Problems on Ages

Let mother's age be 7x years. Then, daughter's age = x years. 7x-4 / x-4 = 19 / 1 → 7x-4=19 (x-4) 19x-7x=76-4 ⇒ 12x = 72 ⇒ x= 6. Mother's age after 4 years (7x + 4)= (7 x 6 + 4) years = 46 years

Let Nishi's age be 6x years. Then, Vinnee's age = 5x years.
6x +9 / 5x+9 = 9/8
⇒ 8 (6x+9)= 9 (5x+9)
48x - 45x = 81 - 72
3x = 9
⇒x= 3.

Difference in their ages = (6x - 5x) = x years = 3 years.

Let the present ages of Amit and his father be 2x and 5x years respectively. Four years from now, the ages of Amit and his father will be (2x + 4) and (5x + 4) years respectively. The ratio of their ages four years from now is (2x + 4) : (5x + 4) = 5 : 11. Solving this equation for x, we get x = 3. Substituting this value in the expression for the father's present age, we get that the father's present age is 5 * 8 = 40years. Therefore, the father's age five years ago was 40- 5 = 35years.

Let the present ages of the father and son be 17x and 7x years respectively. Six years ago, the ages of the father and son were (17x - 6) and (7x - 6) years respectively. The ratio of their ages six years ago was (17x - 6) : (7x - 6) = 3:1. Solving this equation for x, we get x = 3 Substituting this value in the expression for the father's present age, we get that the father's present age is 17 * 3 = 51years.

Let the present ages of Shakti and Kanti be 8x and 7x years respectively.
After 10 years, the ages of Shakti and Kanti will be (8x + 10) and (7x + 10) years respectively.
The ratio of their ages after 10 years will be (8x + 10) : (7x + 10) = 13:12.
Solving this equation for x, we get x = 2
Substituting this value in the expressions for the present ages of Shakti and Kanti, we get that their present ages are 8 * 2= 16 years and 7 * 2= 14 years respectively.
Therefore, the difference between their ages is 16 - 14 = 2 years. 

Let the present ages of A and B be 6x and 5x years respectively. The sum of their ages is (6x + 5x) = 44 years. Solving this equation for x, we get x = 4. Substituting this value in the expressions for the present ages of A and B, we get that their present ages are 6 * 4 = 24 years and 5 * 4 = 20 years respectively. After 8 years, the ages of A and B will be (24 + 8) and (20 + 8) years respectively. The ratio of their ages after 8 years will be (24 + 8) : (20 + 8) = 32 : 28 = 8 : 7. Therefore, the ratio of their ages after 8 years will be 8:7.

Let x be the present age of the daughter.
The age of the mother today is thrice that of her daughter, which means that the mother's age today is 3 * x years.
After 12 years, the age of the mother will be twice that of her daughter, which means that the mother's age will be 2 * (x + 12) years.
Since the mother's age after 12 years is twice that of her daughter, this means that 3 * x = 2 * (x + 12).
Solving this equation for x, we get x = 12.
Therefore, the present age of the daughter is 12 years.  

Let the present age of Mr. Sanyal's son be x years.
The present age of Mr. Sanyal is three times the age of his son, which means that Mr. Sanyal's present age is 3 * x years.
Six years hence, the ages of Mr. Sanyal and his son will be (3 * x + 6) and (x + 6) years respectively.
The ratio of their ages six years hence will be (3 * x + 6) : (x + 6) = 5:2.
Solving this equation for x, we get x = 18
Substituting this value in the expression for Mr. Sanyal's present age, we get that Mr. Sanyal's present age is 3 * 18 = 54 years 

Let the present ages of the man and his daughter be x and y years respectively.
The average of their ages is (x + y)/2 = 34 years.
Four years from now, the ages of the man and his daughter will be (x + 4) and (y + 4) years respectively.
The ratio of their ages four years from now is (x + 4) : (y + 4) = 14:5.
Solving these equations for x and y, we get x = 52 and y = 16
Therefore, the daughter's present age is 16 years. 

