Question

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

Answer 1

Hint: As given in the question the ratio of the number of $ Rs.50 $ notes and $ Rs.20 $ notes is $ 3:5 $ so we will assume the number of $ Rs.50 $ notes be $ 3x $ and the number of $ Rs.20 $ notes be $ 5x $ . Also, we have been given in the question the total number of notes and the total amount so by forming an equation and solving further we will get an answer.

Complete step by step answer:
We have been given that Deveshi has a total of $ Rs.590 $ as currency notes in the denominations of $ Rs.50 $ , $ Rs.20 $ and $ Rs.10 $ .
We have to find the number of notes for each denomination she has.
We have given that the ratio of the number of $ Rs.50 $ notes and $ Rs.20 $ notes is $ 3:5 $ . So let us assume that number of $ Rs.50 $ notes be $ 3x $ and the number of $ Rs.20 $ notes be $ 5x $ .
Also we have total of $ 25 $ notes, so the number of $ Rs.10 $ notes will be $ 25-\left( 3x+5x \right) $
Now, amount of $ Rs.50 $ notes will be $ 50\times 3x=150x $
Now, amount of $ Rs.20 $ notes will be $ 20\times 5x=100x $
Now, amount of $ Rs.10 $ notes will be $ 10\times \left( 25-8x \right)=250-80x $
Now, as given in the question the total amount is $ Rs.590 $ .
So, we have
 $ \begin{align}
  & \Rightarrow 150x+100x+250-80x=590 \\
 & \Rightarrow 250x-80x=590-250 \\
 & \Rightarrow 170x=340 \\
 & \Rightarrow x=\dfrac{340}{170} \\
 & \therefore x=2 \\
\end{align} $
Now, number of $ Rs.50 $ notes will be $ 3x=3\times 2=6 $
Number of $ Rs.20 $ notes will be $ 5x=5\times 2=10 $ .
Number of $ Rs.10 $ notes will be $ 25-\left( 3x+5x \right)=25-\left( 6+10 \right)=9 $
So, Deveshi has $ 6,10 $ and $ 9 $ currency notes in the denominations of $ Rs.50 $ , $ Rs.20 $ and $ Rs.10 $ respectively.

Note:
 Alternatively one can write the possibilities of the denominations of the $ Rs.50 $ , $ Rs.20 $ notes and then shortlisted the possibilities according to the question and calculate the number of notes in that particular case. As given in the question the ratio of the number of $ Rs.50 $ notes and $ Rs.20 $ notes is $ 3:5 $ so the possible number of notes will be
 $ Rs.50=3\text{ notes and }Rs.20=5\text{ notes} $
 $ Rs.50=6\text{ notes and }Rs.20=10\text{ notes} $
 $ Rs.50=9\text{ notes and }Rs.20=15\text{ notes} $