Question

Deveshi has a total of ₹ 590 as
currency notes in the denomination 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

Answer:

$\frak\blue{Given}\begin{cases}\sf{Total \: currency = Rs.590}\\\sf{Denominations: Rs.50,Rs.20,Rs.10}\\\sf{Ratio \: of \: Rs.50 \: \&\: Rs.20 = 3 : 5 }\\\sf{Total \: notes = 25}\\\sf\purple{Notes\: of \: each \: denomination =?}\end{cases}$

Let notes of Rs.50 be 3x and Rs.20 be 5x.

$\therefore$ Notes of Rs.10 = 25 - (3x + 5x) = 25 - 8x.

${\underline{\underline{\bold{According\:to \: question:-}}}}$

$\Rightarrow\sf (50 \times 3x) + (20 \times 5x )+ 10 \times(25-8x) = 590 \\\\\Rightarrow\sf 150x + 100x + 250 - 80x = 590 \\\\\Rightarrow\sf 170x = 590 - 250 \\\\\Rightarrow\sf 170x = 340 \\\\\Rightarrow\sf x =\cancel{\dfrac{340}{170}} \\\\\Rightarrow{\boxed{\sf\green{x = 2}}}$

$\rule{300}{1}$

→Number of Rs.50 notes = 3x = 3 × 2 = 6 notes.

→Number of Rs.20 notes = 5x = 5×2 = 10 notes.

→Number of Rs.10 notes= 25-8x = 25 -(8 × 2) = 9 notes.

${\underline{\boxed{\therefore{\sf\blue{Number\:of\:denominations\: : 6 \: , 10, \: \& \: 9 }}}}}$

Answer 2

Question:-

$\textsf{\red{Deveshi has a total of rs. 590 as currency }}\\\textsf{\red{notes in the denomination of rs. 50,rs.20 and rs. 10.}}\\\textsf{\red{ The ratio of the number of 50 notes }}\\\textsf{and 20 notes is 3:5.if she has a total of 25}\\\textsf{\red{ notes, how many notes of each }}\\\textsf{\red{denomination she has ?}}$

$\huge\boxed{\underline\textsf{Explantion:- }}$

$\textsf{Let the number of 50 notes} \\\textsf{and 20 notes be <strong>3x </strong>and <strong>5x, </strong>respectively. }$

$\textsf{but she has 25 notes in total.}$

Therefore,

$\textsf{the number of 10 notes =25-(3x+5x)}\\\textsf{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:</p><p> =25-8x}$

The amount she has ,

$\textsf{From 50 notes :3x \times 50 = 150x}$

$\textsf{From 20 notes : 5x \times 20 = 100x}$

$\textsf{From 10 notes = (25-8x) \times 10=(250-80x) }$

Hence,

$\textsf{The total money she has }\\\textsf{=150x+100x+(250-80x) }\\\textsf{</p><p> =(170x +250)}$

but she has ₹590.

Therefore,

$\textsf{170x + 250 =590}$

$\textsf{170x=590-250=340}$

$\sf x = \frac{\cancel{340}}{\cancel{170} }$

= 2

Or,

$\textsf{the number of 50 notes she has }$

$\textsf{=3x}$

$\textsf{= 3\times2}$

$\textsf{denomination=6}$

$\rule{300}{2}$

$\textsf{the number of 20 notes she has }$

$\textsf{=5x}$

$\textsf{=5\times2}$

$\textbf{denomination = 10}$

$\rule{300}{2}$

$\textsf{the number of 10 notes she has }$

$\textsf{=25-8x}$

$\textsf{=25-(8\times2)}$

$\textsf{=25-16}$

$\textsf{Denomination = 9}$

$\underline{\underline{\underline{\boxed{\boxed{\boxed{\boxed{\bf{Denomination=\:6,10,9}}}}}}}}$