Solving the Mother-Daughter Age Problem
This problem involves finding the current age of the daughter based on two conditions relating her age to her mother's age at different times.
Setting Up the Equations
Let $D$ represent the daughter's current age and $M$ represent the mother's current age.
- Condition 1: The mother is currently three times as old as her daughter. $ M = 3D $
- Condition 2: 5 years ago, the mother was four times as old as her daughter. Mother's age 5 years ago: $M - 5$ Daughter's age 5 years ago: $D - 5$ $ M - 5 = 4(D - 5) $
Calculating the Daughter's Current Age
We can solve this system of two equations. Substitute the first equation ($M = 3D$) into the second equation:
- Substitute $M = 3D$ into $ M - 5 = 4(D - 5) $: $ 3D - 5 = 4(D - 5) $
- Distribute the 4 on the right side: $ 3D - 5 = 4D - 20 $
- Rearrange the equation to solve for $D$. Subtract $3D$ from both sides: $ -5 = D - 20 $
- Add 20 to both sides: $ -5 + 20 = D $ $ 15 = D $
The daughter's current age is 15 years.
Verification
Let's check the conditions:
- Daughter's current age ($D$) = 15 years.
- Mother's current age ($M$) = $3 \times 15 = 45$ years.
- 5 years ago: Daughter was $15 - 5 = 10$ years old. Mother was $45 - 5 = 40$ years old.
- Was the mother four times as old as the daughter 5 years ago? $40 = 4 \times 10$. Yes, the condition holds true.
Therefore, the daughter's current age is 15 years.
Similar Questions
- Narendra's mother is four times as old as Narendra. Four years ago, his mother was six times as old as Narendra was. What are their Present ages?
- If 3 times a mother's present age is 24 years more than 9 times her daughter's present age, and 4 times the daughter's present age is 2 years less than the mother's present age, then what is the difference (in years) between the ages of the mother and the daughter?
- John is twice as old as Jean. After 3 years, the sum of their ages will be 66 years. What are the present ages of Jean and John, respectively?
- The ages of A and B are in the ratio of 5 : 3. After 5 years the ratio of their ages will be 10 : 7. What is the difference between present ages of A and B(in years)?
- Age of A is 3 times more than that of B and half as that of C. If the sum of their ages is 120 years, what is the age (in years) of A?
- The sum of the reciprocals of the ages of two colleagues is nine times the difference of the reciprocals of their ages. If the ratio of the products of their ages to the sum of their ages is 100 : 9, Find their ages.
- The ages of two persons differ by 15 years. If 5 years ago, the age of the older person was twice that of the younger one, then their present ages (in years) are:
- The ratio of the present ages of Alok and Anil is 3 : 4. If Alok's age 20 years from now will be 62 years, then what is Anil's present age?
- A father is 3 times as old as his son today. After 13 years the father will be twice as old as his son. The present age of the son is:
- A is 6 years older than B. 10 years ago, B's age was three quarters of A's age. Find the present age (in years) of A.
Important Questions from Problems on Age
The age of Dr. Pandey is four times the age of his son. After 10 years, the age of Dr. Pandey will be twice the age of his son. The present age of Dr. Pandey's son is?
Three years ago, the average age of a family of six members was 19 years. Since then, a boy has been born, and the average age of the family is the same today as it was three years ago. What is the age of the boy?
Amita is 2 years older than her friend Amrita. Amita's father is twice as old as Amita, and Amrita is twice as old as her sister. The ages of Amita's father and Amrita's sister differ by 43 years. The sum of the ages (in years) of Amita and Amrita is:
- Narendra's mother is four times as old as Narendra. Four years ago, his mother was six times as old as Narendra was. What are their Present ages?
- If 3 times a mother's present age is 24 years more than 9 times her daughter's present age, and 4 times the daughter's present age is 2 years less than the mother's present age, then what is the difference (in years) between the ages of the mother and the daughter?
