Answer
Verified
359.7k+ views
Hint: We will assume the number as a constant variable and solve the given condition using that constant. After we get that number, we will sum up its digits to find the final answer as asked in the question. We will use the cross-multiplication method for solving the linear equation with one variable.
Complete step-by-step solution:
Let us assume the number as $x$ .
The condition is when $24$ is subtracted from $x$, it reduces to its fourth-seventh.
In arithmetic form the condition can be written as,
$x - 24 = \dfrac{4}{7}x$ ….. (1)
From this equation we get the value of $x$ as,
$x = \dfrac{4}{7}x + 24$
Subtracting $\dfrac{4}{7}x$ from $x$,
$x - \dfrac{4}{7}x = 24$
Taking LCM,
$\dfrac{{7x - 4x}}{7} = 24$
$\dfrac{{3x}}{7} = 24$
Solving for $x$,
$x = \dfrac{{24 \times 7}}{3}$
$x = 56$
We can verify this value of $x$ by substituting it in the L.H.S. and R.H.S. of equation (1),
L.H.S. of equation (1),
$x - 24 = 56 - 24 = 32$
R.H.S. of equation (1),
$\dfrac{4}{7}x = \dfrac{4}{7} \times 56 = 32$
L.H.S. = R.H.S.
Therefore, we get the value of $x$ as $56$.
The digits of $56$ are $5$ and $6$ .
The sum of digits of $56$ is $5 + 6 = 11$ .
The correct option is option C. $11$ .
Note: A linear equation in one variable is an equation that has a maximum of one variable of order $1$. Linear equation in one variable is solved by taking LCM, removing fractions, isolate the variable, and verification of answer. In real life, a linear equation in one variable has many applications and one prominent one is problems on age difference applications.
Complete step-by-step solution:
Let us assume the number as $x$ .
The condition is when $24$ is subtracted from $x$, it reduces to its fourth-seventh.
In arithmetic form the condition can be written as,
$x - 24 = \dfrac{4}{7}x$ ….. (1)
From this equation we get the value of $x$ as,
$x = \dfrac{4}{7}x + 24$
Subtracting $\dfrac{4}{7}x$ from $x$,
$x - \dfrac{4}{7}x = 24$
Taking LCM,
$\dfrac{{7x - 4x}}{7} = 24$
$\dfrac{{3x}}{7} = 24$
Solving for $x$,
$x = \dfrac{{24 \times 7}}{3}$
$x = 56$
We can verify this value of $x$ by substituting it in the L.H.S. and R.H.S. of equation (1),
L.H.S. of equation (1),
$x - 24 = 56 - 24 = 32$
R.H.S. of equation (1),
$\dfrac{4}{7}x = \dfrac{4}{7} \times 56 = 32$
L.H.S. = R.H.S.
Therefore, we get the value of $x$ as $56$.
The digits of $56$ are $5$ and $6$ .
The sum of digits of $56$ is $5 + 6 = 11$ .
The correct option is option C. $11$ .
Note: A linear equation in one variable is an equation that has a maximum of one variable of order $1$. Linear equation in one variable is solved by taking LCM, removing fractions, isolate the variable, and verification of answer. In real life, a linear equation in one variable has many applications and one prominent one is problems on age difference applications.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Change the following sentences into negative and interrogative class 10 english CBSE
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE