Manohar has total of rs 250 as currency notes in the denomination of rs 20 ,rs10 and rs 5. The ratio of the numbers of rs 20 notes and rs10 notes is 3:4. If he has a total of 24 notes,how many notes of each denomination he has?

To solve this, let's work step by step.

Let's assume the number of Rs 20 notes to be 3x, and the number of Rs 10 notes to be 4x.

So, the number of Rs 5 notes can be determined as follows:
Total number of notes = number of Rs 20 notes + number of Rs 10 notes + number of Rs 5 notes
24 = 3x + 4x + number of Rs 5 notes
24 = 7x + number of Rs 5 notes

Since we have the total value of the notes, we can set up another equation based on their denominations:
Total value = (number of Rs 20 notes * value of Rs 20 note) + (number of Rs 10 notes * value of Rs 10 note) + (number of Rs 5 notes * value of Rs 5 note)
250 = (3x * 20) + (4x * 10) + (number of Rs 5 notes * 5)
250 = 60x + 40x + (number of Rs 5 notes * 5)
250 = 100x + (number of Rs 5 notes * 5)

Now, solving these equations simultaneously will help us find the values of x and the number of Rs 5 notes.

From equation 1: 24 = 7x + number of Rs 5 notes
From equation 2: 250 = 100x + (number of Rs 5 notes * 5)

To eliminate the variable "number of Rs 5 notes," we can multiply equation 1 by 5:
5 * 24 = 5 * (7x + number of Rs 5 notes)
120 = 35x + 5 * (number of Rs 5 notes)

Now we can substitute this in equation 2:
250 = 100x + 120 - 5 * (number of Rs 5 notes)
250 = 100x + 120 - 5 * (24 - 7x) (substituting equation 1)

Simplifying this equation:
250 = 100x + 120 - 120 + 35x
250 = 135x
x = 250 / 135
x = 1.85

Now, since the number of notes cannot be decimal, we will round it down to the nearest integer, which is 1.
So, x = 1.

Substituting the value of x back into equation 1:
24 = 7 * 1 + number of Rs 5 notes
24 = 7 + number of Rs 5 notes
number of Rs 5 notes = 24 - 7
number of Rs 5 notes = 17

Therefore, the number of notes of each denomination is:
Rs 20 notes: 3 * 1 = 3
Rs 10 notes: 4 * 1 = 4
Rs 5 notes: 17

So, Manohar has 3 notes of Rs 20, 4 notes of Rs 10, and 17 notes of Rs 5.

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