Question

Aruna has only Rs 1 and Rs 2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is Rs 75 then the number of Rs 1 and Rs 2 coins are respectively.
(A) 35 and 15 (B) 35 and 20 (C) 15 and 35 (D) 25 and 25

Answer 1

Hint: Here we will use the rules as we follow to solve simultaneous linear equations. Initially let’s take arbitrary unknown values to make linear equations according to the given data in the question & then solve it to get the ultimate answer.
 We are using a monotonous equations line where x & y are unknown arbitrarily taken values to be determined & 'a' values are constants.
$x + y = {a_1}$………. (I)
$x - y = {a_2}$………. (II)

Complete step-by-step answer: Let’s assume no. of coins Rs. 1 = $x$ and no. of coins Rs. 2 = $y$
According the question
$x + y = 50$………. (I)
$x = 50 - y$………. (II)
Amount of money from Rs 1 coins $ = 1 \times x = x$
Amount of money from Rs 2 coins $ = 2 \times y = 2y$
According the question
$x + 2y = 75$………. (III)
$x = 50 - y$ putting it at equation ………. (II)
$x + 2y = 75$………. (II)
$
   \Rightarrow 50 - y + 2y = 75 \\
   \Rightarrow 50 + y = 75 \\
   \Rightarrow y = 75 - 50 \\
   \Rightarrow y = 25 \\
$
$y = 50$ putting on an equation ……… (II)
$
  x = 50 - y \\
   \Rightarrow x = 50 - 25 \\
   \Rightarrow x = 25 \\
$

So, the correct answer is “Option D”.

Note: Apply the steps as required to solve simultaneous linear equations with two unknown values & do the calculations carefully so that there would be no chance of technical error.
After getting the numerical values of unknown assumed values, put those determined values in any of the two equations to check whether it is satisfying the both sides of the equation accurately.