Problems on Ages - Quiz

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

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 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.

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.

 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.

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 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 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

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