Let the present age of the son be x + 10 years.
The age of the father 10 years ago was thrice the age of his son, which means that the father's age 10 years ago was 3 * x years.
Ten years from now, the father's age will be twice that of his son, which means that the father's age will be 2 * (x + 20) years.
Since the father's age 10 years ago was thrice the age of his son, and the father's age 10 years from now will be twice that of his son, this means that  (3x +20) = 2 * (x + 20).
Solving this equation for x, we get x = 20.
Therefore, the present ages of the father and son are (20 * 3)+10 = 70 years and 30 years respectively, and the ratio of their ages is 70:30 = 7:3. 

 
Let x be John's age.
Since Mary is 25 years older than John, her age is x + 25.
 The sum of their ages is 65, so x + (x + 25) = 65.
 Simplifying this equation gives 2x = 40, so x = 20.
 Therefore,
 John is 20 years old and Mary is 20 + 25 = 45 years old.

 Solution:

 Since Mary is half as old as John, she is 40 / 2 = <<40/2=20>>20 years old.
 Since Sam is twice as old as Mary,
 he is 2 * 20 = <<2*20=40>>40 years old.

 Therefore, Sam is 40 years old.

 
The daughter is currently 10 years old and the father is currently 40 years old.
 In 10 years, the daughter will be 20 years old and the father will be 50 years old. 

Therefore, the father will be 2.5 times the daughter's age at that time. 

We are given that age ratio of Honey: Piyush = 2: 3
Honey’s age = 2x and Piyush’s age = 3x
One year ago, their age was 2x and 3x.
Hence at present, Honey's age = 2x +1 and Piyush's age = 3x +1
After 5 years, Honey’s age = (2x +1) + 5 = (2x + 6)
Piyush'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 ⇒ x = 3
Piyush's present age = (3x + 1) = (3x 3 + 1) = 10 years
Honey's present age = (2x + 1) = (2x 3 + 1) = 7 years 

Ten years ago:

Mother's age = 3x
Son's age = x
At present:

Mother's age = 3x + 10
Son's age = x + 10
After ten years:

Mother's age = (3x + 10) + 10 = 3x + 20
Son's age = (x + 10) + 10 = x + 20
Mother's age is twice that of son after ten years:
3x + 20 = 2(x + 20)

Solving the equation:
3x + 20 = 2x + 40
x = 20

The present age ratio of the mother to the son is:
(3x + 10) : (x + 10) = 7:3

The mother is currently 70 years old and the son is currently 30 years old 



                          
                        

Saransh's age x years ago = 50 - x
Nazma's age x years ago = 40 - x
The ratio of their ages x years ago was 3:2
Substituting the values:
(50 - x) / (40 - x) = 3/2

Solving the equation:
x = 20

This means that 20 years ago, the ratio of Saransh's age to Nazma's age was 3:2. 

Pranav's age now = 4X
Qureshi's age now = 5X
The ratio of their ages 5 years ago was 7:9
Substituting the values:
(4X - 5) : (5X - 5) = 7:9

Solving the equation:
X = 10

This means that Pranav is currently 40 years old and Qureshi is currently 50 years old. 

Roshan's age = x
Dinesh's age = x - 9
The ratio of their ages is 4:5
Substituting the values:
(x - 9) / x = 4/5

Solving the equation:
x = 45

This means that Roshan is 45 years old and Dinesh is 36 years old. 

Sara's age now = 5x
Vaishali's age now = 3x
The ratio of Sara's age four years ago to Vaishali's age in the future was 1:1
Substituting the values:
(5x - 4) / (3x + 4) = 1/1

Solving the equation:
x = 4

This means that Sara is currently 20 years old and Vaishali is currently 12 years old. The ratio of Sara's age four years from now to Vaishali's age four years ago is 3:1. 

C: x years
B: 2x years
A: 2x + 2 years
Total: 5x = 25 years

Solving for x, we find that C is 5 years old, B is 2 * 5 = 10 years old, and A is 2 * 5 + 2 = 12 years old.
 The total age of all three is 5 * 5 + 10 + 12 = 27 years, as stated in the original question. 

