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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.

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15

notes of Rs.

50

and

18

notes of Rs.

100 .

12

notes of Rs.

50

and

18

notes of Rs.

100

8

notes of Rs.

50

and

25

notes of Rs.

100 .

10

notes of Rs.

50

and

15

notes of Rs.

100

answer is D.

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Detailed Solution

Let

x

and

y

be the number of

50

and

100

notes respectively.
Then,

x + y = 25

.........(1)
And

50 x + 100 y = 2000

.........(2)
Now multiplying (1) from

100

and subtracting from (2) will get,

\Rightarrow 100 (x + y) - (50 x - 100 y) = 100 \times 25 - 2000

\Rightarrow 100 x + 100 y - 50 x - 100 y = 2500 - 2000

\Rightarrow 50 x = 500

\Rightarrow x = 10

Now putting

x = 10

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

.
Therefore, option (4) is correct.

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