NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 3: Pair of Linear Equations in Two Variables - Exercise 3.1
Question 12

Question.  12

12. Aruna has only Re 1 and Rs 2 coins with her. If the total number of coins is 50 and the total amount is Rs 75, then the number of Re 1 and Rs 2 coins are, respectively

(A)

35 and 15

(B)

35 and 20

(C)

15 and 35

(D)

25 and 25

Detailed Answer with Explanation:

Step 1: Define variables.

Let the number of Re 1 coins be \(r\).

Let the number of Rs 2 coins be \(t\).

Step 2: Form equations from the conditions.

Total number of coins is 50:

\(r + t = 50\).

Total value of coins is Rs 75:

\(1 \times r + 2 \times t = 75\).

So the second equation is \(r + 2t = 75\).

Step 3: Solve the system of equations.

Subtract the first equation from the second:

\((r + 2t) - (r + t) = 75 - 50\)

\(t = 25\).

Now substitute \(t = 25\) in the first equation:

\(r + 25 = 50\)

\(r = 25\).

Step 4: Final Answer.

The number of Re 1 coins = 25, and the number of Rs 2 coins = 25.

So the correct option is (D) 25 and 25.

NCERT Exemplar Solutions Class 10 – Mathematics – CHAPTER 3: Pair of Linear Equations in Two Variables – Exercise 3.1 | Detailed Answers