At present, the person's age is one-half of their mother's age plus 8 years. The mother's current age can be represented as x. The person's current age is 2/5x. In 8 years, the person will be 1/2x + 8 years old. Since the person's current age is 2/5x and in 8 years they will be 1/2x + 8 years old, the mother's current age is x. 2/5x = 1/2x + 8 This simplifies to x = 40 years old.

Son's present age: x years
Father's age at son's birth: x years
Father's present age: 38 years
x + x = 38
2x = 38
x = 19
The son's age five years ago was 19 - 5 = 14 years.

Person's present age: x years
Person's age three years in the future: x + 3 years
Person's age three years in the past: x - 3 years
3(x + 3) - 3(x - 3) = x
3x + 9 - 3x + 9 = x
18 = x
The person's current age is 18 years old.

 If you let the present age of Ram be represented by the variable x, 
and the present age of Shyam be represented by x-16, 
then you can set up the equation (x-6) = 3(x-16-6) to represent the statement "6 years ago,
 the Ram was 3 times as old as Shyam." 
Solving this equation for x gives you x = 30, which is the present age of Ram. 

By letting the age of Minu be represented by 4X and the age of Meera be represented by 2X,
you were able to set up the equation 4X + 2X = 6,
which represents the statement "the sum of their ages is 6 years." 
Solving this equation for X gives you X = 1,
which means that Minu is currently 4 years old and Meera is currently 2 years old.  
 
You then correctly found the ratio of their ages after 8 years by adding 8 to both of their
current ages and expressing the result as a ratio: (4+8):(2+8) = 12:10 = 6:5.

x: age of son 10 years ago

3x: age of John 10 years ago  




2(x+20) = 3x+20: in 10 years, John's age will be twice that of the son's age 


x+10: present age of son 


3x+10: present age of John 


x+10 = 30: present age of son is 30 years old 


3x+10 = 70: present age of John is 70 years old 


x = 20: age of son 10 years ago is 20 years 


3x = 60: age of John 10 years ago is 60 years 


70:30 = 7:3: ratio of present ages of John and son is 7:3

x: present age of Vipul A: present age of mother
x = 2/5 * A: Vipul's age is currently two-fifths of the age of his mother
x+8 = 1/2 * A: in eight years, Vipul will be half the age of his mother
x = 16: present age of Vipul is 16 years old
x = 2/5 * A: Vipul's age is currently two-fifths of the age of his mother
16 = 2/5 * A: present age of Vipul is 16 years old
A = 5/2 * 16: present age of mother is 40 years old

Let the present age of the son = x
Then, the present age of the mother = 60 - x
As per the question:
Six years ago, the mother's age was 5 times the age of her son:
(60 - x) - 6 = 5(x - 6)
54 - x = 5x - 30
84 = 6x
x = 84/6
x = 14 years
So, the son's present age is 14 years and his age after 6 years will be 14 + 6 = 20 years.

Let x be the present age of Ruchi. Six years ago, the ratio of Preeti's age to Ruchi's age was 6:5, so six years ago Preeti was 6x years old and Ruchi was 5x years old. After four years, the ratio of their ages will be 11:10, so in four years Preeti will be (6x + 4) years old and Ruchi will be (5x + 4) years old. The ratio of their ages in four years will be 11:10, so: (6x + 4) : (5x + 4) = 11:10 10(6x + 4) = 11(5x + 4) 60x + 40 = 55x + 44 5x = 4 x = 4/5 = 0.8 Ruchi's present age = (5x + 6) = 5 * 0.8 + 6 = 16 years.

Haseena's present age = x Haseena's age in 6 years = x + 6 According to the information given, we can set up the following equation: x + 6 = 26 Solving for x, we get: x = 26 - 6 = 20 This tells us that Haseena's present age is 20 years. If we let the present age of Anushka be represented by a variable y, then we can set up the following equation: y / x = 4/3 Substituting the value of x that we found earlier (x = 20), we get: y / 20 = 4/3 Solving for y, we get: y = 20 * 3/4 = 15 This tells us that Anushka's present age is 15 years.

 If John's present age is represented by x, and his age 5 years ago is x-5,
 and his age in 10 years will be x+10,
 and we are given that John's age in 10 years will be 5 times his age 5 years ago,
 we can set up the equation (x+10)=5(x-5). 

