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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Answer 1

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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?

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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

Let ratio of Rs 50 to Rs 20 be 3x:5x (x be the common factor/variable const)

Therefore, Total no of RS 20 and Rs 50 = 8x

Let no of Rs 10 notes be y

According to question,

y + (5x+3x) =  25  (total no of notes)

==> y+8x =25 ............(i)

Value of Rs 10 notes = 10y

Value of Rs 20 notes = 20 * 5x

                                     =100x

Value of Rs 50 notes =  50 * 3x

                                     =150x

According to question ,

10 y + 100x+150x=590   (total value of currencies)

==> 10y+250x =590

==> 10 (y+25x) =590    (taking out common factors)

==> y +25x =59............(ii)

Subtracting  (ii) from (i) to eliminate ,,

y+25x-(y+8x) =59-25

==>25x-8x = 34   ( y is eliminated)

==>17x=34

====> x=2

So calculating,,

No of Rs 50 notes = 3x =3*2 =[[ 6 notes ]]

No of Rs 20 notes = 5x =5*2 = [[10 notes]]

No of Rs 10 notes ===>

From (i)

We get,

y+8x=25

==> y=25-(8*2)

==> y=9

No of Rs 10 notes = [[9 notes]]

VERIFY

i) 6+10+9=25    

and ii) (10*9) +(20*10)+(50*6)= Rs 590

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