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

Step-by-step explanation:

Ratio of RS 50 notes and RS 20 notes = 3:5. This means that either -

RS 50 notes = 3 and RS 20 notes = 5

RS 50 notes = 6 and RS 20 notes = 10

RS 50 notes = 9 and RS 20 notes = 15

And so on.

But the total amount of all the notes is RS 590, so the amount by alone 50rs and 20rs notes can't be greater than 580 as there must be atleast one 10rs note as well as mentioned in the question. So let's calculate the sums in the above mentioned cases.

RS 50 notes = 3 and RS 20 notes = 5 ; sum 250

RS 50 notes = 6 and RS 20 notes = 10 ; sum 500

RS 50 notes = 9 and RS 20 notes = 15 ; sum 750 which is not possible.

For higher notes cases, sum will be higher.

So we are left with 2 cases only -

Rs 50 notes = 3 and RS 20 notes = 5 ; sum 250 ; for amount to be 590 we'll be needing 24 notes of 10rs. So we get total number of notes as 3+5+24= 32

RS 50 notes = 6 and RS 20 notes = 10 ; sum 500 ; for amount to be 590 we'll be needing 9 notes of 10rs. So we get total number of notes as 6+10+9 = 25 which is what we need. So this is the correct answer

RS 50 notes - 6

RS 20 notes - 10

RS 10 notes - 9

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Answer 2

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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