
ঘ
9

ব্যাখ্যা

প্রশ্ন: The average of 4 consecutive numbers is 5.5 . The largest of these numbers is:

সমাধান:
৪ টি সংখ্যার গড় ৫.৫
৪ টি সংখ্যার সমষ্টি = ৫.৫ × ৪ = ২২

ধরি, সংখ্যাগুলি হল a, a + ১, a + ২, a + ৩
প্রশ্নমতে,
a + a + ১ + a + ২ + a + ৩ = ২২
⇒ ৪a + ৬ = ২২
⇒ ৪a = ১৬
⇒ a = ৪

∴ বড় সংখ্যাটি হল a + ৩
= ৪ + ৩
= ৭

২০৬.

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

২০৭.

5 years ago, sister’s age was 5 times the age of her brother and the sum of present ages of sister and brother is 34 years. What will be the age of her brother after 6 years?

ক
ক) 12 years
খ
খ) 15 years
গ
গ) 13.5 years
ঘ
ঘ) 20 years

ব্যাখ্যা

Question: 5 years ago, sister’s age was 5 times the age of her brother and the sum of present ages of sister and brother is 34 years. What will be the age of her brother after 6 years?

Solution:
Let,
The age of brother 5 years ago was x years
∴ The age of sister 5 years ago was 5x years

The present age of brother is x + 5 years
The present age of sisters is 5x + 5 years

ATQ,
x + 5 + 5x + 5 = 34
⇒ 6x + 10 = 34
⇒ 6x = 24
∴ x = 4

∴ the age of her brother after 6 years will be 4 + 5 + 6 = 15 years

২০৮.

A father said to his son, 'I was as old as you are at the present at the time of your birth'. If the father's age is 52 years now, the son's age five years back was-

ক
19 year
খ
23 year
গ
18 year
ঘ
21 year
ঙ
None

ব্যাখ্যা

Question: A father said to his son, 'I was as old as you are at the present at the time of your birth'. If the father's age is 52 years now, the son's age five years back was-

Solution:
let, at present son is x years old
so, at time of his birth the father was x years old

∴ at present the age of father is = x + x year
= 2x year

2x = 52
⇒ x = 52/2
= 26 year

∴ the son's age five years back was = 26 - 5
= 21 year

২০৯.

A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B?

ক
8
খ
9
গ
10
ঘ
11

ব্যাখ্যা

Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B?

Solution:
Let.
C's age be x years.
Then, B's age = 2x years.
A's age = (2x + 2) years.

ATQ,
(2x + 2) + 2x + x = 27
⇒ 5x = 25
∴ x = 5.

Hence, B's age = 2x = 10 years.

২১০.

The ages of A and B are in the ratio 6 : 5 and the sum of their ages is 44 years. What will be the ratio of their ages after 8 years ?

ক
ক) 4 : 5
খ
খ) 8 : 6
গ
গ) 6 : 9
ঘ
ঘ) 8 : 7

ব্যাখ্যা

Question: The ages of Akash and Belal are in the ratio 6 : 5 and the sum of their ages is 44 years. What will be the ratio of their ages after 8 years ?

Solution:
The ages of Akash and Belal are in the ratio 6 : 5
let, akash is 6x years old and belal is 5x years old
5x + 6x = 44
⇒ 11x = 44
∴ x = 4 years old

So, Akash is 24 years old and belal is 20 years old

After 8 years, Akash is (24 + 8) = 32 years old and belal is (20 + 8) years old
∴ their ratio = 32 : 28
= 8 : 7

২১১.

A is 5 years older than B and 12 years younger than C. B and D are twins. How older is C than D?

ক
17 years
খ
7 years
গ
14 years
ঘ
4 years

ব্যাখ্যা

Question: A is 5 years older than B and 12 years younger than C. B and D are twins. How older is C than D?

Solution:
A এর বয়স = B + 5 বছর
A এর বয়স = C - 12 বছর

যেহেতু
B এবং D যমজ
B = D

∴ B + 5 = C - 12
⇒ D + 5 = C - 12
⇒ C = D + 5 + 12
⇒ C = D + 17

C, D এর চেয়ে 17 বছরের বড়।

২১২.

The present ages of three siblings are in the ratio 4 : 7 : 9. Five years ago, the sum of their ages was 65 years. What is the present age of the eldest sibling?

ক
35 years
খ
45 years
গ
28 years
ঘ
36 years

ব্যাখ্যা

Question: The present ages of three siblings are in the ratio 4 : 7 : 9. Five years ago, the sum of their ages was 65 years. What is the present age of the eldest sibling?

Solution:
Let, present ages of three persons 4x, 7x, 9x

Five years ago, their ages were- (4x - 5), (7x - 5), (9x - 5)

ATQ,
⇒ (4x - 5) + (7x - 5) + (9x - 5) = 65
⇒ 4x + 7x + 9x - 15 = 65
⇒ 20x = 65 + 15
⇒ 20x = 80
⇒ x = 80/20
∴ x = 4

So, eldest person’s present age = 9x = 9 × 4 = 36 years.

২১৩.

Ali got married 7 years ago. His present age is 6/5 times his age at the time of his marriage. What is the present age of Ali?

ক
42 years
খ
44 years
গ
47 years
ঘ
49 years

ব্যাখ্যা

Question: Ali got married 7 years ago. His present age is 6/5 times his age at the time of his marriage. What is the present age of Ali?

Solution:
Let,
Ali's age 7 years ago be x years
His present age is = (x + 7) years

ATQ,
x + 7 = 6x/5
⇒ 5x + 35 = 6x
⇒ x = 35

His present age is = (35 + 7) = 42 years

২১৪.

The present age of three persons are in the ratio 3 : 5 : 6. Four years ago, the sum of their ages was 72 years. The present age of the eldest person is -

ক
32 years
খ
36 years
গ
42 years
ঘ
48 years

ব্যাখ্যা

Question: The present age of three persons are in the ratio 3 : 5 : 6. Four years ago, the sum of their ages was 72 years. The present age of the eldest person is -

Solution:
Let, present ages of three persons 3x, 5x, 6x

Four years ago, their ages were- (3x - 4), (5x - 4), (6x - 4)

ATQ,
⇒ (3x - 4) + (5x - 4) + (6x - 4) = 72
⇒ 3x + 5x + 6x - 12 = 72
⇒ 14x = 72 + 12
⇒ 14x = 84
⇒ x = 84/14
∴ x = 6

So, eldest person’s present age = 6x = 6 × 6 = 36 years.

২১৫.

Jasim was 27 years old when he married Bela. They just celebrated their fifth wedding anniversary, and Bela's age is now 7/8 of Jasim's. How old is Bela?

ক
22 years
খ
25 years
গ
28 years
ঘ
31 years

ব্যাখ্যা

Question: Jasim was 27 years old when he married Bela. They just celebrated their fifth wedding anniversary, and Bela's age is now 7/8 of Jasim's. How old is Bela?

Solution:
jasim's present age = 27 + 5 = 32 years
bela's age = (7/8) × 32 = 28 years

২১৬.

The age of the father ten years ago was thrice the age of his son. Ten years hence, the father's age will be twice the age of his son. What is the ratio of their present ages?

ক
5 : 2
খ
7 : 3
গ
9 : 2
ঘ
13 : 5

ব্যাখ্যা

Question: The age of the father ten years ago was thrice the age of his son. Ten years hence, the father's age will be twice the age of his son. What is the ratio of their present ages?

Solution:
Let,
son's age 10 years ago be x years.
Then, father’s age 10 years ago = 3x years.

Son's present age = (x + 10) years
Father's present age = (3x + 10) years.

according to the question,
(3x + 10) + 10 = 2 (x + 10 + 10)
⇒ 3x + 20 = 2 (x + 20)
⇒ 3x + 20 = 2x + 40
∴ x = 20

Ratio of present ages of father and the son
= (3x + 10)/(x + 10)
= {(3 × 20) + 10}/(20 + 10)
= 70/30
= 7 : 3

২১৭.

Father is 3 times more aged than his daughter. If after 5 years, he would be 3 times of daughter’s age, then further after 5 years, how many times would he be of his daughter’s age?

