10th Class Mathematics Pair of Linear Equations in Two Variables Question Bank MCQs - Pair of Linear Equations in Two Variables

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 Ra 1 and Rs 2 coins is

A) 24,24

B) 25,25

C) 26,26

D) None of these

Correct Answer: B

Solution :

Let the number of Rs 1 coins = x

and the number of Rs 2 coins = y

Then, by given condition,

\[x\text{ }+\text{ }y\text{ }=\text{ }50\] ...(i)

and \[x\times 1+y\times 2=75\]

\[\Rightarrow \,\,\,x+2y=75\] ...(ii)

On subtracting Eq. (i) from Eq. (ii), we get

\[\left( x+2y \right)-\left( x+y \right)=75-50\Rightarrow y=25\]

On substituting y = 25 in Eq. (i), we get

\[x+25=50\Rightarrow x=25\]

Hence, she has 25 coins of Rs 1 and 25 coins of Rs 2.