# Deveshi has a total of Rs 590 as currency notes in the denominations of Rs.50,Rs.20 and Rs.10.The ratio of the number Rs 50 notes and Rs 20 notes is 3:5.If she has a total of 25 notes,how many denominations of each denomination has she? (write with steps)

2
by deva07

2014-07-31T10:36:53+05:30
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
2014-07-31T11:52:59+05:30

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Since Rs 50 & Rs 20 are in the ratio we can write,
No. of Rs 50 notes = 3x
No. of Rs 20 notes = 5x
As She has a total of 25 notes,
So, we can write,
No. of Rs 10 notes = 25-(3x+5x) = 25-8x

Now we calculate the actual amount of each notes,
Rs 50 note amount to = 50×3x = 150x
Rs 20 note amount to = 20×5x = 100x
Rs 10 note amount to = 10×(25-8x) = 250-80x

Total sum of money he has = Rs 590
According to the problem,
150x + 100x + 250 - 80x = 590
170x = 340
x = 2

Now we find out the actual no of notes in each case,
No. of Rs 50 notes = 3 × 2 = 6 ; No. of Rs 20 notes = 5 × 2 = 10 ; No.of Rs 10 notes = 25-(8 × 2) = 9