ক
ক) 1 (1/2) times
খ
খ) 2 times
গ
গ) 2.5 times
ঘ
ঘ) 3 times

ব্যাখ্যা

Let daughter’s age be x and father’s age be 3x.
Father's age is 3 times more aged than his daughter,
therefore father’s present age = x + 3x = 4x
After 5 years,
The father’s age is 3 times more than his daughter's age.
(4x + 5) = 3 (x + 5)
(4x+5) = 3 (x+5)
(4x + 5) = 3 (x + 5)
x = 10

After 5 years it was (4x + 5),
then after further 5 years, father’s age = (4x +10) and daughter’s age = (x + 10)
(4x + 10)/(x + 10)
= [{(4 × 10) + 10}/(10 + 10)]
= 50/20
= 5/2
= 2.5
After further 5 years, the father will be 2.5 times of daughter’s age.

২১৮.

Three years ago, the average of A, B, and C was 27 years and that of A and C, 5 years ago was 20 years. B’s present age is-

ক
ক) 20 years
খ
খ) 30 years
গ
গ) 40 years
ঘ
ঘ) 50 years

ব্যাখ্যা

Question: Three years ago, the average of A, B, and C was 27 years and that of A and C, 5 years ago was 20 years. B’s present age is-

Solution:
Three years ago, the average of A, B, and C was 27 years old
total age 3 years ago = (27 × 3) = 81 years
So, at present their total age is = 81 + 3 + 3 + 3 = 90 years

average of A and C, 5 years ago was 20 years
total age 5 years ago = (20 × 2) = 40 years
At present, total age of A and C is = 40 + 5 + 5 = 50 years

∴ B's present age is = 90 - 50 years = 40 years

২১৯.

The ages of Saha and Akash are in the ratio 9 : 8 respectively. After 5 years, the ratio of their ages will be 10 : 9. What is the difference in their ages?

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

ব্যাখ্যা

Question: The ages of Saha and Akash are in the ratio 9 : 8 respectively. After 5 years, the ratio of their ages will be 10 : 9. What is the difference in their ages?

Solution:
The ages of Saha and Akash are 9x and 8x
After 5 years, the ratio of their ages will be (9x + 5) and (8x + 5)

(9x + 5) /(8x + 5) = 10/9
⇒ 81x + 45 = 80x + 50
⇒ x = 5

∴ the difference in their ages is = 9x - 8x
= x
= 5 years

২২০.

Present ages of Abir and Rubel are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Rubel's present age in years?

ক
22 years
খ
24 years
গ
26 years
ঘ
28 years

ব্যাখ্যা

Question: Present ages of Abir and Rubel are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Rubel's present age in years?

Solution:
Let,
the present ages of Abir and Rubel be 5a years and 4a years respectively

Then,
(5a + 3)/(4a +3) = 11/9
⇒ 9(5a + 3) = 11(4a + 3)
⇒ 45a + 27 = 44a + 33
⇒ 45a - 44a = 33 - 27
⇒ a = 6

∴ Rubal's present age = 4a = 4 × 6 = 24 years

২২১.

Amir is 40 years old and Rezwan is 50 years old. How many years ago was the ratio of their ages 3 : 5?

ক
ক) 10 years
খ
খ) 18 years
গ
গ) 25 years
ঘ
ঘ) 30 years

ব্যাখ্যা

Question: Amir is 40 years old and Rezwan is 50 years old. How many years ago was the ratio of their ages 3 : 5?

Solution:
Let x years ago the ratio of their ages were 3 : 5

ATQ,
(40 - x)/(50 - x) = 3/5
⇒ 200 - 5x = 150 - 3x
⇒ 5x - 3x = 200 - 150
⇒ 2x = 50
∴ x = 25

২২২.

Five siblings, born three years apart, have a combined age of 100 years. What is the age of the youngest one?

ক
24 years
খ
10 years
গ
12 years
ঘ
14 years

ব্যাখ্যা

Question: Five siblings, born three years apart, have a combined age of 100 years. What is the age of the youngest one?

Solution:
Let the ages of siblings be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.

Then,
x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 100
⇒ 5x = 100 - 30
⇒ 5x = 70
⇒ x = 14

∴ Age of the youngest sibling = x = 14 years.

২২৩.

Rakib correctly remembers that his father's birthday is before 20th January but after 16th January, whereas his sister correctly remembers that their father’s birthday is after 18th January but before 23rd January. On which date in January is definitely their father's birthday?

ক
ক) 18
খ
খ) 19
গ
গ) 20
ঘ
ঘ) Missing data

ব্যাখ্যা

According to Rakib 17th, 18th or 19th ...... (i)
According to her sister 19th, 20th, 21st or 22nd ......(ii)
From (i) and (ii) ⇒ 19th
Answer: 19

২২৪.

If 5 years ago, the ratio of age of Hasan and Rina was 1 : 2 and after 15 years from present their ratio would be 5 : 6. Find the age of Rina after 20 years.

ক
30 years
খ
45 years
গ
35 years
ঘ
38 years

ব্যাখ্যা

Question: If 5 years ago, the ratio of age of Hasan and Rina was 1 : 2 and after 15 years from present their ratio would be 5 : 6. Find the age of Rina after 20 years.

Solution:
Let, present age of Hasan be x
and present age of Rina be y.

Then, according to question
(x - 5)/(y - 5) = 1/2
⇒ 2x - 10 = y - 5
⇒ x = (y + 5)/2 .............(1)

Also,
(x + 15)/(y + 15) = 5/6
⇒ 6x + 90 = 5y + 75
⇒ 6x + 15 = 5y

Putting value of x from equation 1, we get
3y + 15 + 15 = 5y
⇒ 2y = 30
⇒ y = 15

∴ Age of Rina after 20 years = 15 + 20 = 35 years.

২২৫.

A mother is twice as old as her son. If 20 years ago, the age of the mother was 10 times the age of the son, what is the present age of the mother?

ক
38 years
খ
40 years
গ
43 years
ঘ
45 years

ব্যাখ্যা

Question: A mother is twice as old as her son. If 20 years ago, the age of the mother was 10 times the age of the son, what is the present age of the mother?

Solution:
Let the age of son = x years
∴ Age of mother would be = 2x years

As per question 20 years ago;
10 (x - 20) = 2x - 20
⇒ 10x - 200 = 2x - 20
⇒ 10x - 2x = - 20 + 200
⇒ 8x = 180
⇒ x = 180/8
∴ x = 22.5

∴ Mother's age is = 2 × 22.5 = 45 years

২২৬.

Six years ago Anika was P times as old as Benu was. If Anika is now 17 years old, how old is Benu now in terms of P?

ক
ক) (11/P) + 6
খ
খ) (P/11) + 6
গ
গ) 17 - (P/6)
ঘ
ঘ) 17/P
ঙ
ঙ) 17p - 6

ব্যাখ্যা

Let Benu’s age now be B.
Anika’s age now is A.
(A - 6) = P(B - 6)
But A is 17 and therefore 11 = P(B - 6)
11/P = B - 6
(11/P) + 6 = B

২২৭.

A father is three times as old as his son. After fifteen years father will be twice as old as his son age that time. What is the present age of the son?

ক
ক) 15 years
খ
খ) 20 years
গ
গ) 30 years
ঘ
ঘ) 45 years

ব্যাখ্যা

Question: A father is three times as old as his son. After fifteen years father will be twice as old as his son age that time. What is the present age of the son?

Solution:
Let, the son's age be x years
and the father's age is = 3x years

ATQ,
3x + 15 = 2(x + 15)
⇒ 3x + 15 = 2x + 30
⇒ x = 15

২২৮.

B’s age after 12 years would be equal to 4 times his age 6 years ago. Find his age 5 years hence?

ক
10 years
খ
12 years
গ
17 years
ঘ
20 years

ব্যাখ্যা

Question: B’s age after 12 years would be equal to 4 times his age 6 years ago. Find his age 5 years hence?

Solution:
Let B’s present age be ‘x’ years.

According to the question,
x + 12 = 4(x - 6)
⇒ x + 12 = 4x - 24
⇒ 3x = 36
⇒ x = 12

∴ B’s present age = 12 years

Therefore, B’s age 5 years hence = 12 + 5 = 17 years

২২৯.

The difference between the ages of a father and his son is 40% of the father’s age. If the son is 18 years old, find the father’s age.

ক
38 years
খ
45 years
গ
30 years
ঘ
40 years

ব্যাখ্যা

Question: The difference between the ages of a father and his son is 40% of the father’s age. If the son is 18 years old, find the father’s age.

Solution:
Let
Let father’s age = x

Then,
x - 18 = 40% of x
⇒ x - 18 = 40x/100
⇒ x - 18 = 2x/5
⇒ x - 2x/5 = 18
⇒ (5x - 2x)/5 = 18
⇒ 3x = 90
∴ x = 30

So the father’s age is 30 years.

