Five years ago, Nuri was thrice as old as Sonu. After ten years from now, Nuri will be twice as old as Sonu. Present age of Nuri and Sonu respectively are:
40 years, 20 years
Understanding the Nuri and Sonu Age Problem
This question asks us to find the present ages of two individuals, Nuri and Sonu, based on given information about their ages at different points in time.
Let's define variables for their present ages:
- Let Nuri's present age be \(N\) years.
- Let Sonu's present age be \(S\) years.
Setting Up Equations from the Problem Statement
The problem provides two pieces of information relating their ages at different times:
Condition 1: Five years ago
Five years ago:
- Nuri's age was \(N - 5\) years.
- Sonu's age was \(S - 5\) years.
The problem states that five years ago, Nuri was thrice as old as Sonu. This can be written as an equation:
\(N - 5 = 3 \times (S - 5)\)
Let's simplify this equation:
\(N - 5 = 3S - 15\)
Adding 5 to both sides gives our first equation:
Equation 1: \(N = 3S - 10\)
Condition 2: Ten years from now
Ten years from now:
- Nuri's age will be \(N + 10\) years.
- Sonu's age will be \(S + 10\) years.
The problem states that ten years from now, Nuri will be twice as old as Sonu. This can be written as an equation:
\(N + 10 = 2 \times (S + 10)\)
Let's simplify this equation:
\(N + 10 = 2S + 20\)
Subtracting 10 from both sides gives our second equation:
Equation 2: \(N = 2S + 10\)
Solving the System of Linear Equations
We now have a system of two linear equations with two variables (\(N\) and \(S\)):
1) \(N = 3S - 10\)
2) \(N = 2S + 10\)
Since both equations are already solved for \(N\), we can set the expressions for \(N\) equal to each other. This is using the substitution method:
\(3S - 10 = 2S + 10\)
Now, we need to solve this equation for \(S\). Let's move the terms involving \(S\) to one side and the constant terms to the other side:
Subtract \(2S\) from both sides:
\(3S - 2S - 10 = 10\)
\(S - 10 = 10\)
Add 10 to both sides:
\(S = 10 + 10\)
\(S = 20\)
So, Sonu's present age is 20 years.
Now that we have the value of \(S\), we can substitute it back into either Equation 1 or Equation 2 to find the value of \(N\). Let's use Equation 2:
\(N = 2S + 10\)
Substitute \(S = 20\):
\(N = 2(20) + 10\)
\(N = 40 + 10\)
\(N = 50\)
So, Nuri's present age is 50 years.
Present Ages of Nuri and Sonu
Based on our calculations from the problem statement:
- Present age of Nuri: 50 years
- Present age of Sonu: 20 years
Therefore, the present age of Nuri and Sonu respectively are 50 years and 20 years.
Verification
Let's check if these ages satisfy the original conditions:
- Five years ago: Nuri was \(50 - 5 = 45\) years old. Sonu was \(20 - 5 = 15\) years old. Is Nuri's age thrice Sonu's age? \(45 = 3 \times 15\). Yes, \(45 = 45\). The first condition is satisfied.
- Ten years from now: Nuri will be \(50 + 10 = 60\) years old. Sonu will be \(20 + 10 = 30\) years old. Will Nuri be twice Sonu's age? \(60 = 2 \times 30\). Yes, \(60 = 60\). The second condition is satisfied.
The calculated ages (Nuri 50, Sonu 20) correctly satisfy both conditions given in the problem statement.
Revision Table: Key Concepts for Age Problems
| Concept | Description | How it applies here |
|---|---|---|
| Variables | Using letters (like \(N\), \(S\)) to represent unknown quantities. | \(N\) for Nuri's present age, \(S\) for Sonu's present age. |
| Translating Words to Math | Converting phrases into algebraic expressions and equations. | "Thrice as old as Sonu" \(\rightarrow 3S\); "Five years ago" \(\rightarrow \text{age}-5\). |
| System of Equations | Two or more equations involving the same variables. | We got two equations relating \(N\) and \(S\). |
| Solving Equations | Using algebraic methods (substitution, elimination) to find variable values. | We used substitution by setting expressions for \(N\) equal. |
Additional Information: Solving Linear Equations
Age problems often lead to systems of linear equations. A linear equation is an equation between two variables that gives a straight line when plotted on a graph. A system of linear equations involves two or more such equations with the same variables.
Common methods for solving a system of two linear equations include:
- Substitution Method: Solve one equation for one variable (e.g., solve for \(N\) in terms of \(S\)), then substitute that expression into the other equation. This reduces the system to a single equation with one variable, which can then be solved. This is the method we used in the detailed solution above.
- Elimination Method: Multiply one or both equations by constants so that the coefficients of one variable are opposites. Then, add the equations together to eliminate that variable, resulting in a single equation with one variable.
Choosing the best method depends on the form of the equations. If one variable is already isolated (like \(N\) in our equations), substitution is often the simplest approach.
Important Questions from Non-Verbal Reasoning
Choose the alternative which most closely resembles the water image of the given figures.
Select a figure from the given four alternatives, which when placed in the blank space of the problem figure would complete the pattern.
Choose the alternative which most closely resembles the mirror image of the given combination: MARKER
Among the four answer figures, which one can be formed from the cut-out pieces given below?
Find the alternative which contains figure (A) as its part.
