Age Problem: Kamlesh and Prathmesh Calculation
This solution explains how to find Kamlesh's present age using the provided information about the sum of ages and their future ages.
Setting Up the Equations
Let K represent Kamlesh's present age and P represent Prathmesh's present age.
- The sum of their present ages is 52: \(K + P = 52\) (Equation 1)
- After 2 years, Kamlesh's age will be \(K + 2\) and Prathmesh's age will be \(P + 2\).
- The condition is that Kamlesh's age will be three times Prathmesh's age after 2 years: \(K + 2 = 3(P + 2)\) (Equation 2)
Solving for Kamlesh's Present Age (K)
Use the equations to find K.
- From Equation 1, express P in terms of K: \(P = 52 - K\)
- Substitute this into Equation 2: \(K + 2 = 3((52 - K) + 2)\)
- Simplify the equation: \(K + 2 = 3(54 - K)\) \(K + 2 = 162 - 3K\)
- Combine K terms on one side and constants on the other: \(K + 3K = 162 - 2\) \(4K = 160\)
- Solve for K: \(K = \frac{160}{4}\) \(K = 40\)
Kamlesh's present age is 40 years.
Verification
If Kamlesh is 40, Prathmesh is \(52 - 40 = 12\). After 2 years, Kamlesh will be 42 and Prathmesh will be 14. Since \(42 = 3 \times 14\), the condition is met.
Similar Questions
- Among five people named V, W, X, Y and Z, each have a certain age. Y is four times the age of X. V is two times the age of X. Y is five times the age of W. The age of W is 12. If Z is thrice the age of V, what is the age of Z?
- Among five people named V, W, X, Y and Z, each have a certain age. The age of X is 12. V is four times the age of Z. Y is half the age of V. W is thrice the age of X. If Z is one ninth the age of W, what is the age of Y?
- Consider the given question and decide which of the following statements is sufficient to answer the question.
What is the birth year of Mr. Rajesh?
Statements:
1. At present Mr. Rajesh is 25 years younger to his father
2. Mr. Rajesh’s sister who was born on 1974 is 35 years younger to his father - 15 years ago, Shyam was twice as old as Prabhat. Five years from now Prabhat’s age will be $\frac{5}{8}$ of Shyam’s age. What is Shyam’s current age?
Important Questions from Problem on Age
The average age of a husband and his wife was 20 years at the time of their marriage. After 6 years, they have a 2 -year old child. Find the present average age of the family.
The ratio of the ages of A, B and C, 5 years ago, was 4 : 5 : 7. The sum of their present ages is 135 years. What will be the sum of the ages (in years) of B and C, 3 years from now?
The ratio of the present age of Mahesh and Ajay is 3 : 2 respectively. After 8 years. Ratio of their age will be 11: 8. What will be the present age of Mahesh’s son if his age is half of the present age of Ajay?
In a school, the average age of boys and girls together is 16.8 years, the average age of boys is 15.4 years, and the average age of girls is 18.2 years. The ratio of number of boys to girls in the school is:
The difference between age of Sunita and Sheela is 12 years. If 9 years ago, elder's age was 4 times of younger's age, then what are their present age?
A. 11 and 23
B. 15 and 27
C. 13 and 25
D. 23 and 35