২৩০.

Four years ago, the average age of A and B was 18 years. At present the average age of A, B and C is 24 years. What would be the age of C after 4 years.

ক
ক) 26 years
খ
খ) 28 years
গ
গ) 32 years
ঘ
ঘ) 34 years

ব্যাখ্যা

Sum of the ages of A and B, 4 years ago = 18 × 2 = 36 years
Sum of the present age of A and B = 4 + 4 + 36 = 44 years
Sum of the present ages of A, B and C = 24 × 3 = 72 years
⇒ Present age of C = 72 - 44 = 28 years

∴ C's age after 4 years = 28 + 4 = 32 years.

২৩১.

If a 32-year-old man is replaced by a new man, then the average age of 42 men increases by 1 year. What is the age of the new man?

ক
ক) 72 years
খ
খ) 74 years
গ
গ) 76 years
ঘ
ঘ) 77 years

ব্যাখ্যা

প্রশ্ন : If a 32 year old man is replaced by a new man, then the average age of 42 men increases by 1 year. What is the age of the new man?

সমাধান :

Let initially the average age of 42 men be x
⇒ Total age of 42 men = 42x

Now, a 32 year old man is replaced by a new man
⇒ New Total age = 42 × (x + 1)

∴ 42 × (x + 1) - 42x = Age of the New man - 32
⇒ 42x + 42 - 42x = Age of the New man - 32
⇒ Age of the New man - 32 = 42

∴ Age of the New man = 42 + 32 = 74 years

২৩২.

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
ক) 36 years
খ
খ) 38 years
গ
গ) 40 years
ঘ
ঘ) 42 years

ব্যাখ্যা

Let mother's present age be x years
Therefore, person's present age = 2x/5 years
2x/5 + 8 = (x + 8)/2
or, x = 40 years

২৩৩.

4 years ago, the ratio of 1/2 of A’s age that time and four times of B’s age at the time were 5:12. Eight years hence, 1/2 of A’s age at that time will be less than B’s age at that time by 2 years. What is B’s present age?

ক
ক) 10 years
খ
খ) 14 years
গ
গ) 12 years
ঘ
ঘ) 5 years

ব্যাখ্যা

Let the present age of A be a years and that of B be b years
Then, 4 years ago,
A's age = (a - 4)
B's age = (b - 4)
Now, according to the given information in question,
{(a - b)/2}/4(b - 4) = 5/12 or (a - 4)/2(4b - 16) = 5/12 or (a - 4)/(4b - 16) = 5/6
By cross multiplying we get
or, 6a - 24 = 20b - 80
or, 6a - 20b = -56
or, 10b - 3a = 28
After 8 years,
(a + 8)2 + 2 = b + 8
or, a/2 + 4 + 2 = b + 8
or, b - a/2 = -2
or, 2b - a = -4 .......(i)
a = 2b + 4 ......(ii)
Putting the value of a in equation (i), we get
10b - 3(2b + 4) = 28
or, 4b = 40
∴ b = 10
Hence, the present age of B is 10 years.

২৩৪.

One year ago, Muna was four times as old as her daughter. Six years hence, Muna's age will exceed her daughter's age by 9 years. The ratio of the present ages of Muna and her gaughter is-

ক
10 : 3
খ
11 : 4
গ
12 : 5
ঘ
13 : 4

ব্যাখ্যা

Solution: One year ago, Muna was four times as old as her daughter. Six years hence, Muna's age will exceed her daughter's age by 9 years. The ratio of the present ages of Muna and her gaughter is-

Solution:
Let,
daughter's age one years ago be = x years
Then, Muna's age one years ago be = 4x years

ATQ,
(4x + 1) + 6 = (x + 1 + 6) + 9
⇒ (4x + 7) = (x + 16)
⇒ 4x - x = 16 - 7
⇒ 3x = 9
∴ x = 3

Ratio of Muna and her daughter age now = (4x + 1)/(x + 1)
= (4 · 3 + 1)/(3 + 1) = 13/4
= 13 : 4

২৩৫.

A’s current age is three times B’s current age. Eight years ago, A’s age was five times B’s age at that time. Find the difference between their present ages.

ক
28 years
খ
36 years
গ
32 years
ঘ
24 years

ব্যাখ্যা

Question: A’s current age is three times B’s current age. Eight years ago, A’s age was five times B’s age at that time. Find the difference between their present ages.

Solution:
Let,
B's current age = x
A's current age = 3x

ATQ,
3x - 8 = 5(x - 8)
⇒3x - 8 = 5x - 40
⇒ 5x - 3x= 40 - 8
⇒ 2x = 32
∴ x = 16

∴ B's current age = 16 years
∴ A's current age = (3 × 16) = 48 years

So the difference between their present ages = (48 - 16) = 32 years

২৩৬.

X's age 3 years ago was three times the present age of Y. At present Z's age is twice the age of Y. Also Z is 12 years younger than X. What is the present age of Z?

ক
15 years
খ
24 years
গ
12 years
ঘ
18 years

ব্যাখ্যা

Question: X's age 3 years ago was three times the present age of Y. At present Z's age is twice the age of Y. Also Z is 12 years younger than X. What is the present age of Z?

Solution:
Let the present age of Y be a years
Three years ago X's age = 3a years
Then, present age of X is (3a + 3)
Z's present age = 2a

According to question
(3a + 3) - 2a = 12
a = 9 year

∴ Present age of Z = 2a = 2 × 9 = 18 years

২৩৭.

If Sohel was 35 years old 7 years ago, how old was he x years ago?

ক
45 - x
খ
40 - x
গ
47- x
ঘ
42 - x

ব্যাখ্যা

Sohel was 35 years old 7 years ago
Therefore, Mario's present age = 35 + 7 = 42 years
x years ago, his age = (42 - x) years

২৩৮.

The ratio of the present ages of A and B is 3 : 4. If the difference between their ages is 6 years, what is B’s present age?

ক
18 years
খ
24 years
গ
30 years
ঘ
36 years

ব্যাখ্যা

Question: The ratio of the present ages of A and B is 3 : 4. If the difference between their ages is 6 years, what is B’s present age?

Solution:
Let,
Present age of A = 3x
Present age of B = 4x

ATQ,
4x - 3x = 6
∴ x = 6

∴ B's present age is 4 × 6 = 24 years

২৩৯.

12 years ago the difference in age between Puja and Sejan was 6 years. What is the difference now?

ক
6 years
খ
12 years
গ
2 years
ঘ
none of the above

ব্যাখ্যা

Question: 12 years ago the difference in age between Puja and Sejan was 6 years. What is the difference now?

Solution:
The difference in age remains the same as they both pass the same period of time together.
so, at present, their age difference is 6 years.

২৪০.

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

২৪১.

Five years ago, the average age of A and B was 18 years. At present the average age of A, B, and C is 24 years. What would be the age of C after 5 years?

ক
32 years
খ
31 years
গ
33 years
ঘ
36 years

ব্যাখ্যা

Question: Five years ago, the average age of A and B was 18 years. At present the average age of A, B, and C is 24 years. What would be the age of C after 5 years?

Solution:
The sum of the ages of A and B, 5 years ago = 18 × 2 = 36 years.
The sum of the present age of A and B = 5 + 5 + 36 = 46 years.
Sum of the present ages of A, B, and C = 24 × 3 = 72 years.

∴ Present age of C = 72 - 46 = 26 years.

∴ C's age after 5 years = 26 + 5 = 31 years.

২৪২.

8 years ago, the ratio of A's age to B's age was 4:5. At present the ratio of is 4: 5. At present, the ratio of B's age to C's age is 4 : 5. At present, the difference between A's age and C's age is 20 years, then what is the sum of the ages of A, B and C?

ক
ক) 138 years
খ
খ) 164 years
গ
গ) 148 years
ঘ
ঘ) 152 years

ব্যাখ্যা

A এর বর্তমান বয়স= 4x + 8 বছর
B এর বর্তমান বয়স = 5x + 8 বছর
ধরি
C এর বর্তমান বয়স = y বছর
প্রশ্নমতে,
(5x + 8)/y = 4/5
25x + 40 = 4y
25x - 4 y = - 40 .............(i)

y - (4x + 8) = 20
y - 4x - 8 = 20
4x - y = - 28 .............(ii)
(ii) নং সমীকরণকে 4 দ্বারা গুণ করে (i) নং হতে বিয়োগ করে পাই
25x - 4 y - (16x - 4y ) = - 40 - (-112)
25x - 4 y - 16x + 4y = -40 + 112
9x = 72
x = 8

x এর মান (ii) নং সমীকরণে বসিয়ে পাই
4x - y = - 28
4×8 - y = - 28
32 - y = - 28
- y = - 28 -32
- y = -60
y = 60

C এর বর্তমান বয়স = 60 বছর
A এর বর্তমান বয়স = 4x + 8 = 4 × 8 + 8 = 40 বছর
B এর বর্তমান বয়স = 5x + 8 = 5 × 8 + 8= 48 বছর

A +B + C = 40 + 48 + 60 = 148 বছর

২৪৩.

