Question

Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:

Meena went to a bank to withdraw Rs. $2000.$ She asked the cashier to give her Rs. $50$ and Rs. $100$ notes only. Meena got $25$ notes in all. Find how many notes of Rs. $50$ and Rs. $100$ she received

• A. $15$ notes of Rs. $50$ and $18$ notes of Rs. $100.$
• B. $12$ notes of Rs. $50$ and $18$ notes of Rs. $100$.
• C. $8$ notes of Rs. $50$ and $25$ notes of Rs. $100.$
• D. $10$ notes of Rs. $50$ and $15$ notes of Rs. $100$.

Answer 1

The correct option is D $10$ notes of Rs. $50$ and $15$ notes of Rs. $100$.

Let $x$ and $y$ be the number of ' $50$ and '$100$ notes.respectively.

Then, $x+y=25$ ....(1)
and $50x+100y=2000$ ...(2)
Now multiplying (1) from $100$ and (2) from (1) subtracting (2) from (1) will get
$\Rightarrow 100(x+y)-1(50x-100y)=100\times 25-1\times 2000$
$\Rightarrow 100x+100y-50x-100y=2500-2000$
$\Rightarrow 50x=500$
$\Rightarrow x=10$
Now putting $x$ in (1)
$\Rightarrow 10+y=25$
$\Rightarrow y=25-10$
$\Rightarrow y=15$
Hence Meena Received $10$ notes of Rs. $50$ and $15$ notes of Rs. $100$.