1. Sneha is twice as old as Jyoti was two years ago. If difference between their ages be 2 years, how old is Sneha today? 2. 5 years ago, Priya's mother was 3 times older than her daughter. After 10 years, the mother will be twice older than the daughter. What is the present age of Priya?
(Explanation is a must.)
Answers
Let the age of Jyoti, two years ago, be .
Two years ago, the age of two people Sneha and Jyoti was and year old.
Hence, now is the age of Jyoti and is the age of Sneha.
Now, the difference of their ages is 2 years.
As it is said that the difference of their ages is 2 years,
But, is the age of Jyoti two years ago. Hence, today Sneha is years.
Let the age of Priya, five years ago, be .
Five years ago, the age of Priya's mother and Priya was and years old.
Hence, ten years later from now, is the age of Priya's mother and is the age of Priya.
At that time, the mother will be twice older than the daughter.
As it is said that the mother will be twice older than the daughter,
And the present age of Priya is years.
G I V E N :
1. Sneha is twice as old as Jyoti was two years ago. If difference between their ages be 2 years, how old is Sneha today ?
2. 5 years ago, Priya's mother was 3 times older than her daughter. After 10 years, the mother will be twice older than the daughter. What is the present age of Priya ?
S O L U T I O N :
1) Let us assume ⬇
Sneha's age be a and Jyoti's age be b
According to the question, Sneha is twice as old as jyoti 2 years ago
Hence, Sneha's present age be a = 2b
After which we are given that she was two years ago having twice the age as Jyoti. So, 2 will be substracted from 2b
Sneha's age = 2b + 2
Now, difference between their ages is 2 yrs
So, we get
- a - b = 2
Now, putting a = 2b we get
- 2b - b = 2
- b = 2
Now, Sneha's present = 2b + 2 = 2(2) + 2 = 6 yrs
Henceforth, Sneha's present age is 6 yrs
2) Let us assume ⬇
Priya's age five years before be 5a
So, her mother's age be a
Present age :
Here, as we assumed their five years so five years later must be their present ages
Priya's age be 5a + 5
Mother's age be a + 5
After 10 years :
Priya's age becomes (5a + 5) + 10
Her mother is twice as old as her daughter
Mother's age becomes 2[(a + 5) + 10]
Finding a :
- (5a + 5) + 10 = 2[(a + 5) + 10]
- 5a + 5 + 10 = 2(a + 5 + 10)
- 5a + 15 = 2a + 30
- 5a - 2a = 30 - 15
- 3a = 15
- a = 5
Priya's present age = a + 5 = 5 + 5 = 10 years
Henceforth, Priya's present age is 10 years