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?
14 years
Understanding Age Ratio Problems
This problem involves finding the present age of Rajni based on the given ratios of present ages and future ages of two individuals, Neelam and Rajni.
Setting Up the Age Variables
We are given that the ratio of the present ages of Neelam and Rajni is 6 : 7. We can represent their present ages using a common variable, say x.
- Let Neelam's present age be \( 6x \) years.
- Let Rajni's present age be \( 7x \) years.
Calculating Future Ages
The problem states that after four years, their ages will be in the ratio of 8 : 9. We need to calculate their ages after four years.
- Neelam's age after 4 years = \( 6x + 4 \) years.
- Rajni's age after 4 years = \( 7x + 4 \) years.
Forming the Equation
According to the problem, the ratio of their ages after four years is 8 : 9. We can set up an equation using this information:
$$ \frac{\text{Neelam's age after 4 years}}{\text{Rajni's age after 4 years}} = \frac{8}{9} $$
Substituting the expressions for their future ages:
$$ \frac{6x + 4}{7x + 4} = \frac{8}{9} $$
Solving the Equation for x
To find the value of x, we will cross-multiply:
$$ 9(6x + 4) = 8(7x + 4) $$
Distribute the numbers on both sides:
$$ 54x + 36 = 56x + 32 $$
Now, rearrange the terms to solve for x. Subtract \( 54x \) from both sides:
$$ 36 = 2x + 32 $$
Subtract 32 from both sides:
$$ 36 - 32 = 2x $$
$$ 4 = 2x $$
Divide by 2:
$$ x = \frac{4}{2} $$
$$ x = 2 $$
Determining Rajni's Present Age
We found that \( x = 2 \). The question asks for the present age of Rajni. Rajni's present age was represented as \( 7x \).
Rajni's present age = \( 7x = 7 \times 2 \)
Rajni's present age = 14 years.
Final Answer
Rajni's present age is 14 years.
Important Questions from Problem on Age
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:
X said to Y, "At the time of your birth I was twice as old as you are at present." If the present age of X is 42 years, then consider the following statements:
1. 8 years ago, the age of X was five times the age of Y.
2. After 14 years, the age of X would be two times the age of Y.
Which of the above statements is/are correct?
The total of the ages of Niraj, Umesh and Dhiraj is 93 years. Ten years ago, the ratio of their ages was 2 : 3 : 4 respectively. What is the present age of Dhiraj ?
A father is nine times as old as his son and the mother is eight times as old as the son. The sum of the father's and the mother's age is 51 years. What is the age of the son ?
Read the following passage and answer the questions below it.
A, B, C, D, E and F are cousins. No two cousins are of the same age, but everyone's birthday falls on the same date of the same month. The youngest is 17 years old and the eldest E is 22 years old. F is somewhere between B and D in age. A is older than B. C is older than D. A is one year older than C.
Which one of the following is possible?
