10 years ago simrans mother was 4 times older than her daughter . after 10 years the mother will be twice oder than her daughter . find present age of simran
Simran's present age=x
Simran's age 10 years ago = x-10
Her mother's age 10 years ago = 4(x-10)
Simran's age after 10 years= x+10
Her mother's age after 10years =2( x+ 10 )
ATQ,
2(x-10) +20 = 4 (x+10)
2x- 20 +20=4x+40
2x=4x+40
4x-2x=40
x= 40 ÷ 2
x= 20
Simran's present age is 20 years
Simran's present age=x
Simran's age 10 years ago = x-10
Her mother's age 10 years ago = 4(x-10)
Simran's age after 10 years= x+10
Her mother's age after 10years =2( x+ 10 )
ATQ,
2(x-10) +20 = 4 (x+10)
2x- 20 +20=4x+40
2x=4x+40
4x-2x=40
x= 40 ÷ 2
x= 20
Simran's present age is 20 years
Good
Well, it seems like Simran's mother must have really enjoyed being older than her daughter! Let's do some math to find out their present ages.
Let's assume that Simran is currently 'S' years old and her mother is 'M' years old.
We are given that 10 years ago, Simran's mother was 4 times older than Simran. So, we can write the equation: M - 10 = 4(S - 10).
Next, we are told that after 10 years, the mother will be twice as old as Simran. So, we can also write the equation: M + 10 = 2(S + 10).
Now, let's solve these equations:
M - 10 = 4S - 40
M + 10 = 2S + 20
Simplifying the first equation:
M = 4S - 30
Substituting this value of M into the second equation:
4S - 30 + 10 = 2S + 20
4S - 20 = 2S + 20
2S = 40
S = 20
So, Simran is currently 20 years old. But we need to find the present age of Simran's mother, so let's substitute this value of S back into the equation for M:
M = 4(20) - 30
M = 80 - 30
M = 50
Therefore, Simran's mother is currently 50 years old.
Hope that helps!
To find the present age of Simran, we can use a system of equations based on the information given.
Let S be the present age of Simran and M be the present age of her mother.
According to the problem, "10 years ago, Simran's mother was 4 times older than her daughter." This can be written as:
M - 10 = 4(S - 10) ---------(Equation 1)
Also, the problem states that "after 10 years, the mother will be twice older than her daughter." This can be written as:
M + 10 = 2(S + 10) ---------(Equation 2)
To solve this system of equations, we can use the substitution or elimination method.
Let's use the substitution method.
From Equation 1, we can simplify it as:
M - 10 = 4S - 40
M = 4S - 30
Now we can substitute M in Equation 2 with the value of 4S - 30:
4S - 30 + 10 = 2(S + 10)
4S - 20 = 2S + 20
4S - 2S = 20 + 20
2S = 40
S = 40/2
S = 20
Therefore, the present age of Simran is 20 years old.
m = 2s
(m-10) = 4(s-10)
Substitute 2s for m in the second equation and solve for s.