deveshi has a total of ₹590 notes in the denomination of ₹50 notes and ₹20 notes is 3:5 if she had a total of 25 notes how many notes of each denomination does she have
Answers
Let
No. of currency notes of Rs 50 = 3x
No. of currency notes of Rs 20 = 5x
No. of currency notes of Rs 10 = 25 - (3x+5x) = 25 - 8x
Amount made by Rs 50 notes = 50 × 3x = 150x
Amount made by Rs 20 notes = 20 × 5x = 100x
Amount made by Rs 10 notes = 10 × (25 - 8x) = 250 - 80x
Total money = 590
⇒ 150x + 100x + 250 - 80x = 590
⇒ 170x = 340
⇒ x = 2
Denominations:
Rs 50 = 3 × 2 = 6
Rs 20 = 5 × 2 = 10
Rs 10 = (25 - 8 × 2) = 9
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Step-by-step explanation:
Let 50 rupee notes = 3k and
20 rupee notes = 5k,
where k is some constant.
So total 50 and 20 rupee notes = 8k
Amount in 50 rupee notes = 50*3k = 150k
Amount in 20 rupee notes = 20*5k = 100k
Amount in 10 rupee notes = 10*remaining possible notes = 10*(25–8k) = 250–80k
So we get the equation that:
150k + 100k + 250–80k = 590
170k + 250 = 590
170k = 340
k = 2
So Deveshi has:
3*2 = 6 Rs.50 notes
5*2 = 10 Rs. 20 notes
25 - 16 = 9 Rs.10 notes