Five years ago, the ratio of the ages of Tarun and Saurabh was 4 ∶ 1. After five years, the ratio of their ages will be 2 ∶ 1. What is the present age (in years) of Saurabh?
10
Understanding the Age Ratio Problem
This question involves solving a problem based on the ratio of ages of two individuals, Tarun and Saurabh, at different points in time. We are given their age ratio five years ago and their projected age ratio five years from now. Our goal is to find Saurabh's current age.
Setting Up Variables for Past Ages
Let's represent the ages of Tarun and Saurabh five years ago using a variable. The ratio of their ages five years ago was given as 4 ∶ 1.
- Let Tarun's age five years ago be $4x$ years.
- Let Saurabh's age five years ago be $1x$ or $x$ years.
Here, $x$ is a common factor for their ages at that time.
Calculating Present Ages
To find their present ages, we need to add 5 years to their ages from five years ago.
- Tarun's present age = (Tarun's age five years ago) + 5 = $4x + 5$ years.
- Saurabh's present age = (Saurabh's age five years ago) + 5 = $x + 5$ years.
Determining Ages After Five Years
Next, let's find their ages five years from the present time. We add another 5 years to their present ages.
- Tarun's age after five years = (Tarun's present age) + 5 = $(4x + 5) + 5 = 4x + 10$ years.
- Saurabh's age after five years = (Saurabh's present age) + 5 = $(x + 5) + 5 = x + 10$ years.
Formulating the Equation Using Future Age Ratio
We are given that the ratio of their ages after five years will be 2 ∶ 1. We can set up an equation using the ages we just calculated.
Ratio of Tarun's age to Saurabh's age after five years:
$\frac{\text{Tarun's age after 5 years}}{\text{Saurabh's age after 5 years}} = \frac{2}{1}$
Substituting the expressions for their ages:
$\frac{4x + 10}{x + 10} = \frac{2}{1}$
Solving the Age Ratio Equation
Now, we solve this equation to find the value of $x$. We can cross-multiply:
$1 \times (4x + 10) = 2 \times (x + 10)$
$4x + 10 = 2x + 20$
To isolate the $x$ terms, subtract $2x$ from both sides:
$4x - 2x + 10 = 2x - 2x + 20$
$2x + 10 = 20$
To isolate the $x$ term further, subtract 10 from both sides:
$2x + 10 - 10 = 20 - 10$
$2x = 10$
Finally, divide both sides by 2 to find the value of $x$:
$\frac{2x}{2} = \frac{10}{2}$
$x = 5$
Calculating Saurabh's Present Age
We found that $x = 5$. Saurabh's present age was represented by the expression $x + 5$.
Saurabh's present age = $x + 5 = 5 + 5 = 10$ years.
Thus, Saurabh's present age is 10 years.
| Time Period | Tarun's Age | Saurabh's Age | Ratio |
|---|---|---|---|
| Five years ago | $4x = 4 \times 5 = 20$ | $x = 1 \times 5 = 5$ | 20 : 5 = 4 : 1 (Matches given) |
| Present Age | $4x + 5 = 20 + 5 = 25$ | $x + 5 = 5 + 5 = 10$ | 25 : 10 = 5 : 2 |
| After five years | $4x + 10 = 20 + 10 = 30$ | $x + 10 = 5 + 10 = 15$ | 30 : 15 = 2 : 1 (Matches given) |
Revision Table for Age Ratio Problems
| Concept | Description | How to Apply |
|---|---|---|
| Representing Ages with Variables | Use a common variable (e.g., $x$) to represent a part of the ratio. | If ratio is A:B, ages can be $Ax$, $Bx$. |
| Calculating Past/Future Ages | Add or subtract years from the current or assumed age. | Past age = Present age - Years; Future age = Present age + Years. |
| Setting up Equation | Use the given ratio at a specific time to form an algebraic equation. | $\frac{\text{Age 1}}{\text{Age 2}} = \frac{\text{Ratio Part 1}}{\text{Ratio Part 2}}$ |
| Solving Linear Equations | Use algebraic techniques (cross-multiplication, isolating variable) to find the value of the variable. | Combine like terms, perform inverse operations. |
Additional Information on Age Ratio Calculations
Age ratio problems are a common type in quantitative aptitude tests. They typically involve using ratios to represent the proportional relationship between the ages of two or more people at different points in time. The key is to set up a consistent algebraic representation of the ages across these time periods and then use the given ratio at one of those times to form an equation. Solving this equation allows you to find the value of the variable, which can then be used to determine the actual ages at any specified time (past, present, or future).
Always read the question carefully to identify which time period each ratio refers to (e.g., 'five years ago', 'present', 'after five years') and what age you are ultimately asked to find (e.g., Tarun's present age, Saurabh's age five years from now).
Similar Questions
- The radius of a circle is 90 cm. If the radius of this circle is increased to 99 cm, then what will be the percentage increase in the area of this circle?
In a class of 95 students, all play at least one of the three games — snooker, chess and tennis. 42 students play snooker, 49 play tennis, and 43 play chess. The total number of students who play any and only two games is 29. The 5 students play all the three games. The number of students who play only snooker and only chess is equal. 11 students play only snooker and tennis. 6 students play only snooker and chess. How many students play only tennis?
The average score (runs/match) of Mithali before the start of the women's national series was 45. In the women's national series of 10 matches, her total score was 500 runs. Find the total number of matches played by her till date, if her new average after the series is 47.5.
The sum of the current ages of Shipra and Malini is 65 years. After 5 years, Shipra’s age will be 15 years more than Malini’s age. What is Malini’s current age?
Which two sings should be interchanged in the following equation to make it correct?
10 + 5 ÷ 10 × 8 – 10 = 16Two mixtures contain milk and juice in the ratio of 2 : 1 and 4 : 5. If equal volumes of the two mixtures are mixed together, what would be ratio of milk to juice in the resulting mixture?
Rs. 820 is divided among 6 men, 8 women, and 12 boys in such a way that every woman gets an amount equal to that received by one man and one boy combined and that every man gets one and a half times the amount received by a boy. What is the total amount received by 8 women?
Hemant buys a dozen eggs for Rs. 5.50 per egg. While carrying them, two eggs wasted when fall down and get damaged. He sells the balanced eggs at Rs. 7.70 per egg. Find the net profit earned by him in the overall deal.
Product A is costlier than product B by Rs. 2. If the price of product A is increased by two times the price of product B. the new price of product A become Rs. 17. What is the price of product B?
A recent survey of married couples in Indian metro cities showed that 20% of the couples have only child, 45% of the remaining couples have two children, and the rest of the couples have three or more children. What is the percentage of couples with three or more children?
Important Questions from Quant Based Puzzle
- There are deers and peacocks in a zoo. By counting heads they are 80. The number of their legs is 200. How many peacocks are there?
- A certain number of horses and an equal number of men are going somewhere. Half of the owners are on their horses' back while the remaining ones are walking along leading their horses. If the number of legs walking on the ground is 70, how many horses are there?
- A, B, C, D and E play a game of cards. A says to B, "If you give me three cards, you will have as many as E has and if I give you three cards, you will have as many as D has". A and B together have 10 cards more than what D and E together have. If B has two cards more than what C has and the total number of cards be 133, how many cards does B have?
- A player holds 13 cards of four suits, of which seven are black and six are red. There are twice as many diamonds as spades and twice as many hearts as diamonds. How many clubs does he hold?
There are fourteen teams playing in a tournament. If every team plays one match with every other team, how many matches will be played in the tournament?
