Question

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 has a total of 25 notes, how many notes of each denomination she has?

Answer 1

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.