5 years ago, the age of Diksha's grandfather was 6 times that of Diksha and after 10 years from now, her Grandfather will be 3 times of her age. Find the ratio of Diksha and her Grandfather’s present age.
Answers
Given :
- 5 years ago, the age of Diksha's grandfather was 6 times that of Diksha.
- After 10 years from now, her Grandfather will be 3 times of her age.
To find :
- The ratio of Diksha and her Grandfather’s present age =?
Step-by-step explanation :
First Case :
5 years ago, the age of Diksha's grandfather was 6 times that of Diksha.
As per question,
Let, the present age Diksha's be, x.
Then, the present age of Diksha's grandfather be, y.
Now,
5 years ago,
Diksha's age = x - 5
Diksha's grandfather age = y - 5
According to the question,
x - 5 = 6(y - 5)
x - 5 = 6y - 30
x - 6y = - 30 + 5
x - 6y = - 25 ...... (i)
Second Case :
After 10 years from now, her Grandfather will be 3 times of her age.
Let, the present age Diksha's be, x.
Then, the present age of Diksha's grandfather be, y.
After 10 years from now,
Diksha's age = x + 10
Diksha's grandfather age = y + 10
According to the question,
x + 10 = 3(y + 10)
x + 10 = 3y + 30
x - 3y = 30 - 10
x - 3y = 20 ......(ii)
Subtracting equation (i) from (ii), we get,
x - 3y - (x - 6y) = 20 -(-25)
x - 3y - x + 6y = 20 + 25
3y = 45
y = 45/3
y = 15.
On putting the value of y = 15 in equation (i), we get,
x - 6y = - 25
x - 6 × 15 = - 25
x - 90 = - 25
x = - 25 + 90
x = 65.
Therefore, We got the value of x and y = 15 and 65 respectively,
Now,
The ratio of Diksha and her Grandfather’s present age,
Ratio = Diksha's present age/Diksha's grandfather present age.
Substituting the values, we get,
= 15/65
= 3/13
Therefore, the ratio of Diksha and her Grandfather’s present age = 3 : 13.
Answer:
Given :
5 years ago, the age of Diksha's grandfather was 6 times that of Diksha.
After 10 years from now, her Grandfather will be 3 times of her age.
To find :
The ratio of Diksha and her Grandfather’s present age =?
Step-by-step explanation :
First Case :
5 years ago, the age of Diksha's grandfather was 6 times that of Diksha.
As per question,
Let, the present age Diksha's be, x.
Then, the present age of Diksha's grandfather be, y.
Now,
5 years ago,
Diksha's age = x - 5
Diksha's grandfather age = y - 5
According to the question,
x - 5 = 6(y - 5)
x - 5 = 6y - 30
x - 6y = - 30 + 5
x - 6y = - 25 ...... (i)
Second Case :
After 10 years from now, her Grandfather will be 3 times of her age.
Let, the present age Diksha's be, x.
Then, the present age of Diksha's grandfather be, y.
After 10 years from now,
Diksha's age = x + 10
Diksha's grandfather age = y + 10
According to the question,
x + 10 = 3(y + 10)
x + 10 = 3y + 30
x - 3y = 30 - 10
x - 3y = 20 ......(ii)
Subtracting equation (i) from (ii), we get,
x - 3y - (x - 6y) = 20 -(-25)
x - 3y - x + 6y = 20 + 25
3y = 45
y = 45/3
y = 15.
On putting the value of y = 15 in equation (i), we get,
x - 6y = - 25
x - 6 × 15 = - 25
x - 90 = - 25
x = - 25 + 90
x = 65.
Therefore, We got the value of x and y = 15 and 65 respectively,
Now,
The ratio of Diksha and her Grandfather’s present age,
Ratio = Diksha's present age/Diksha's grandfather present age.
Substituting the values, we get,
= 15/65
= 3/13
Therefore, the ratio of Diksha and her Grandfather’s present age = 3 : 13.
hope it helps !!!!!!!!!!!!