Deveshi has a total of ` 590 as currency notes in the denominations of 50, ` 20 and ` 10. The ratio of the number of ` 50 notes and ` 20 notes is 3:5. If she hasa total of 25 notes, how many notes of each denomination she has?
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: Let the number of ` 50 notes and ` 20 notes be 3x and 5x, respectively.
But she has 25 notes in total.
Therefore, the number of ` 10 notes = 25 – (3x + 5x) = 25 – 8x
The amount she has
from ` 50 notes : 3x × 50 = ` 150x
from ` 20 notes : 5x × 20 = ` 100x
from ` 10 notes : (25 – 8x) × 10 = ` (250 – 80x)
Hence the total money she has =150x + 100x + (250 – 80x) = ` (170x + 250)
But she has ` 590. Therefore, 170x + 250 = 590
or 170x = 590 – 250 = 340
or x =340/170 = 2
The number of ` 50 notes she has = 3x
= 3 × 2 = 6
The number of ` 20 notes she has = 5x = 5 × 2 = 10
The number of ` 10 notes she has = 25 – 8x
= 25 – (8 × 2) = 25 – 16 = 9
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