Solving this equation gives us x+10=5x-25, or 4x=35,
 which means John's present age is 8.75 years.

If the age of Rohan is represented by y,
 and Rahul is 15 years older than Rohan, meaning his age is y+15,
 then Rahul's age 5 years ago was y+15-5. Rohan's age 5 years ago was y-5.

 If we are given that 5 years ago, Rahul was 3 times as old as Rohan, 
we can set up the equation (y+15-5)=3(y-5). 

Solving this equation gives us y+10=3y-15, or 2y=25,
 which means Rohan is 12.5 years old. This means that Rahul is 27.5 years old. 

 "If the ages of two individuals are given in the ratio A:B,
 then the ages can be represented as Ax and Bx.

 In this case,
 we are given that the age ratio of Harry and Peter is 5:6,
 meaning Harry's age is 5x and Peter's age is 6x.

One year ago, their ages were 5x and 6x, respectively, 
so their present ages are 5x+1 and 6x+1. 

After 4 years, Harry's age will be (5x+1)+4=(5x+5) and Peter's age will be (6x+1)+4=(6x+5). 

If the ratio of their ages after 4 years is given as 6:7,
 we can set up the equation (5x+5):(6x+5)=6:7. 

Solving this equation gives us x=5,
 meaning Peter's present age is 6x+1=(6x5)+1=31 years 
and Harry's present age is 5x+1=(5x5)+1=26 years.

 If the age of the mother 10 years ago was 3 times the age of her son,
 and the mother's age in 10 years will be twice the age of her son,
 
the equation can be represented as:

3x+10+10=2(x+10+10)
3x+20=2x+40
x=20

The present ratio of the mother's age to the son's age is 

(3x+10):(x+10) = (3*20+10):(20+10) = 70:30 = 7:3.



                          
                        

Let x represent the number of years ago.

At present:

Sharad's age = 60 years
Santosh's age = 80 years
x years ago:

Sharad's age = 60 - x years
Santosh's age = 80 - x years
Ratio of their ages x years ago was 4:6:

(60 - x) : (80 - x) = 4 : 6
6(60 - x) = 4(80 - x)
360 - 6x = 320 - 4x
x = 20
Therefore, 20 years ago, the ratio of their ages was 4:6 

 If the ratio of Rohan's age 4 years ago and Rahul's age after 4 years is 1:1,
 and the present ratio of their ages is 5:3, the equation can be represented as:
(5x-4)/(3x+4)=1/1

Solving this equation gives us x=4, 
which means that the ratio between Rohan's age 4 years 
in the future and Rahul's age 4 years in the past is 
(5x+4):(3x-4) = 24:8 = 3:1.

Let the present ages of the three colleagues be 3x, 5x, and 7x respectively.
The sum of their ages four years ago is equal to their present ages minus 4 years for each of them, 

which is equal to (3x - 4) + (5x - 4) + (7x - 4) = 48.
Combining like terms, we get 15x - 12 = 48.
Adding 12 to both sides, we get 15x = 60.
Dividing both sides by 15, we get x = 4.

Therefore, the present ages of the three colleagues are
 3x = 3 * 4 = 12 years, 5x = 5 * 4 = 20 years, 
and 7x = 7 * 4 = 28 years.

M:D = 9:5
M*D = 1125

We can find the value of x by solving the second equation:

MD = 1125
M = 9x
D = 5x
9x5x = 1125
45x^2 = 1125
x^2 = 25
x = sqrt(25)
x = 5

Substituting this value back into the first equation,
 we get the ratio of their ages after five years:

M+5:D+5 = (9x+5):(5x+5) = (95+5):(55+5) = 50:30

So the ratio of their ages after five years is 5:3.

Five years ago, the ratio of Omkar's age to Nitin's age was 8:7.
In three years, the ratio of Omkar's age to Nitin's age will be 12:11.
You are asked to find Nitin's present age.

