1. ਜੇਕਰ ਅਸੀਂ ਅੰਸ਼ ਵਿੱਚ 1 ਜੋੜ ਦੇਈਏ ਅਤੇ ਹਰ ਵਿੱਚ 1 ਘਟਾ ਦੇਈਏ ਤਾਂ ਭਿੰਨ 1 ਵਿੱਚ ਬਦਲ ਜਾਂਦੀ ਹੈ। ਜੇਕਰ ਸਿਰਫ ਹਰ ਵਿੱਚ 1 ਜੋੜ ਦੇਈਏ ਤਾਂ ਇਹ 1/2 ਬਣ ਜਾਂਦੀ ਹੈ। ਭਿੰਨ ਪਤਾ ਕਰੋ? 2. 5 ਸਾਲ ਪਹਿਲਾਂ ਨੂਰੀ ਦੀ ਉਮ... 1. ਜੇਕਰ ਅਸੀਂ ਅੰਸ਼ ਵਿੱਚ 1 ਜੋੜ ਦੇਈਏ ਅਤੇ ਹਰ ਵਿੱਚ 1 ਘਟਾ ਦੇਈਏ ਤਾਂ ਭਿੰਨ 1 ਵਿੱਚ ਬਦਲ ਜਾਂਦੀ ਹੈ। ਜੇਕਰ ਸਿਰਫ ਹਰ ਵਿੱਚ 1 ਜੋੜ ਦੇਈਏ ਤਾਂ ਇਹ 1/2 ਬਣ ਜਾਂਦੀ ਹੈ। ਭਿੰਨ ਪਤਾ ਕਰੋ? 2. 5 ਸਾਲ ਪਹਿਲਾਂ ਨੂਰੀ ਦੀ ਉਮਰ ਸੋਨੂ ਦੀ ਉਮਰ ਦਾ ਤਿੰਨ ਗੁਣਾ ਸੀ। 10 ਸਾਲ ਬਾਅਦ ਨੂਰੀ ਦੀ ਉਮਰ ਸੋਨੂ ਦੀ ਉਮਰ ਦਾ ਦੋ ਗੁਣਾ ਹੋ ਜਾਵੇਗੀ। ਨੂਰੀ ਅਤੇ ਸੋਨੂ ਦੀ ਉਮਰ ਕਿੰਨੀ ਹੈ?

Understand the Problem

The question is asking to solve two math problems:

Find a fraction given two conditions: (a) If 1 is added to the numerator and subtracted from the denominator, the fraction becomes 1. (b) If 1 is added only to the denominator, the fraction becomes 1/2.
Solve an age problem: 5 years ago, Noori was three times as old as Sonu. 10 years later, Noori will be twice as old as Sonu. Find their current ages, and Noori's and Sonu's age.

Answer

Fraction: $\frac{3}{5}$ Noori: 50 years, Sonu: 20 years

Steps to Solve

Solving the fraction problem: Define variables

Let the fraction be $x/y$, where $x$ is the numerator and $y$ is the denominator.

Set up equations based on the given conditions

$ \frac{x+1}{y-1} = 1 $ $ \frac{x}{y+1} = \frac{1}{2} $

Simplify the first equation

$x + 1 = y - 1$ $x - y = -2$ (Equation 1)

Simplify the second equation

$2x = y + 1$ $2x - y = 1$ (Equation 2)

Solve the system of equations

Subtract Equation 1 from Equation 2: $(2x - y) - (x - y) = 1 - (-2)$ $2x - y - x + y = 3$ $x = 3$

Substitute the value of $x$ into Equation 1 to find $y$

$3 - y = -2$ $y = 3 + 2$ $y = 5$

Solving the age problem: Define variables

Let Noori's current age be $x$ years and Sonu's current age be $y$ years.

Set up equations based on the given conditions

5 years ago: $x - 5 = 3(y - 5)$

10 years later: $x + 10 = 2(y + 10)$

Simplify the first equation

$x - 5 = 3y - 15$ $x - 3y = -10$ (Equation 3)

Simplify the second equation

$x + 10 = 2y + 20$ $x - 2y = 10$ (Equation 4)

Solve the system of equations

Subtract Equation 3 from Equation 4: $(x - 2y) - (x - 3y) = 10 - (-10)$ $x - 2y - x + 3y = 20$ $y = 20$

Substitute the value of $y$ into Equation 4 to find $x$

$x - 2(20) = 10$ $x - 40 = 10$ $x = 50$

Fraction problem answer: The fraction is $\frac{3}{5}$. Age problem answer: Noori is 50 years old and Sonu is 20 years old.

More Information

The fraction problem involves setting up a system of linear equations based on the given conditions and then solving for the numerator and denominator. The age problem also involves creating a system of linear equations, representing the ages of Noori and Sonu at different times, and solving for their current ages.

Tips

For the fraction problem, a common mistake is to misinterpret the problem statement and set up the equations incorrectly. For example, adding/subtracting to the wrong part of the fraction
For the age problem, a common mistake is not to correctly express the ages in the past and future in terms of the current ages, leading to incorrect equations. Omitting parenthesis is also a common mistake.

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