পিতা ও পুত্রের বয়সের সমষ্টি ৭৪ বছর। এক বছর পূর্বে তাদের বয়সের অনুপাত ছিলো ৫ : ১ বছর। পিতার বর্তমান বয়স কত?

ক
৫৫ বছর
খ
৬৮ বছর
গ
৬১ বছর
ঘ
৬৪ বছর
ঙ
কোনোটিই নয়

ব্যাখ্যা

প্রশ্ন: পিতা ও পুত্রের বয়সের সমষ্টি ৭৪ বছর। এক বছর পূর্বে তাদের বয়সের অনুপাত ছিলো ৫ : ১ বছর। পিতার বর্তমান বয়স কত?

সমাধান:
ধরি,
এক বছর পূর্বে পিতা ও পুত্রের বয়স যথাক্রমে = ৫ক ও ক বছর
পিতার বর্তমান বয়স = (৫ক + ১) বছর
পুত্রের বর্তমান বয়স = (ক + ১) বছর

প্রশ্নমতে,
(ক + ১) + (৫ক + ১) = ৭৪
⇒ ৬ক + ২ = ৭৪
⇒ ৬ক = ৭৪ - ২
⇒ ৬ক = ৭২
∴ ক = ১২

সুতরাং, পিতার বর্তমান বয়স = (৫ × ১২ + ১)
= ৬১ বছর

২৪৪.

Rina is now three times as old as Tuhin. Four years ago, she was five times as old as Tuhin was. How old is Rina now?

ক
12 years
খ
15 years
গ
18 years
ঘ
20 years
ঙ
24 years

ব্যাখ্যা

Question: Rina is now three times as old as Tuhin. Four years ago, she was five times as old as Tuhin was. How old is Rina now?

Solution:
Let,
Tuhin's present age = x years
∴ Rina's present age = 3x years

ATQ,
3x - 4 = 5(x - 4)
⇒ 5x - 20 = 3x - 4
⇒ 5x - 3x = 20 - 4
⇒ 2x = 16
∴ x = 8

So Rina's present age = (3 × 8) = 24 years

২৪৫.

The present ages of A and B are 42 and 36 years, respectively. After K years, the ratio of ages of B to A will be 15 : 17.What is value of K?

ক
9 years
খ
12 years
গ
5 years
ঘ
6 years
ঙ
None of these

ব্যাখ্যা

Question: The present ages of A and B are 42 and 36 years, respectively. After K years, the ratio of ages of B to A will be 15 : 17.What is value of K?

Solution:
ATQ after k years,
(36 + k)/(42 + k) = 15/17
⇒ 612 + 17k = 630 + 15k
⇒ 17k - 15k = 630 - 612
⇒ 2k = 18
∴ k = 9

২৪৬.

The sum of ages of 7 children born at the intervals of 5 years each is 154 years. What is the age of the youngest child?

ক
6
খ
7
গ
8
ঘ
9
ঙ
10

ব্যাখ্যা

Let the ages of children be x, (x + 5), (x + 10), (x + 15), (x + 20), (x + 25) and (x + 30) years.
Then, x + (x + 5) + (x + 10) + (x + 15) + (x + 20) + (x + 25) + (x + 30) = 154
or, 7x + 105 = 154
or, 7x = 49
or, x = 7
∴ the age of the youngest child is 7 years.

২৪৭.

The sum of the age of father and son is 50. Five years back their ratio was 7 : 1. After five years son's age will be -

ক
ক) 45 years
খ
খ) 10 years
গ
গ) 20 years
ঘ
ঘ) 15 years

ব্যাখ্যা

Question: The sum of the age of father and son is 50. Five years back their ratio was 7 : 1. After five years son's age will be -

Solution:
ধরি,
৫ বছর পূর্বে পিতা ও পুত্রের বয়স ছিলো যথাক্রমে ৭ক এবং ক
প্রশ্নমতে,
৭ক + ক + ৫ + ৫ = ৫০
৮ক = ৪০
ক = ৫

৫ বছর পূর্বে পিতা ও পুত্রের বয়স ছিলো যথাক্রমে ৩৫ বছর এবং ৫ বছর।
৫ বছর পর বয়স হবে যথাক্রমে ৪৫ বছর ও ১৫ বছর।

২৪৮.

If Raihan was 22 years old 6 years ago, how old was he x years ago?

ক
ক) x - 28
খ
খ) 18 - x
গ
গ) 28 - x
ঘ
ঘ) x - 18

ব্যাখ্যা

Question: If Raihan was 22 years old 6 years ago, how old was he x years ago?

Solution:
৬ বছর আগে, রায়হানের বয়স ২২ বছর
বর্তমানে রায়হানের বয়স = ২২ + ৬ বছর
= ২৮ বছর

x বছর আগে তার বয়স = ২৮ - x বছর

২৪৯.

১৫ জন ব্যক্তির গড় বয়স ২৮ বছর। তাদের মধ্যে দুইজন ব্যক্তির বয়সের গড় ৫৪ বছর। তাহলে বাকি ১৩ জন ব্যক্তির বয়সের গড় কত হবে?

ক
২৮ বছর
খ
২৬ বছর
গ
২৯ বছর
ঘ
২৪ বছর
ঙ
২৫ বছর

ব্যাখ্যা

প্রশ্ন: ১৫ জন ব্যক্তির গড় বয়স ২৮ বছর। তাদের মধ্যে দুইজন ব্যক্তির বয়সের গড় ৫৪ বছর। তাহলে বাকি ১৩ জন ব্যক্তির বয়সের গড় কত হবে?

সমাধান:
১৫ জন ব্যক্তির মোট বয়স = (২৮ × ১৫) = ৪২০ বছর
দুইজন ব্যক্তির মোট বয়স (৫৪ × ২) = ১০৮ বছর

∴ ১৩ জন ব্যক্তির মোট বয়স = (৪২০ - ১১০) বছর = ৩১২ বছর
∴ ১৩ জন ব্যক্তির বয়সের গড় = (৩১২/১৩) বছর = ২৪ বছর

২৫০.

Rahim's present age is 9 times as Karim's age. After 9 years, Rahim's age would be 3 times as Karim's age. What is the present age of Karim?

ক
ক) 3 years
খ
খ) 9 years
গ
গ) 12 years
ঘ
ঘ) 27 years

ব্যাখ্যা

Question: Rahim's present age is 9 times as Karim's age. After 9 years, Rahim's age would be 3 times as Karim's age. What is the present age of Karim?

Solution:
Let, Karim's present age be x years
and Rahim's present age is = 9x years

Now,
Karim's age after 9 years = (x + 9) years
Rahim's age after 9 years = (9x + 9) years

ATQ,
9x + 9 = 3(x + 9)
⇒ 9x + 9 = 3x + 27
⇒ 6x = 18
⇒ x = 3

২৫১.

The captain of a cricket team of 11 members is 25 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?

ক
ক) 23 years
খ
খ) 22 years
গ
গ) 24 years
ঘ
ঘ) 25 years

ব্যাখ্যা

Let the average age of the whole team by x years.
11x - (25 + 28) = 9(x -1)
11x - 53 = 9x - 9
11x - 9x = 44
2x = 44
x = 22.

So, average age of the team is 22 years.

২৫২.

Ten years ago A was half of B in age. If the ratio of their present ages is 3 : 4, what is the present age of A?

ক
ক) 10 years
খ
খ) 15 years
গ
গ) 20 years
ঘ
ঘ) 25 years

ব্যাখ্যা

Question: Ten years ago A was half of B in age. If the ratio of their present ages is 3 : 4, what is the age present of A?

Solution:
Let, B's age 10 years ago = 2x years
and A's age 10 years ago = x years

Now,
A's age at present = (x + 10) years
B's age at present = (2x + 10) years

ATQ,
(x + 10) / (2x + 10) = 3/4
⇒ 4X + 40 = 6X + 30
⇒ 2x = 10
⇒ x = 5

∴ A's age at present = (5 + 10) = 15 years

২৫৩.

