Question

in a purse there are 20 rupee notes ten rupee notes and 50 rupee notes the number of 50 rupee notes exceeds 2 times the number of 10 rupee note by 1 the number of 20 rupee notes are 5 less than the number of 10 rupee notes if the total value of the money in a purse is 860 find the number of each variety of notes

Answer 1

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Answer 2

There are 7 numbers of ₹10 notes, 2 numbers of ₹20 notes and 15 numbers of ₹50 notes in the purse.

Step-by-step explanation:

Given:

In a purse there are 20 rupee notes 10 rupee notes and 50 rupee notes.

Let the number of ₹10 note be 'x'.

Now Given:

The number of 50 rupee notes exceeds 2 times the number of 10 rupee note by 1.

Hence we can say that;

the number of ₹50 note = $2x+1$

Also;

The number of 20 rupee notes are 5 less than the number of 10 rupee notes.

Hence we can say that;

the number of ₹20 note = $x-5$

Again Given:

Total Value in purse = ₹860

Value of ₹10 notes = $10x$

Value of ₹20 notes = $20(x-5)=20x-100$

Value of ₹50 notes = $50(2x+1)=100x+50$

Now we know that;

Total Value in purse is sum of Value of ₹10 notes and Value of ₹20 notes and Value of ₹50 notes.

framing in equation form we get;

$10x+20x-100+100x+50 =860\\\\130x-50=860$

Adding both side by 50 using Addition property of equality we get;

$130x-50+50=860+50\\\\130x =910$

Now Dividing both side by 130 using Division property of equality we get;

$\frac{130x}{130}=\frac{910}{130}\\\\x=7$

Number of ₹10 notes = 7

Number of ₹20 notes = $x-5= 7-5 = 2$

Number of ₹20 notes = $2x+1=2\times7+1=14+1 = 15$

Hence There are 7 numbers of ₹10 notes, 2 numbers of ₹20 notes and 15 numbers of ₹50 notes in the purse.