Question

A sum of 800rs is in the form of denominations of 10rs and 20rs. If the total number of notes is 50, find the number of notes each type.​

Answer 1

Answer:

There are 30 notes of Rs. 20 and 20 notes of Rs. 10.

Step-by-step explanation:

Given amount = Rs. 800

The amount is in denominations = Rs. 10 and Rs. 20

Total number of notes = 50

Let the number of notes be :

• Rs. 10 denominations = x
• Rs. 20 denominations = y

Total notes = 50

$\sf{\longrightarrow} \: x + y = 50$

$\sf{\longrightarrow} \: x = 50 - y$

So,

• Rs. 10 denominations = (50 – y)
• Rs. 20 denominations = y

Value of the notes :

• Rs. 10 = 10(50 – y)
• Rs. 20 = 20(y)

___________________

According to the Question,

The amount is Rs. 800.

$\sf{\longrightarrow} \: 10(50 - y) + 20(y)= 800$

$\sf{\longrightarrow} \: 500 - 10y+ 20y= 800$

$\sf{\longrightarrow} \: 10y= 800 - 500$

$\sf{\longrightarrow} \: 10y= 300$

$\sf{\longrightarrow} \: y= \dfrac{300}{10}$

$\sf{\longrightarrow} \: y=30$

Rs. 20 notes = 30

___________________

Rs. 10 notes =

$\sf{\longrightarrow} \: x = 5 0 - 30$

$\sf{\longrightarrow} \: x = 20$

Rs. 10 notes = 20

Therefore, there are 30 notes of Rs. 20 and 20 notes of Rs. 10.

Answer 2

Step-by-step explanation:

Given -

Amount is Rs. 800

In the form of notes of Rs. 10 and Rs. 20

The total notes are 50

Notes of each type = ??

Consider the notes of Rs. 20 as 'z' and Rs. 10 as '50 - z'

Value of Rs. 10 = 10 × (50 - z)

Value of Rs. 20 = 20 × (z)

==> Value of Rs. 10 notes + Value of Rs. 20 notes = Rs. 800

==> 500 - 10z + 20z = 800

==> 10z = 800 - 500

==> 10z = 300

==> z = 300/10

==> z = 30

Number of 20 Rupees notes is 30.

10 Rupees notes = (50 - 30) = 20

Hence, Rs. 10 notes are 20 and Rs. 20 notes are 30.