Question

John has a total of ₹1460 as currency notes in the denominations of ₹50, ₹20, and ₹10. The ratio of the number of ₹50 notes and ₹20 notes is 4:3. If he has a total of 70 notes, how many notes of each denomination he have?

Answer 1

Given :-

Total amount= ₹ 1460

The ratio of the number of ₹ 50 notes and ₹ 20 notes = 4:3

Total notes = 70

To FinD :-

How many notes of each denomination he have?

Solution :-

The ratio of ₹ 50 and ₹ 20 notes = 4:3.

It means that -

Number of ₹ 50 notes = 4x

And the total amount of ₹ 50 notes = 50 × 4x

= 200x

Number of ₹ 20 notes = 3x

And the total amount of ₹ 20 notes = 20 × 3x

= 60x

Now, the number of ₹ 10 notes = Total Number of notes - ₹ 50 notes and ₹ 20 notes

Number of ₹ 10 notes = 70 - 4x - 3x = (70 - 7x)

And the total amount of ₹ 10 notes = 10 × (70-7x)

Now According to the question -

Amount of ₹ 10 notes + Amount of ₹ 20 notes + Amount of ₹ 50 notes = 1460

10 × (70 - 7x) + 60x + 200x = 1460

700 - 70x + 60x + 200x = 1460

700 - 10x + 200x = 1460

700 + 190x = 1460

190x = 1460-700

190x = 760

x = $\frac{760}{190}$

x = 4

• Now the Number of ₹ 10 notes = 70 - 7x

Putting the value of x

= 70 - 7 × 4

= 70 - 28

= 42

• The number of ₹ 20 notes = 3x

= 3× 4

= 12

• The number of ₹ 50 notes = 4x

= 4 × 4

= 16

So John have 42 notes of ₹ 10 , 12 notes of ₹ 20 and 16 notes of ₹ 50.