Using this information, you can set up the following equations:

Omkar's age 5 years ago: 8x
Nitin's age 5 years ago: 7x
Omkar's age now: 8x + 5
Nitin's age now: 7x + 5
Omkar's age in 3 years: 8x + 8
Nitin's age in 3 years: 7x + 8

The problem states that the ratio of Omkar's age to Nitin's age five years ago was 8:7, 
so we can set up the following equation:

(8x)/(7x) = 8/7

Simplifying this equation gives us:

8x = 8/7 * 7x
8x = 8x

Since these two expressions are equal, we can set up the following 
equation to represent the ratio of Omkar's age to Nitin's age in three years:

(8x + 8)/(7x + 8) = 12/11

Solving this equation for x gives us:

88x + 88 = 84x + 96
4x = 8
x = 2

Substituting this value for x into the equation for Nitin's age now gives us:

Nitin's age now = 7x + 5 = 7 * 2 + 5 = 19 years

Therefore, Nitin's present age is 19 years.

If the difference in ages between the two people is 16 years,
 then the elder person is 16 years older than the younger person.
 Let X be the present age of the younger person. The elder person is X + 16 years old.

Six years ago, the elder person was X + 16 - 6 = X + 10 years old.

At that time, the elder person was 3 times as old as the younger person, 
so the younger person was (X + 10)/3 years old.

Six years ago, the younger person was X - 6 years old,
 so we can set up the following equation:

(X + 10)/3 = X - 6

Solving this equation gives us X = 14.

The present age of the younger person is 14 years,
 so the present age of the elder person is 14 + 16 = 30 years.

 Let G be Gaurav's age one year ago and S be Sachin's age one year ago.

Then, Gaurav's age 4 years hence = G + 4 = 6x + 5

Sachin's age 4 years hence = S + 4 = 7x + 5

We can set up the following equation:

6x + 5 = 7x + 5

Solving this equation gives us:

x = 5

Therefore, Sachin's present age = S + 1 = 7x + 1 = 7 * 5 + 1 = 36 years

 Let A be Abhay's age 10 years ago and F be Abhay's father's age 10 years ago.

Then, Abhay's age after 6 years = A + 10 + 6 = x + 16

Father's age after 6 years = F + 10 + 6 = 5x + 16

We can set up the following equation:

x + 16 = 3/7 * (5x + 16)

Solving this equation gives us:

x = 8

Therefore, Abhay's father's present age = F + 10 = 5x + 10 = 5 * 8 + 10 = 50 years.

 Let's call the age Rajeev is currently X years old.

In 15 years, Rajeev will be X + 15 years old.

5 years ago, Rajeev was X - 5 years old.

Thus, 5 years from now, Rajeev will be X - 5 + 5 = X years old.

Therefore, in 15 years, Rajeev will be 5 times as old as he was 5 years ago, or 5 * (X - 5) = X + 15.

Solving for X, we get:

5 * (X - 5) = X + 15
5X - 25 = X + 15
4X - 25 = 15
4X = 40
X = 10

Therefore, Rajeev is currently 10 years old.

Ankit's age: x years
Nikita's age: y years

Equation: 2y - x = 4
Substituting the expression for Nikita's age: 2(240/x) - x = 4
Multiplying through the parentheses: 480 - x^2 = 4x
Combining like terms: x^2 + 4x - 480 = 0
Factoring: (x+24)(x-20) = 0
Solving: x = 20 or x = -24

Since Ankit's age cannot be negative, we know that Ankit's age is 20 years. 

Son's age: x years
Father's age: y years

Equation 1: y = 3 + 3x
Equation 2: y + 3 = 2(x + 3) + 10
Substituting equation 1 into equation 2: 3 + 3x + 3 = 2(x + 3) + 10
Combining like terms: 3x + 6 = 2x + 16
Subtracting 2x from both sides: x + 6 = 16
Subtracting 6 from both sides: x = 10
Substituting this value for x into equation 1: y = 3 + 3x
Substituting 10 for x: y = 3 + 3 * 10
Simplifying: y = 3 + 30
Simplifying further: y = 33
Therefore, the father's present age is 33 years.

