I have in my purse 5, 10 and 20 rupee notes totalling 500 rupees. Total number of notes is 45. The total number of 5 and 10 rupee notes is 15 more than the number of 20 rupee notes. Find their numbers by Cramer's Rule?

1 Answer
Shwetank Mauria
Jun 11, 2017

I have #20# notes of Rs.#5# denomination, #10# notes of Rs.#10# denomination and #15# notes of denomination Rs.#20#.

Explanation:

Suppose I have #x# notes of Rs.#5# denomination, #y# notes of Rs.#10# denomination and then we have #45-x-y# notes of denomination Rs.#20#.

As total number of #5# and #10# rupee notes is #15# more than the number of #20# rupee notes, we have #x+y=(45-x-y)+15#

or #x+y=60-x-y# or #2x+2y=60# or #x+y=30# or #y=30-x#

Hence we have #x# notes of Rs.#5# denomination, #30-x# notes of Rs.#10# denomination and then we have #45-x-y=45-x-(30-x)=15# notes of denomination Rs.#20#.

And their value is #5x+10xx(30-x)+15xx20=5x+300-10x+300=600-5x#

and #600-5x=500# i.e. #5x=600-500=100# and #x=100/5=20#

Hence, I have #20# notes of Rs.#5# denomination, #10# notes of Rs.#10# denomination and #15# notes of denomination Rs.#20#.

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