The ages of A and B are in the ratio 5 : 4 and sum of their ages is 54 years. What will be the ratio of their ages after 6 years?

ক
ক) 2 : 3
খ
খ) 3 : 5
গ
গ) 5 : 1
ঘ
ঘ) 6 : 5

ব্যাখ্যা

Question: The ages of A and B are in the ratio 5 : 4 and sum of their ages is 54 years. What will be the ratio of their ages after 6 years?

Solution:
A's age = (54 × 5)/9 = 30 years
and B's age = 54 - 30 = 24 years

Ratio of their ages after 6 years,
= (30 + 6) : (24 + 6)
= 6 : 5

২৫৪.

Rajeev's age after 15 year will be 5 times his age 5 year back. What is the present age of rajeev?

ক
ক) 12
খ
খ) 14
গ
গ) 22
ঘ
ঘ) 10

ব্যাখ্যা

Let Rajeev's present age be x year.
Rajeev's age after 15 year = (x + 15) year.
Rajeev's age 5 year back = (x - 5) year
Then ATQ,
x + 15 = 5 (x - 5)
x + 15 = 5x - 25
=> x = 10
Hence, Rajeev's present age = x = 10 year.

২৫৫.

At present, the ratio between the ages of Hassan and Hossain is 4 : 3. After 6 years, Hassan's age will be 26 years. What is the age of Hossain at present?

ক
20 years
খ
25 years
গ
15 years
ঘ
10 years

ব্যাখ্যা

Question: At present, the ratio between the ages of Hassan and Hossain is 4 : 3. After 6 years, Hassan's age will be 26 years. What is the age of Hossain at present?

Solution:
Let, the present ages of Hassan and Hossain be 4x years and 3x years respectively.

ATQ,
4x + 6 = 26
⇒ 4x = 20
∴ x = 5

∴ Hossain's age = 3x = 15 years.

২৫৬.

The difference between the ages of the two men is 10 years. 15 years ago, the elder one was twice as old as the younger one. The present age of the elder man is-

ক
25 years
খ
30 years
গ
35 years
ঘ
45 years

ব্যাখ্যা

Question: The difference between the ages of the two men is 10 years. 15 years ago, the elder one was twice as old as the younger one. The present age of the elder man is-

Solution:
Let, their ages be x years and (x + 10) years.

ATQ,
(x + 10 - 15) = 2(x - 15)
⇒ x - 5 = 2x - 30
⇒ 2x - 30 - x + 5 = 0
⇒ x - 25 = 0
∴ x = 25

∴ Present age of the elder man = x + 10 = 25 + 10 = 35 years.

২৫৭.

The average age of girls in a nursery class is 5 years and that of boys is 5.7 years. If the average age of the students in the class is 5.5 years, what could be the possible number of boys and girls respectively in the class?

ক
ক) 10, 20
খ
খ) 30, 50
গ
গ) 100, 500
ঘ
ঘ) 150, 375

ব্যাখ্যা

Let the number of boy and girl be y and z
5z + 5.7y = 5.5(y + z)
5.5z - 5z = 5.7y - 5.5y
0.5z = 0.2y
5z = 2y
z : y = 2 : 5 = 75 × 2 : 75 × 5 = 150 : 375
--------------------------------------------
নার্সারি শ্রেণির বালিকাদের গড় বয়স ৫ বছর এবং বালকদের গড় বয়স ৫.৭ বছর। ছাত্রছাত্রীদের গড় বয়স ৫.৫ বছর হলে, ছাত্রছাত্রীদের সম্ভাব্য সংখ্যা কত?

মনে করি, ছাত্র ও ছাত্রীদের সংখ্যা যথাক্রমে y ও z
সুতরাং 5z + 5.7y = 5.5(y + z)
5.5z - 5z = 5.7y - 5.5y
0.5z = 0.2y
5z = 2y
z : y = 2 : 5
সুতরাং ছাত্রীদের সংখ্যা ২ জন হলে ছাত্রদের সংখ্যা ৫ জন
ছাত্রীদের সংখ্যা ১৫০ জন হলে ছাত্রদের সংখ্যা ৫ × ১৫০/২ = ৩৭৫ জন যা অপশনে আছে।

২৫৮.

Twice the age of X is thrice the age of Y. 8 years back, the difference between the ages of X and Y was 18 years. What is the present age of X?

ক
50 years
খ
53 years
গ
54 years
ঘ
55 years

ব্যাখ্যা

Question: Twice the age of X is thrice the age of Y. 8 years back, the difference between the ages of X and Y was 18 years. What is the present age of X?

Solution:
2 times the age of X = 3 times the age of Y
Difference between X and Y 8 years back = 18 years

2X = 3Y
⇒ X : Y = 3 : 2

Let the present age of X and Y be 3R and 2R respectively
⇒ 3R - 2R = 18
⇒ R = 18

∴ 3R = 3 × 18 = 54
∴ The present age of X is 54 years

২৫৯.

A mother is twice as old as her son. If 20 years ago, the age of the mother was 10 times the age of the son, what is the present age of the mother?

ক
38 years
খ
40 years
গ
43 years
ঘ
45 years

ব্যাখ্যা

Let the age of son = X years

∴Age of mother would be =2X

As per question 20 years ago;
10 (X -20) = 2X - 20
⇒ 10X - 200 = 2X - 20
⇒ 10X - 2X= - 20 + 200
⇒ 8X = 180
⇒ X= 180/8
= 22.5 years

∴Age of mother = 22.5 × 2 = 45 years.

২৬০.

X’s age 3 years ago was three times the present age of Y. At present Z’s age is twice the age of Y and also Z is 12 years younger than X. What is the present age of Z?

ক
17 years
খ
20 years
গ
16 years
ঘ
18 years

ব্যাখ্যা

Question: X’s age 3 years ago was three times the present age of Y. At present Z’s age is twice the age of Y and also Z is 12 years younger than X. What is the present age of Z?

Solution:
Let,
Their present age is X, Y, Z respectively.

As X’s age 3 years ago was three times the present age of Y.
X - 3 = 3y
X - 3y = 3……….(i)

Z’s age is twice the age of Y
∴ Z = 2Y……….(ii)

Z is 12 years younger than X
∴ X - 12 = Z
Or, X - 12 = 2Y [ putting Z = 2Y from equation (ii) ]
Or, X - 2Y = 12……..(iii)

(iii) - (i),
X - 2Y - X + 3Y = 12 - 3
Or, Y = 9

So, the present age of Y is 9.
∴ the present age of Z is = 2Y = 2 x 9 = 18 years.

২৬১.

A is four years older than B, who is thrice as old as C. If the total of the ages of A, B, and C is 46, how old is A?

ক
16 years
খ
24 years
গ
18 years
ঘ
22 years

ব্যাখ্যা

Question: A is four years older than B, who is thrice as old as C. If the total of the ages of A, B, and C is 46, how old is A?

Solution:
Let
C's age be = a years
Then, B's age = 3a years
A's age = (3a + 4) years

∴ (3a + 4) + 3a + a = 32
⇒ 7a + 4 = 46
⇒ 7a = 42
⇒ a = 6

Hence, A's age = (3 × 6) + 4 = 22 years.

২৬২.

The present age of three persons are in the ratio of 4 : 7 : 9. Eight years ago, their total age was 56 years. In five years what will be the age of the youngest person?

ক
20 years
খ
21 years
গ
22 years
ঘ
19 years

ব্যাখ্যা

Question: The present age of three persons are in the ratio of 4 : 7 : 9. Eight years ago, their total age was 56 years. In five years what will be the age of the youngest person?

Solution:
Present age ratio of three persons is 4 : 7 : 9

Let,
Their age is 4X, 7X and 9X respectively.

ATQ,
4X - 8 + 7X - 8 + 9X - 8 = 56
Or, 20X - 24 = 56
Or, 20X = 80
Or, X = 4

∴ The present age of the youngest person is = 4X = 4 x 4 = 16 years.
In five years, his age will be = (16 + 5 ) = 21 years.

২৬৩.

Topu's age is (1/6)th of her father's age. Topu's father's age will be twice of Arif's age after 10 years. If Arif's 8th birthday was celebrated 2 years ago,then what is Topu's present age?

ক
4 years
খ
5 years
গ
6 years
ঘ
8 years

ব্যাখ্যা

Question: Topu's age is (1/6)th of her father's age. Topu's father's age will be twice of Arif's age after 10 years. If Arif's 8th birthday was celebrated 2 years ago,then what is Topu's present age?

