Question

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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

$\huge{\underline{\underline{\boxed{\mathfrak{Question}}}}}$

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?

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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 = Rs 150x

from ₹20 notes: 5x × 20 = Rs 100x

from ₹10 notes: ( 25 - 8x ) × 10 = Rs ( 250 - 80x )

Hence, the total money she has = 150x + 100x + ( 250 - 80x ) = Rs ( 170x + 250 )

But she has Rs 590.

Therefore, 170x + 250 = 590

170x = 590 - 250

170x = 340

x = 340/170

x = 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

Answer 2

$\huge{\underline{\boxed{\mathfrak{Solution:-}}}}$

•Given

$• \: Devshi \: \: has \: \: 590 \: \: Rupees$

$= > Rs.50,20 \: and \: 10 \: are \: there - > \: Total \: 25 \: notes$

$= > \: Rs.50 \: and \: Rs.20 \: - > 3:5$

$= > \: Notes \: of \: Rs.50 \: = \: 3x$

$= > \: Notes \: of \: Rs.20 \: = \: 5x$

$= > Notes \: of \: Rs.10 \: = \: 25− \: ( \: 3x \: + \: 5x \: ) \: =25 \: − \: 8x.$

$•Amount \: in \:  50  \: Rupee \: notes ⇒50 \: × \: 3x \: = \: 150x</p><p></p><p>$

$•Amount \: in \:  20 \:  Rupee \: notes ⇒ \: 20× \: 5x \: = \: 100x.</p><p> \\ • \: Amount \: in  \: 10 \:  Rupee \: notes  \: ⇒ \: 10( \: 25 \: − \: 8x \: )= \: 250 \: − \: 80x</p><p></p><p>$

Total Amount =590

$⇒150x+100x+250−80x \\ =590$

$\\ ⇒250−80x=590−250</p><p></p><p> \\ ⇒170x=340</p><p></p><p> \\ ∴x=2</p><p>$

So Deveshi has

$Notes \: of \: Rs.50 \: \\ =3(2) \: =6:i.e \: ; \: 150(2) \: \\ = \: 300Rs.$

$Notes \: of \: Rs.20 \: \\ =5(2)= \: 10/i.e;100(2) \\ = \: 200Rs.$

$Notes \: o \: f Rs.10 \\ = \: 25−8(2)=9 /i.e; \\ =90Rs$