Important Formulas and Concepts on Ages
Important Formulas
- If the present age is x, then n times the age is nx.
- If the present age is x, then age n years later/hence = x + n.
- If the present age is x, then age n years ago = x – n.
- The ages in a ratio a : b will be ax and bx.
- If the present age is x, then 1/n of age is x/n.
Important Concepts on Problems on Ages
Concept 1
x years ago the age of A was n1 times the age of B, and at present A’s age is n2 times that of B, then;
A’s current = ((n1 - 1) / (n1 - n2)) * ((n1 - n2) / (n1 - 1)) * n1 * x years.
B’s current age = ((n1 - 1) / (n1 - n2)) * ((n1 - n2) / (n1 - 1)) * (n1 - n2) * x years.
Concept 2
The present age of A is n1 times the present age of B. After x years, age of A becomes n2 times the age of B, then;
A’s current = ((n2 - 1) / (n2 - n1)) * ((n1 - n2) / (n1 - 1)) * (n1 - n2) * x years.
B’s current age = ((n2 - 1) / (n2 - n1)) * ((n1 - n2) / (n1 - 1)) * (n2 - 1) * x years.
Question and Answer
Question 1:
Saina Nehwal is 8 years older than her cousin. Her cousin is 24 years younger than his mother. If the ratio between the ages of Saina and her cousin’s mother is 7 : 11. What will be the age of Saina’s cousin after 3 years?
Answer: 23 years
Explanation: (provide explanation here)
Question 2:
Tiger’s present age is acquired, if we subtract 9 years from Arav’s present age and divide the remainder by 14. If Mohan’s age is 8 years and he is 3 years elder to Arav, then find Tiger’s present age.
Answer: 79 years
Explanation: (provide explanation here)
Question 3:
Erika was five times older than Gigi ten years ago. The age of an Erika will be twice that of a Gigi in five years. How old were Erika’s compared to Gigi five years ago?
Answer: 3:1
Explanation: (provide explanation here)