Solution:
Arif's present age
= (8 + 2) years
= 10 years
After 10 year's Topu's father's age = 2(10 + 10) = 40 years
Topu's father's current age = 40 - 10 = 30 years
Topu's age = (1/6) × 30 = 5 years

২৬৪.

A father is three times as old as his son. After fifteen years the father will be twice as old as his son's age at that time. Hence the father's present age is-

ক
ক) 36
খ
খ) 42
গ
গ) 45
ঘ
ঘ) 48
ঙ
ঙ) None of these

ব্যাখ্যা

Question: A father is three times as old as his son. After fifteen years the father will be twice as old as his son's age at that time. Hence the father's present age is-

Solution:
ধরি, পুত্রের বয়স x বছর
পিতার বয়স 3x বছর

১৫ বছর পর পুত্রের বয়স x + 15 বছর
১৫ বছর পর পিতার বয়স 3x + 15 বছর

প্রশ্নমতে,
3x + 15 = 2 (x + 15)
⇒ 3x + 15 = 2x + 30
⇒ 3x - 2x = 30 - 15
⇒ x = 15

পিতার বর্তমান বয়স = 3 × 15 বছর
= 45 বছর

২৬৫.

The average age of A, B and C is 30 years. If the difference between B's age and A's age is same as the difference between C's age and B's age. If D is 40 years older than B then what is the sum of the age of B and D?

ক
ক) 70 years
খ
খ) 30 years
গ
গ) 80 years
ঘ
ঘ) 100 years

ব্যাখ্যা

The average age of A, B and C is 30 years. Therefore, the total age of (A + B + C) = 3 × 30 = 90 years
age of (B - A) = age of (C - B)
age of (A + C) = age of 2B
age of (2B + B) = 90
age of 3B = 90
age of B = 30 years
age of D = age of (B + 40) = (40 + 30) years = 70 years
Therefore, age of ( B + D) = (30 + 70) years = 100 years
-------------------------------------------------------------
A, B ও C এর গড় বয়স ৩০ বছর। B ও A এর বয়সের পার্থক্য C ও B এর বয়সের পার্থক্যের সমান। যদি D, B এর চেয়ে ৪০ বছরের বড় হয় তবে B ও D এর বয়সের সমষ্টি কত?

A, B ও C এর গড় বয়স ৩০ বছর। সুতরাং মোট বয়স ৩০ × ৩ = ৯০ বছর।
B ও A এর বয়সের পার্থক্য C ও B এর বয়সের পার্থক্যের সমান।
(A + C) এর বয়স = ২B এর বয়স
(২B + B) এর বয়স = ৯০ বছর
৩B এর বয়স = ৯০
B এর বয়স = ৯০/৩ = ৩০ বছর
D এর বয়স = (B + ৪০) বছর = (৪০ + ৩০) বছর = ৭০ বছর
সুতরাং ( B + D) এর বয়স = (৩০ + ৭০) বছর = ১০০ বছর

২৬৬.

Sagar is 50 years old and Nazma 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: Sagar is 50 years old and Nazma 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: Sagar is 50 years and Nazma is 40 years
x years ago:
Sagar’s age = (50 - x) and Nazma's age = (40 - x)
Given, the ratio of their ages was 3 : 2
(50 - x)/(40 - x) = 3/2
Solving, we get: x = 20
Therefore, the answer is 20 years.

২৬৭.

7 years ago, son’s age was 1/5th of the father’s age. If the ratio of their present ages is 1:3, what will be the ratio of their ages after 7 years?

ক
ক) 2:5
খ
খ) 3:5
গ
গ) 5:11
ঘ
ঘ) 3:7
ঙ
ঙ) None of above

ব্যাখ্যা

Let,
7 years ago son’s age was x years old and father’s age was 5x year.
Now,
(x+7)/(5x+7) = 1/3,
so x = 7
Son’s age = 7 + 7 = 14
Father’s age= 5 × 7 + 7 = 42
After 7 years,
Son’s age : Father’s age = 21:49 = 3:7

২৬৮.

The present ages of three persons are in the ratio of 4 : 7 : 9. Six years ago, the sum of their ages was 62. What was the age of the oldest person six years ago?

ক
36 years
খ
30 years
গ
28 years
ঘ
21 years
ঙ
16 years

ব্যাখ্যা

Question: The present ages of three persons are in the ratio of 4 : 7 : 9. Six years ago, the sum of their ages was 62. What was the age of the oldest person six years ago?

Solution:
Let their present ages are 4x, 7x and 9x years respectively.
∴ 6 years ago, their present ages are (4x - 6), (7x - 6) and (9x - 6) respectively.

ATQ,
(4x - 6) + (7x - 6) + (9x - 6) = 62
⇒ 20x - 18 = 62
⇒ 20x = 62 + 18
⇒ x = 80/20
⇒ x = 4

∴ Their present ages are (4 × 4) =16, (7 × 4) = 28 and (9 × 4) = 36 years respectively.
∴ Age of the oldest person six years ago is (36 - 6) = 30 years.

২৬৯.

A is 50 years old and B is 35 years old. How many years ago was the ratio of their ages 3 : 2?

ক
8 Years
খ
2 Years
গ
5 Years
ঘ
10 Years

ব্যাখ্যা

Question: A is 50 years old and B is 35 years old. How many years ago was the ratio of their ages 3 : 2?

Solution:
Let,
'x' years ago the ratio of their ages was 3 : 2

ATQ,
(50 - x) : (35 - x) = 3 : 2
⇒ (50 - x)/(35 - x) = 3/2
⇒ 105 - 3x = 100 - 2x
⇒ 3x - 2x = 105 - 100
∴ x = 5

২৭০.

The age of a father 10 years ago was thrice the age of his son. 10 years hence, the father's age will be twice that of his son. Father's present age is :

ক
70 years
খ
60 years
গ
80 years
ঘ
90 years

ব্যাখ্যা

Question: The age of a father 10 years ago was thrice the age of his son. 10 years hence, the father's age will be twice that of his son. Father's present age is :

Solution:
Let, son's age 10 years ago be X years
Then, father age 10 years ago = 3X years

Son's age now = (X + 10) years,
Father age now = (3X + 10) years

( 3X + 10 ) + 10 = 2[( X + 10 )+10]
⇒ 3X + 20 = 2( X + 20 )
⇒ 3X + 20 = 2X + 40
⇒ X = 20

∴ fathers age is = 60 + 10 = 70 years

২৭১.

Jamal is now four times older than Arif. In 30 years, he will be 18 years older than Arif. What is Jamal's age now in years?

ক
24
খ
28
গ
32
ঘ
none

ব্যাখ্যা

Question: Jamal is now four times older than Arif. In 30 years, he will be 18 years older than Arif. What is Jamal's age now in years?

Solution:
Let,
Age of Arif = x
Age of Jamal = 4x

ATQ,
4x + 30 = (x + 30) + 18
⇒ 3x = 18
∴ x = 6

∴ Jamal's age = 4 × 6 = 24 years

২৭২.

A mother told her daughter, "I was your present age at the time of your birth." If the mother is currently 38 years old, what was the daughter’s age five years ago?

ক
20 years.
খ
15 years.
গ
14 years.
ঘ
25 years.

ব্যাখ্যা

Question: A mother told her daughter, "I was your present age at the time of your birth." If the mother is currently 38 years old, what was the daughter’s age five years ago?
Solution:
Let,
Daughter present age = x years
Mother's present age = (x + x) years
= 2x years

ATQ,
2x = 38
⇒ x = 19
So daughter age five years back was = 19 - 5
= 14 years.

২৭৩.

Today, Jakir is twice as old as Moin. In 5 years, Jakir will be 1.5 times as old as Moin. How old is Jakir today?

ক
12
খ
10
গ
15
ঘ
20

ব্যাখ্যা

Question: Today, Jakir is twice as old as Moin. In 5 years, Jakir will be 1.5 times as old as Moin. How old is Jakir today?

Solution:
Let Jakir’s age = J, Moin’s age = M.
Given:
⇒ J=2M --------------------(Equation 1)
In 5 years:
⇒ J+5=1.5(M+5)J+5=1.5(M+5) ---(Equation 2)

Substitute J=2M (equation 1) in equation (2),
⇒ 2M+5=1.5M+7.5 ⟹ 0.5M=2.5
⟹ M=5
Then, J=2×5=10
Answer: 10

২৭৪.

