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?​

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

Solution :

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 x 50 = ₹150x

from ₹20 notes: 5x x 20 = ₹100x

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

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

➸ ₹(170x +250)

now, 170x + 250 = 590

or 170x = 590 - 250 = 340

➸ x = 340/170

➸ x = 2

The number of ₹50 notes she has

➸ 3x

➸ 3 x 2

➸ 6

The number of ₹20 notes she has

➸ 5x

➸ 5 x 2

➸ 10

The number of ₹10 notes she has

➸ 25 - 8x

➸ 25 - (8 x 2)

➸ 25 - 16

➸ 9