Question

16. A sum of 500 is in the form of denominations of 75 and 10. If the total number of notes is 90. find the number of notes of each type.​

Answer 1

Correct Question :

A sum of ₹ 500 is in the form of notes of denominations of ₹ 5 and ₹ 10. If the total number of notes is 90, find the number of notes of each type.

Given :

• A sum of ₹ 500 is in the form of notes of denominations of ₹ 5 and ₹ 10.
• The total number of notes is 90.

To Find :

The number of notes of each type.

Solution :

• Let the no of ₹ 5 notes be “x”.

∴ No of ₹ 10 notes be “90 – x”.

• Value of ₹ 5 notes = ₹5 × x = ₹5x
• Value of ₹ 10 notes = ₹10 × (90 - x) = ₹(900 - 10x)

• It is given the sum of the amount is ₹500.

According to the question,

$\\ :\implies\sf5x+(900-10x)=500$

$\\ :\implies\sf5x+900-10x=500$

$\\ :\implies\sf5x-10x=500-900$

$\\ :\implies\sf-5x=-400$

$\\ :\implies\sf\not{-}5x=\not{-}400$

$\\ :\implies\sf5x=400$

$\\ :\implies\sf x=\dfrac{400}{5}$

$\\ :\implies\sf x=\cancel{\dfrac{400}{5}}$

$\\ \therefore\boxed{\bf x=80.}$

The value of x is 80.

So,

• No of ₹5 notes = x = 80
• No of ₹10 notes = 90 - x = 90 - 80 = 10

No of ₹5 notes = 80.

No of ₹10 notes = 10.