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
8 : 3
খ
7 : 3
গ
9 : 4
ঘ
9 : 2

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:
Let, 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.

ATQ,
(3x + 10) +10 = 2 [(x + 10) + 10]
⇒ (3x + 20) = 2[x + 20]
⇒ 3x + 20 = 2x + 40
⇒ 3x - 2x = 40 - 20
⇒ x = 20

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

২৭৫.

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. What is the present age of the mother?

ক
30
খ
35
গ
40
ঘ
50

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. What is the present age of the mother?

Solution:
Let the age of the person’s mother be ‘x years
Age of the person = (2x/5)

After 8 years, age of the person’s mother = ‘x + 8’ years
Age of the person after 8 years = (2x/5) + 8 years

According to question:
(2x/5) + 8 = (1/2)(x + 8)
⇒ (2x/5) + 8 = (x/2) + 4
⇒ (x/2) - (2x/5) = 8 - 4
⇒ (5x - 4x)/10 = 4
⇒ x/10 = 4
∴ x = 40

So, the present age of his mother is 40 years

২৭৬.

A is 50 years old and B is 35 years old. How many years ago was the ratio of their ages 3 : 2?

ক
5 Years
খ
3 Years
গ
6 Years
ঘ
7 Years

ব্যাখ্যা

Question: A is 50 years old and B is 35 years old. How many years ago was the ratio of their ages 3 : 2?

Solution:
Let,
'x' years ago, the ratio of their ages was 3 : 2

ATQ,
(50 - x) : (35 - x) = 3 : 2
⇒ (50 - x)/(35 - x) = 3/2
⇒ 105 - 3x = 100 - 2x
⇒ 3x - 2x = 105 - 100
∴ x = 5

২৭৭.

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

ক
2 times
খ
3 times
গ
1/2 times
ঘ
4 times

ব্যাখ্যা

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

Solution:
Let, Shafin's present age be = a years.
Then, father's present age = (a + 3a) years
= 4a years

ATQ,
(4a + 8) = (5/2)(a + 8)
⇒ 8a + 16 = 5a + 40
⇒ 3a = 24
∴ a = 8

Hence, the required times = (4a + 16)/(a + 16)
= 48/24
= 2

২৭৮.

The average age of a group of 10 students is 15 years. When 5 more students join the group, the average age increase by 1 year. The average age of the new students is?

ক
16
খ
18
গ
20
ঘ
23

ব্যাখ্যা

Question: The average age of a group of 10 students is 15 years. When 5 more students join the group, the average age increase by 1 year. The average age of the new students is?

Solution:
Total age of 10 students = 10 × 15 = 150 years

Total age of 15 students = 15 × 16 = 240 years

Total age of 5 new students = 240 - 150 = 90 years

∴ Average age of 5 new students = 90/5 = 18 years

২৭৯.

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.

Solution:
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.

২৮০.

The ages of Moni and Roni are in the ratio 6 : 5 respectively. After 10 years, the ratio of their ages will be 8 : 7. What is the difference in their ages now?

ক
5 years
খ
8 years
গ
12 years
ঘ
4 years

ব্যাখ্যা

Question: The ages of Moni and Roni are in the ratio 6 : 5 respectively. After 10 years, the ratio of their ages will be 8 : 7. What is the difference in their ages now?

Solution:
Let the present ages of Moni and Roni be 6x and 5x respectively, where x is a common factor.

After 10 years, the ratio of their ages will be 8 : 7. then,
⇒ (6x + 10) : (5x + 10) = 8 : 7
⇒ 6x + 10/5x + 10 = 8/7
⇒ 7(6x + 10) = 8(5x + 10)
⇒ 42x + 70 = 40x + 80
⇒ 42x - 40x = 80 - 70
⇒ 2x = 10
⇒ x = 10/2
∴ x = 5

Now,
Moni's age = 6x = 6 × 5 = 30 years
Roni's age = 5x= 5 × 5 = 25 years

∴ The difference in their ages now = 30 − 25 = 5 years

২৮১.

A is younger than B by 7 years. If their ages are in the respective ratio of 7 : 9, how old is A?

ক
ক) 18
খ
খ) 22
গ
গ) 24
ঘ
ঘ) None of these

ব্যাখ্যা

Let B's age be x years
Therefore, A's age = (x - 7) years
(x - 7)/x = 7/9
⇒ 7x = 9x - 63
⇒ 2x = 63
⇒ x = 31.5
A's age = 31.5 - 7 = 24.5 years

২৮২.

Product of present age of Rahim and Latif is 2223 years and their present age ratio is 19 : 13 find the difference age of Rahim and Latif.

ক
20
খ
22
গ
16
ঘ
18

ব্যাখ্যা

Question: Product of present age of Rahim and Latif is 2223 years and their present age ratio is 19 : 13 find the difference age of Rahim and Latif.

Solution:
Let, age of Rahim be 19x and age of Latif be 13x
Then, product of their ages = 19x × 13x = 247x²
⇒ 247x² = 2223
⇒ x² = 9
∴ x = 3

Hence, required difference = 19x - 13x = 6x = 6 × 3 = 18 years

২৮৩.

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

ক
ক) 2 times
খ
খ) 2.5 times
গ
গ) 2.75 times
ঘ
ঘ) 3 times
ঙ
ঙ) 3.5 times

ব্যাখ্যা

Let Roni's present age be x years. Then, father's present age =(x + 3x) years = 4x years.
there4 (4x + 8) = (5/2)(x + 8)
=> 8x + 16 = 5x + 40
=> 3x = 24
=> x = 8.

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

২৮৪.

Eight years back, Ashik's age was (1/8)th of Zaber's age. Ten years from now, Zaber's age will be double of Ashik's age. How old is Ashik now?

ক
11 years
খ
8 years
গ
15 years
ঘ
13 years

ব্যাখ্যা

Question: Eight years back, Ashik's age was (1/8)th of Zaher's age. Ten years from now, Zaher's age will be double of Ashik's age. How old is Ashik now?

Solution:
ধরি,
জহিরের বর্তমান বয়স = ক বছর
৮ বছর পূর্বে জহিরের বয়স = (ক - ৮) বছর
∴ ৮ বছর পূর্বে আশিকের বয়স = (ক - ৮)/৮ বছর

বর্তমানে,
আশিকের বয়স = {(ক - ৮)/৮} + ৮ বছর
= (ক - ৮ + ৬৪)/৮ বছর
= (ক + ৫৬)/৮ বছর

∴ ১০ বছর পর জহিরের বয়স হবে = ক + ১০ বছর
∴ ১০ বছর পর আশিকের বয়স হবে = {(ক + ৫৬)/৮} + ১০ বছর
= (ক + ৫৬ + ৮০)/৮ বছর
= (ক + ১৩৬)/৮ বছর

প্রশ্নমতে,
ক + ১০ = ২ × {(ক + ১৩৬)/৮}
⇒ ক + ১০ = (ক + ১৩৬)/৪
⇒ ৪(ক + ১০) = ক + ১৩৬
⇒ ৪ক + ৪০ = ক + ১৩৬
⇒ ৪ক - ক = ১৩৬ - ৪০
⇒ ৩ক = ৯৬
⇒ ক = ৯৬/৩
∴ ক = ৩২

∴ আশিকের বর্তমান বয়স = (৩২ + ৫৬)/৮ বছর
= ৮৮/৮ বছর
= ১১ বছর

২৮৫.

The sum of the present ages of a father and his son is 60 years. five years ago, father's age was four times the age of the son. So now the son's age will be-

ক
25
খ
10
গ
15
ঘ
20

ব্যাখ্যা

Question: The sum of the present ages of a father and his son is 60 years. five years ago, father's age was four times the age of the son. So now the son's age will be-

Solution:
Let the present ages of son and father be x and (60 - x) years respectively.

Then,
(60 - x) - 5 = 4(x - 5)
⇒ 55 - x = 4x - 20
⇒ 5x = 75
∴ x = 15

২৮৬.

The sum of the present ages of a father and his son is 50 years. Three years ago, father's age was three times the age of the son. After three years, father's age will be:

ক
36 years
খ
39 years
গ
42 years
ঘ
33 years

ব্যাখ্যা

Question: The sum of the present ages of a father and his son is 50 years. Three years ago, father's age was three times the age of the son. After three years, father's age will be:

Solution:
Let,
The present ages of son = a
then, the present age of father = 50 - a

Then, (50 - a) - 3 = 3(a - 3)
⇒ 47 - a = 3a - 9
⇒ 4a = 56
⇒ a = 14

∴ Father's age after 3 years = (50 - 14) + 3 = 39 years.

