# Salil’s age is 23 years, more than half of Sargams’s age. Five years ago, the sum of their ages was 55 years. Find their present age.

Last updated date: 29th Mar 2023

•

Total views: 207.3k

•

Views today: 5.84k

Answer

Verified

207.3k+ views

**Hint:**We will consider Salil’s age be $x$ years and Sargams’s age $y$ years. Then from the given data we will form two equations and then we will solve them to get the value of $x$ and $y$. These will be the ages or we can say present ages of Salil and Sargam.

**Complete step by step solution:**

Let the present ages of Salil and Sargam be x and y years respectively.

The first condition is, Salil’s age is $23$ years more than half of Sargams’s age. This can be formed in the equation as,

\[x = \dfrac{y}{2} + 23\] ….equation (1)

taking the LCM on RHS,

\[x = \dfrac{{y + 23 \times 2}}{2}\]

On cross multiplying $2$ and taking the product on RHS,

\[2x = y + 46\]

Taking the variables on one side we get,

\[2x - y = 46\] this is simplified equation (1)

Now from the second condition, five years ago, the sum of their ages was $55$ years. This can be formed in the equation as,

\[\left( {x - 5} \right) + \left( {y - 5} \right) = 55\] …..equation (2)

On solving the brackets,

\[x + y - 10 = 55\]

Taking the constants on one side we get,

\[x + y = 55 + 10\]

\[\Rightarrow x + y = 65\] this is simplified equation (2)

On adding equation1 and equation (2),

\[2x - y + x + y = 46 + 65\]

Cancelling y and adding the x terms from the equation we get,

\[3x = 111\]

Now on dividing 111 by 3 we get,

\[x = \dfrac{{111}}{3}\]

\[ \Rightarrow x = 37\]

Now this is the present age of Salil. Now putting this value in any of the simplified equations we get,

\[ y = 65 - x \\

\Rightarrow y = 65 - 37 \\

\Rightarrow y = 28 \\

\]

This is the present age of Sargam.

**Therefore, the present ages of Salil and Sargam are 37 years and 28 years respectively.**

**Note:**

Note that forming the equation using the data or condition is the most important part of these problems. Because solution of the equation is the answer of the question.

Also note that some years before is subtracting this number from the present age and some years from now means adding that number in the present age.

Recently Updated Pages

If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE