Six years ago the ratio of the ages of vimal and saroj was6:5. 4 years hence the ratio of their age will be 11:10 . What is the sarojs age at present?
Answers
Answer:
Vimal = 18 yrs.
Saroj = 16 yrs.
Step-by-step explanation:
Let the present ages of Vimal and Saroj are x and y yrs. respectively.
Six yrs. ago,
Age of Vimal = (x-6) yrs.
Age of Saroj = (y-6) yrs.
But, it's given that,
Their ages were in the ratio of 6:5.
Therefore, we will get,
=> (x-6)/(y-6) = 6/5
=> 5(x-6) = 6(y-6)
=> 5x - 30 = 6y - 36
=> 5x - 6y - 30 + 36 = 0
=> 5x - 6y + 6 = 0
=> 10x - 12y + 12 = 0 ......(1)
Now,
4 yrs. hence,
Age of Vimal = (x+4) yrs.
Age of Saroj = (y+4) yrs.
But, it's given that,
Their ages will be in the ratio of 11:10
Therefore, we will get,
=> (x+4)/(y+4) = 11/10
=> 10(x+4) = 11(y+4)
=> 10x + 40 = 11y + 44
=> 10x - 11y + 40 - 44 = 0
=> 10x - 11y - 4 = 0 .......(2)
Now, subtracting eqn (2) from (1), we get,
=> -12y - (-11y) + 12 - (-4) = 0
=> -12y + 11y + 12 + 4 = 0
=> -y + 16 = 0
=> y = 16
Substituting this value in eqn (2),
=> 10x - 176 - 4 = 0
=> 10x - 180 = 0
=> 10x = 180
=> x = 180/10
=> x = 18
Hence, the present ages of Vimal and Saroj are 18 and 16 yrs. respectively.
Let present age of Vimal be x years old and that of Saroj be y years.
So, According to Question, 6 years ago their ages were :- x - 6/ y - 6 = 6/5
5x - 6y = -6
Again, 4 years after,
x + 4/ y + 4 = 11/10
10x - 11y = -4
After solving these equations, we get
y = 8
and hence
The current age of Saroj is 8 years.
Hope it helps
Thank you, have a great day
Keep Smiling
Stay Safe Stay home