২৮৭.

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

ক
38 years
খ
30 years
গ
20 years
ঘ
25 years

ব্যাখ্যা

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.

২৮৮.

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?

ক
ক) 5:6
খ
খ) 7:3
গ
গ) 10:3
ঘ
ঘ) 11:7

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

২৮৯.

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?

ক
13 years
খ
20 years
গ
17 years
ঘ
12 years
ঙ
15 years

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.

২৯০.

Today is Hasan's 12^th birthday and his father's 40^th birthday. How many years from today will Hasan's father be twice as old as Hasan at that time?

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

ব্যাখ্যা

Question: Today is Hasan's 12^th birthday and his father's 40^th birthday. How many years from today will Hasan's father be twice as old as Hasan at that time?

Solution:
Given that,
Today, Hasan is 12 years old
And his father is 40 years old

Age difference = 40 - 12 = 28 years (constant)

Let after x years, father's age = 2 × Hasan's age

Now,
Hasan's age after x years = 12 + x
Father's age after x years = 40 + x

ATQ,
40 + x = 2 × (12 + x)
⇒ 40 + x = 24 + 2x
⇒ x = 40 - 24

∴ x = 16

So, in 16 years, Hasan's father will be twice as old as Hasan.

২৯১.

Sibli is younger than Simul by 7 years, and the ratio of their ages is 7 : 9. What is the age of Sibli?

ক
24 years
খ
23.5 years
গ
24.5 years
ঘ
25 years

ব্যাখ্যা

Question: Sibli is younger than Simul by 7 years, and the ratio of their ages is 7 : 9. What is the age of Sibli?

Solution:
Let the age of Sibli and Simul be 7x and 9x respectively

According to the Question:
7x = 9x - 7
⇒ 2x = 7
∴ x = 7/2 = 3.5

So, Sibli's age = 7x = 7 × 3.5 = 24.5 years

২৯২.

The product of the ages of A and B is 240. If twice the age of B is more than A’s age by 4 years, what was B’s age 2 years ago?

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

ব্যাখ্যা

Question: The product of the ages of A and B is 240. If twice the age of B is more than A’s age by 4 years, what was B’s age 2 years ago?

Solution:
Let A’s present age be x years.
Then, B’s present age = 240/x years

ATQ,
2 × (240/x) - x = 4
⇒ 480 - x² = 4x
⇒ x² + 4x - 480 = 0
⇒ (x + 24)(x - 20) = 0
∴ x = 20 [Negative value is not acceptable]

∴ B’s present age = 240/20 = 12 years
Thus, B’s age 2 years ago = 12 - 2 = 10 years

২৯৩.

Today is Sumon's birthday. One year, from today he will be twice as old as he was 12 years ago. How old is Sumon today?

ক
20 years
খ
22 years
গ
25 years
ঘ
30 years

ব্যাখ্যা

Question: Today is Sumon's birthday. One year, from today he will be twice as old as he was 12 years ago. How old is Sumon today?

Solution:
আজকে সুমনের বয়স = x বছর
১ বছর পর সুমনের বয়স হবে = (x + 1) বছর

শর্তমতে,
x + 1 = 2(x - 12)
⇒ x + 1 = 2x - 24
∴ x = 25

২৯৪.

The present age of a father is 5 times that of his son. After 8 years, the ratio will be 3 : 1. Find their age gap.

ক
8
খ
32
গ
40
ঘ
48

ব্যাখ্যা

Question: The present age of a father is 5 times that of his son. After 8 years, the ratio will be 3 : 1. Find their age gap.

Solution:
Let the present age of the son = x years.
Present age of the father = 5x years.

After 8 years:
Son = x + 8
Father = 5x + 8
Given ratio after 8 years = 3 : 1

Accordingly,
(5x + 8) / (x + 8) = 3
⇒ 5x + 8 = 3(x + 8)
⇒ 5x + 8 = 3x + 24
⇒ 5x - 3x = 24 - 8
⇒ 2x = 16
∴ x = 8

Present ages of
Son = x = 8 years
And Father = 5x = 40 years

Age gap = 40 - 8 = 32

So the age gap is 32 years.

২৯৫.

18 years ago, a man was three times as old as his son. Now, the man is twice as old as his son. The sum of the present ages of the man and his son is = ?

ক
ক) 54 years
খ
খ) 72 years
গ
গ) 105 years
ঘ
ঘ) 108 years
ঙ
ঙ) 111 years

ব্যাখ্যা

Let the son's age 18 years ago be x years,
Then man's age 18 years ago = 3x years
(3x+18) = 2(x+18)
⇒ 3x+18 = 2x+36
⇒ x = 18
Sum of their present ages
⇒ (3x+18+x+18) years
⇒ (4x+36) years
⇒ (4×18+36) years
⇒ 108 years

২৯৬.

The average age of father and son is 30 years. After 6 years, the ratio of the age of them is 5 : 1. The present age of son is

ক
ক) 4
খ
খ) 6
গ
গ) 12
ঘ
ঘ) 14

ব্যাখ্যা

The average age of father and son is 30 years.
The total age of father and son is 30 × 2 = 60 years.
Suppose, after 6 years, the age of father and son are 5x and x years respectively.
5x - 6 + x - 6 = 60
⇒ 6x = 72
∴ x = 12
present age of son is 12 - 6 = 6 years.
------------------------------------------------------
পিতা ও পুত্রের বয়সের গড় ৩০ বছর। ৬ বছর পরে তাদের বয়সের অনুপাত ৫ঃ১ হলে, পুত্রের বর্তমান বয়স কত?

পিতা ও পুত্রের বয়সের গড় ৩০ বছর হলে, তাদের মোট বয়স = ৩০ × ২ = ৬০ বছর
মনে করি, ৬ বছর পরে, পিতার বয়স 5x ও পুত্রের বয়স x বছর
5x - 6 + x - 6 = 60
⇒ 6x = 72
∴ x = 12
পুত্রের বর্তমান বয়স ১২ - ৬ = ৬ বছর

২৯৭.

In a family the average age of the father and mother is 38 years whereas the average age of father, mother and their only daughter is 28 years. Then the age of the daughter is -

ক
7 years
খ
6 years
গ
5 years
ঘ
4 years
ঙ
8 years

ব্যাখ্যা

The age of the daughter = (3 × 28) - (2 × 38)
= 84 - 76
= 8 years

২৯৮.

Tomal is younger than Jamal by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Jamal?

ক
24.5 years
খ
30.5 years
গ
31.5 years
ঘ
32 years

ব্যাখ্যা

Question: Tomal is younger than Jamal by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Jamal?

Solution:
Let Jamal's age be x years.
Then, Tomal's age = (x - 7) years.

ATQ,
(x - 7)/x = 7/9
⇒ 9((x - 7) = 7x
⇒ 9x - 63 = 7x
⇒ 9x - 7x = 63
⇒ 2x = 63
∴ x = 31.5

Jamal's age is 31.5 years.

২৯৯.

Age of a mother 10 years ago was 3 times the age of her son. After 10 years, the 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

ব্যাখ্যা

We are given that,
age of mother 10 years ago was 3 times the age of her son
So,
let the age of the son be x and as the mother's age is 3 times the age of her son, let it be 3x, three years ago.
At present,
Mother's age will be (3x + 10) and son's age will be (x + 10)
After 10 years,
Mother's age will be (3x + 10) +10 and son’s age will be (x + 10) + 10

Mother's age is twice that of son
(3x + 10) +10 = 2 [(x + 10) + 10]
(3x + 20) = 2[x + 20]
Solving the equation, we get x = 20
We are asked to find the present ratio.
(3x + 10) : (x + 10) = 70 : 30
(3x + 10) : (x + 10) = 7 : 3.

৩০০.

After 15 years, Rahul’s age will be five times what it was 5 years before. How old is Rahul now?

ক
12 years
খ
10 years
গ
9 years
ঘ
16 years

ব্যাখ্যা

Question: After 15 years, Rahul’s age will be five times what it was 5 years before. How old is Rahul now?

Solution:
Given that,
Rahul’s age after 15 years will be five times his age 5 years ago.

Let Rahul’s present age = x years

According to the question:
⇒ x + 15 = 5(x - 5)
⇒ x + 15 = 5x - 25
⇒ 5x - x = 15 + 25
⇒ 4x = 40
∴ x = 10

∴ Rahul is 10 years old now.