In four years time khurail mother will be three time as old as khurail . Six years ago his mother was seven times as old as him
Find khurail present age and
His mother age at time of his birth?
Draw a number line, and label points -6, 0 for "now", and 4
put khurail age on top of line and the mothers age at the bottom
in the following way:
4 years from now:
khurail --- x years
mother ---- 3x
now:
khurail ---- x-4
mother ---- 3x-4
6 years ago:
khurail --- x-10
mother --- 3x - 10
but 3x-10 = 7(x-10)
3x-10 = 7x - 70
-4x = -60
x = 15
sub in ....
etc.....
Let's solve this step by step.
Let's assume Khurail's present age as "K" and his mother's present age as "M".
According to the information given, in four years, Khurail's mother will be three times as old as Khurail. We can write this as an equation:
(M + 4) = 3(K + 4) ---(1)
Also, six years ago, Khurail's mother was seven times as old as Khurail. We can write this as another equation:
(M - 6) = 7(K - 6) ---(2)
Now, we have a system of two equations with two unknowns. Let's solve them together.
First, let's simplify equation (1):
M + 4 = 3K + 12
M = 3K + 12 - 4
M = 3K + 8 ---(3)
Now, substitute equation (3) into equation (2):
3K + 8 - 6 = 7(K - 6)
3K + 2 = 7K - 42
2 + 42 = 7K - 3K
44 = 4K
K = 44/4
K = 11
So, Khurail's present age is 11.
Now, substitute the value of K into equation (3) to find M:
M = 3 * 11 + 8
M = 33 + 8
M = 41
So, Khurail's mother's present age is 41.
To find his mother's age at the time of Khurail's birth, we need to subtract Khurail's present age from his mother's present age:
Mother's age at the time of Khurail's birth = M - K
Mother's age at the time of Khurail's birth = 41 - 11
Mother's age at the time of Khurail's birth = 30
So, Khurail's mother was 30 years old at the time of his birth.
To solve this problem, let's assume Khurail's present age is represented by "K" and his mother's present age is represented by "M."
From the given information, we can set up two equations:
Equation 1: In four years' time, Khurail's mother will be three times as old as Khurail.
(M + 4) = 3(K + 4)
Equation 2: Six years ago, Khurail's mother was seven times as old as him.
(M - 6) = 7(K - 6)
Now, we can solve these equations simultaneously to find the values of K and M.
Solving Equation 1:
Expand the equation: M + 4 = 3K + 12
Rearrange the terms: M - 3K = 12 - 4
M - 3K = 8 (Equation A)
Solving Equation 2:
Expand the equation: M - 6 = 7K - 42
Rearrange the terms: M - 7K = -42 + 6
M - 7K = -36 (Equation B)
To solve these equations more easily, we will use the method of substitution.
Using Equation A, we can express M in terms of K:
M = 3K + 8
Substitute this value of M into Equation B:
3K + 8 - 7K = -36
Combine like terms: -4K + 8 = -36
Rearrange the terms: -4K = -36 - 8
Simplify: -4K = -44
Divide by -4: K = (-44) / (-4)
Simplify: K = 11
Khurail's present age (K) is 11 years.
Now, substitute this value of K into Equation A to find M:
M = 3K + 8
M = 3(11) + 8
M = 33 + 8
M = 41
Khurail's mother's present age (M) is 41 years.
To find the mother's age at the time of Khurail's birth, subtract Khurail's present age from his mother's present age:
Mother's age at Khurail's birth = M - K
= 41 - 11
= 30
Therefore, Khurail's mother was 30 years old when he was born.