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
The sum of the ages of a mother, son, and daughter is 70 years. If the mother is thrice as old as her son, and the daughter is 5 years older than her brother, how old is the mother?
The ages of Anita and Sunita differ by 30 years. If 5 years ago, Anita was 3 times as old as Sunita, then the present age of Sunita is:
The present ages of three persons are in the ratio 4 : 5 : 6. Eight years ago, the sum of their ages was 51. Find the present age of the eldest person.
The sum of the ages of Yash and his father is 90 years. When Yash is as old as his father’s present age, he will be five times as old as his son Suraj’s present age. Suraj will be 12 years older than Yash’s present age, when Yash is as old as his father at present. How old is Suraj at present?
- The sum of the ages of a grandfather, his son, and his grandson is 128 years. The grandfather is twice as old as his son, and the son is five times as old as the grandson. Determine the age (in years) of the grandson.
- 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?
- The sum of the present ages of Bunty and Bubbly is 64 years. After 2 years from now, Bunty's age will be three times that of Bubbly's age. Bunty's present age (in years) is:
- Among five people named V, W, X, Y and Z, each have a certain age. X is twice the age of V. V is three times the age of Y. Y is one-fifth the age of W. The age of W is 15. If Z's age is equal the age of X, what is the age of Z?
- Among five people named V, W, X, Y and Z, each have a certain age. X is thrice the age of V. The age of V is 12. Y is half the age of Z. W is twice the age of Y. If Z's age is equal to the age of X, what is the age of W?
- 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?
Important Questions from Problem on Age
The ratio of present ages of Neelam and Rajni is 6 : 7. After four years, their ages will be in the ratio of 8 : 9. What is the present age of Rajni?
Five years ago the age of the son was one third of that of his mother at that time. If the sum of their present ages is 70 years, then find the present age of the mother.
Jaya is 36 years old and her son Bharat is 11 years old. In how many years will Jaya be twice as Bharat's age?
Five years ago, father's age was 5 times that of his son and after 3 years he will be 3 times as old as his son. Find the present age of son.
The ratio of a father's age to his son's age is 3 ∶ 2 The product of the numbers representing their age is 486. The ratio of their ages after 5 years will be:
