When i was 3/5th of your present age, you were 1/3rd of my present age. If my present age after 4 years will be 40 then after how many years will your age be 40?
Answers
Given : When i was 3/5th of your present age, you were 1/3rd of my present age.
my present age after 4 years will be 40
To Find : after how many years will your age be 40
Solution:
my present age after 4 years will be 40
Hence present age = 40 - 4 = 36 years
one third of present age = 36/3 = 12 years
3/5th of present age = (3/5) P = 3P/5
P - (36 - 3P/5) = 12
=> 8P/5 = 48
=> P = 30
30 + X = 40
=> X = 40 - 30
=> X = 10
after 10 Years age be 40
Present ages =
MY 36 and YOUR 30
i was 3/5th of your present age, = (3/5)30 = 18 Years ( 36 - 18 = 18 years before)
you were 1/3rd of my present age = (1/3)36 = 12 = 30 - 18
my present age after 4 years will be 40 ( 36 + 4)
after 10 years your age 30 + 10 = 40
Hence 10 Year is the correct answer
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Answer:
Let us denote myself to be 'A' and other person to be 'B'.
Let the present age of 'A' be x and present age of 'B' be y.
It is given that, when A was 3/5th age of B, the age of B was 1/3rd the age of A.
We are also given that, after 4 years from the present age of A, A would turn 40 years old. Hence we get:
⇒ x + 4 = 40
⇒ x = 40 - 4
⇒ x = 36 years.
Hence the present age of 'A' is 36 years.
Applying this to the first part of question we get:
The age of 'B' when A was 3/5th of B's age is given as 1/3rd of present age of A.
⇒ (3/5) of y = Age of A
⇒ (1/3) of x = Age of B
⇒ Age of A - Age of B = Age difference ...(i)
We know that, Age difference is common throughout our lifetime. Hence the age difference in present ages will also be the same. Hence using (i) we get:
⇒ (3y)/5 - [(1)/3] × 36 = Age difference
⇒ 3y/5 - 12 = Age difference ...(ii)
Now the age difference in their present ages is also same as above, since it cannot change every year. Hence we get:
⇒ Present age of A - Present Age of B = Age difference
⇒ 36 - y = Age Difference ...(iii)
Substituting the value of Age difference from (ii) in (iii) we get:
⇒ 36 - y = 3y/5 - 12
⇒ 36 + 12 = 3y/5 + y
⇒ 48 = (3y + 5y) / 5
⇒ 48 = 8y/5
⇒ 8y = 48 × 5
⇒ 8y = 240
⇒ y = 240/8
⇒ y = 30
Hence the present age of 'B' is 30 years.
Therefore after 10 years, the age of B will be equal to 40.