A person’s present age is two fifth of the age of his
mother. After 8 years, he will be one-half of the age
of his mother. What is the present age of his mother?
Let mother’s present age = M, person’s present age = P.
Given: P=25M ...(1)
After 8 years: P+8=12(M+8) ...(2)
Substitute P from (1) into (2): 25M+8=12(M+8)
Multiply both sides by 10 to clear denominators: 4M+80=5M+40
80−40=5M−4M
40=M
Answer: The mother’s present age is 40 years.
1
Sum of ages of Anu and Bhanu is 10 years more than the sum of ages of Bhanu, Chanu, and Dhanu. The average age of Chanu and Dhanu is 19 years. Find the average age of Anu and Dhanu if Dhanu is 10 years
elder than Chanu.
Let the ages be:
Anu = A, Bhanu = B, Chanu = C, Dhanu = D
Given:
1) A+B=10+B+C+D⇒A=10+C+D
2) Average age of Chanu and Dhanu = 19 ⇒C+D2=19⇒C+D=38
3) Dhanu is 10 years elder than Chanu: D=C+10
Substitute D in C+D=38: C+(C+10)=38⇒2C=28⇒C=14
D=14+10=24
Now, A=10+C+D=10+14+24=48
Average age of Anu and Dhanu: A+D2=48+242=722=36
Answer: The average age of Anu and Dhanu is 36 years.
3
Rakesh says to Mahesh, “I am as old as you were when I was one-third as old as you are.” If the sum of their ages is 60 years, find the present age of Mahesh (in years).
From the statement:
Rakesh says, "I am as old as you were when I was one-third as old as you are"
That is, when Rakesh was 13M, Mahesh's age was R
So, time passed = R−13M
Then Mahesh's age was: M−(R−13M)=R
Now solve the equation:
M−(R−13M)=R M−R+13M=R 43M=2R 4M=6R⇒2M=3R⇒M=32R
Now plug into R+M=60 R+32R=60⇒52R=60⇒R=24 M=32×24=36
Answer: Mahesh's present age is 36 years.
1
In
which year was Arjun born?
Arjun at present is 25 years younger
to his mother. Arjun’s brother, who was born in 1964, is 35 years younger to
his mother.
Arjun’s brother was born in 1964 and is 35 years younger than their mother.
We want: Arjun’s birth year.
Step 1: Calculate the mother's birth year:
1964+35=1999
So, the mother was born in 1999.
Step 2: Arjun is 25 years younger than his mother:
1999−25=1974
Therefore, Arjun was born in 1974.
✅ Final Answer: Arjun was born in 1974
1
A person's present age is two-fifth of the age
of his mother. After 8 years, he will be one
half of the age of his mother. What is the
present age of the mother?