Twinkle 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 of Rs. 50 notes and Rs. 20 notes is $ 3: 5 $. If she has a total of 25 notes, how many Rs. 20 notes does she have?

Given:

Twinkle 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 of Rs. 50 notes and Rs. 20 notes is \( 3: 5 \).

Total number of notes $=25$.

To do: 

We have to find the number of notes of Rs. 20.

Solution:

Let the number of Rs. 50 notes be $x$, the number of Rs. 20 notes be $y$ and the number of Rs. 10 notes be $z$.

The total number of notes $= 25$

Let $x=3k$ and $y=5k$

This implies,

$z=25-(x+y)$

$z=25-(3k+5k)$

$z=25-8k$

Total amount only in Rs. 50 notes $= 50x=50(3k)=150k$

Total amount only in Rs. 20 notes $=20y=20(5k)=100k$

Total amount only in Rs. 10 notes $=10z=10(25-8k)=250-80k$

Total amount $=Rs.\ 590$

$150k + 100k + 250-80k = 590$

$170k=590-250$

$170k=340$

$k=2$

$\Rightarrow x=3k=3(2)=6$

$\Rightarrow y=5k=5(2)=10$

$\Rightarrow z=25-8k=25-8(2)=25-16=9$

Therefore, the number of Rs. 20 notes she has is 10.