Question
If 3 times Mary’s present age is 18 years more than 5 times Diya's present age, and 2 times Diya's present age is 3 years less than Mary's present age, then what is the difference (in years) between the ages of Mary and Diya?
This question was previously asked in
RRB NTPC 2024 CBT 1 Question Paper (28-Aug-2025) (Shift 3)
The correct answer is
12
Age Difference Calculation for Mary and Diya
Let M represent Mary's present age and D represent Diya's present age.
Formulating Age Equations
Translate the given information into algebraic equations:
- "3 times Mary’s present age is 18 years more than 5 times Diya's present age": $3M = 5D + 18 \quad (1)$
- "2 times Diya's present age is 3 years less than Mary's present age": $2D = M - 3 \quad (2)$
Solving the System of Equations
We can solve this system using substitution:
- From Equation (2), express Mary's age (M) in terms of Diya's age (D): $M = 2D + 3$
- Substitute this expression for M into Equation (1): $3(2D + 3) = 5D + 18$
- Simplify and solve for D: $6D + 9 = 5D + 18$ $6D - 5D = 18 - 9$ $D = 9$ So, Diya's present age is 9 years.
- Substitute the value of D back into the expression for M: $M = 2(9) + 3$ $M = 18 + 3$ $M = 21$ So, Mary's present age is 21 years.
Calculating the Age Difference
Find the difference between Mary's age and Diya's age:
$ \text{Difference} = M - D $ $ \text{Difference} = 21 - 9 $ $ \text{Difference} = 12 $The difference between Mary's and Diya's ages is 12 years.
Was this answer helpful?
Similar Questions
- If 2 times a son's age is added to his father's age, the sum is 46 years. If 2.5 times the father's age is added to the son's age, the sum is 97 years. What is the father's age (in years)?
- If 2 times the age of Ram is 25 years more than 9 times the age of Ramya, and 5 times the age of Ramya is 4 years less than the age of Ram, then what is the difference (in years) between the ages of Ram and Ramya?
- The present ages of Sheo Kumar and Dileep Kumar are in the ratio of $9 : 10$. After $11\text{ years}$ this ratio will become $10 : 11$. What are the present ages of Sheo Kumar and Dileep Kumar?
- Ten years ago, X was 5 years old and his age was half of the age of Y. At that time, Z was 8 years younger than his brother P. Z was 18 years old at that time. What is the ratio of the respective ages of Z and P at present?
- 4 times the present age of P exceeds the present age of Q by 19 years. After 5 years, 3 times the age of Q will be 27 years less than 9 the age of P. The present age of Q is (in years):
- 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?
- Lima's father is four times as old as Lima. Four years ago, his father was six times as old as he was then. Find the present age of his father.
- 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:
- 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?
Important Questions from Problems on Age
- The ratio of the ages of two persons, P and Q, is 3 : 4. After 6 years, the ratio of their ages will become 4 : 5. What is the present age of P?
- If 2 times a son's age is added to his father's age, the sum is 46 years. If 2.5 times the father's age is added to the son's age, the sum is 97 years. What is the father's age (in years)?
- If 2 times the age of Ram is 25 years more than 9 times the age of Ramya, and 5 times the age of Ramya is 4 years less than the age of Ram, then what is the difference (in years) between the ages of Ram and Ramya?
- The present ages of Sheo Kumar and Dileep Kumar are in the ratio of $9 : 10$. After $11\text{ years}$ this ratio will become $10 : 11$. What are the present ages of Sheo Kumar and Dileep Kumar?
- Ten years ago, X was 5 years old and his age was half of the age of Y. At that time, Z was 8 years younger than his brother P. Z was 18 years old at that time. What is the ratio of the respective ages of Z and P at present?
Need Expert Advice?
Upcoming Exams
RRB ALP
July 28, 2026
RRB Group D
August 03, 2026
Test Series
Railways
RRB NTPC Under Graduate 2026 New Mock Test Series
1459 Tests 2 Tests Free
215 Attempts
4.3(512)
English, Hindi, Telugu +7 More
More Questions from RRB NTPC
