Question

Nitya and Satya have some marbles with them. Nitya says to Satya, “If you have given one marble to me, we will have an equal number of marbles. Satya says to Nitya, “If you give me one marble, I will have twice the marbles you have.” How many marbles do Nitya and Satya have respectively?
A.4, 6
B.5, 7
C.6, 4
D.7, 5

Answer 1

Hint: Simultaneous equations can be solved using a substitution method. For instance, if there are two simultaneous equations of the form \[p + q = c\] and $ p - q = d $ . Then find the value of $ p $ in terms of $ q $ using the first equation and substitute it in the second equation to find the value of \[q\].

Complete step-by-step answer:
A mathematical event in which some information based on the problem is presented in simple language and not by using mathematical symbols. Such a mathematical event is called word problem. Word problems can be defined using words and numbers. It can be solved by formulating equations and solving them simultaneously based on the number of variables.
Let us assume $ n $ and $ s $ be the number of marbles Nitya and Satya has respectively.
If Satya gives one marble to Nitya, they will have an equal number of marbles.
In the form of the equation, the statement can be written as $ n + 1 = s - 1 $
After simplifying the equation, we get,
 $
\Rightarrow s - n = 2\\
\Rightarrow s = n + 2......\left( 1 \right)
 $
If Nitya gives one marble to Satya, Satya will have twice the marbles Nitya has.
In the form of the equation, the statement can be written as $ 2\left( {n - 1} \right) = s + 1 $
After simplifying the equation, we get,
 $
\Rightarrow 2n - 2 = s + 1\\
\Rightarrow 2n - s = 3......\left( 2 \right)
 $
To find the number of marbles present with Satya and Nitya, we need to solve equations (1) and (2).
Here, we need to substitute the value of $ s $ from equation (1) into equation (2).
 $\Rightarrow 2n - \left( {n + 2} \right) = 3 $
After simplifying the equation, we can get the number of marbles present with Nitya.

$\Rightarrow 2n - n - 2 = 3 $
$\Rightarrow n - 2 = 3 $
$\Rightarrow n = 5 $

We need to substitute the value of $ n = 5 $ in the equation (1) to find \[s\].
Therefore, the number of marbles with Nitya and Satya have 5 and 7 marbles respectively.

So, the correct answer is “Option B”.

Note: In this type of question, variables should be assumed properly. The conditions given in the question are to be formulated using addition, multiplication, subtraction or division operation. The number of variables must always be equal to the number of equations in order to find the values of the variables successfully.