Son's age 8 years ago: x years
Rohit's age 8 years ago: y years
Son's age after 8 years: z years
Rohit's age after 8 years: w years

Equations:

y = 4x
z = x + 16
w = 4x + 16
2z = w
Substituting the expression for z and w:

2(x + 16) = 4x + 16
2x + 32 = 4x + 16
2x = 16
x = 8
Substituting this value for x into the expressions for the son's and Rohit's ages:
Son's present age: x + 8 = 8 + 8 = 16 years
Rohit's present age: 4x + 8 = 4 * 8 + 8 = 40 years

Let P's present age be 3x and Q's present age be 4x. Ten years ago, P's age was half of Q's age, so we can write this as: (3x - 10) = 1/2(4x - 10) Solving for x, we get: 6x - 20 = 4x - 10 2x = 10 x = 5 Thus, the total of their present ages is 7x = 7 * 5 = 35.

Let the ages of Ashok, Anil, and Ajay 5 years ago be 3x, 4x, and 5x years, respectively. 
Then, their present ages are (3x + 5), (4x + 5), and (5x + 5) years.

The sum of their present ages is 75 years, so we can write this as:

(3x + 5) + (4x + 5) + (5x + 5) = 75

Solving for x, we get:

12x + 15 = 75
12x = 60
x = 5

Thus, Anil's present age is (4x + 5) = (4 * 5 + 5) = 25 years.

Let Cindy's current age be x. Then, Mindy's age is 3x.
According to the question, we can write this as: 3x - 4 = 4(x - 4)

Simplifying the right side of the equation, we get:
3x - 4 = 4x - 16

Solving for x, we get:
x = 12

Thus, 5 years from now, Cindy's age will be 12 + 5 = 17 years

Let C be x years old.
Then B is 2x years old.
And A is (2x)+2 years old.
So the equation is: x+(2x)+((2x)+2)=27
This simplifies to: 5x+2=27
Subtracting 2 from both sides gives: 5x=25
Dividing both sides by 5 gives: x=5
So C is 5 years old.
B is 25=10 years old.
A is (25)+2=12 years old.
Therefore, B is 10 years old.

Solution

Let Tina's age be 9x years.Then Rakesh age be 10x years

5(9x-10)=4(10x-10)

45x-40x=50-40

5x=10

Solution

Let mother's age be x years.Then ,man's age =2x/5 years.

2x/5+8=1/2(x+8)

2x/5+8=1/2x+4

½x-2x/5=4

5x-4x=40

Solution

Samir's age=¼×father's age

Then Samir's age =x years,Reema's age=3/2×x years.and Father's age=4x years.

solution

let their ages be x years and (x-16) years

(x-6)=3{(x-16)-6}

x-6=3(x-22)

3x-x=66-6

2x=60

x=30

solutions

A's age =44×6/11=24

B's age =(44-24)=20

Ratio of their ages after 8 years=(24+8)/(20+8)=32/28=8/7

solution

let Nishi age be 6x years. Then then Venee's age equal to 5x years

(6x+9)/(5x+9)=9/8=8(6x+9)=9(5x+9)

48x-45x=81-72

3x=9

Solution:

let Samina age be 7x years.Then Suhana age be 3x years

(7x+6)/(3x+6)=5/3

3(7x+6)=5(3x+6)

21x+18=15x+30

6x=12

Solution

Let renu's age 10 years ago be x years

Then her father's age 10 years ago be 5x years

(x+10)+6=3/7×[(5x+10)+6]

x+10=3/7(5x+16)

7x+112=15x+48

8x=64

x=8

Solution

Let their ages be x years and (x+10) years

(x+10-15)=2(x-15)

x-5=2x-30

x=25

present age of the elder man =(x+10) years=(25+10)=35 years

Solution

let son's age 10 years ago be x years then man age 10 years ago be 3x years

sons present age equal to (x+10) man's present age=(3x+10)years

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

3x+20=2(x+20)

3x+20=2x+40

x=20

Solution

let Son age beX years then sanial age be 3x years

3x+6/x+6=5/2

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

6x+12=5x+30

x=18

present age of Sanial =3x years=3(18)=34 years

Output:

let the ages of Kunal and Sagar 6 years ago be 6x and 5x years

then (6x+6)/(5x+6)=11/10=6x+10/5x-10=11/10

60x+100=55x+110