Question

a sum <br />of rupees 800 is in the form of 10 rupee notes and 20 notes only if the total numbers of notes is 50 find the number of notes of each type ​

Answer 1

Answer:-

$\sf{Number \ of \ 10 \ rupee \ notes \ is \ 20 \ and}$

$\sf{number \ of \ 20 \ rupee \ notes \ is \ 30.}$

Given:

• A sum of rupees 800 is in the form of 10 rupee notes and 20 rupee notes.

• Total number of notes is 50.

To find:

• The number of notes of each type.

Solution:

$\sf{Let \ the \ number of \ 10 \ rupee \ notes \ be \ x}$

$\sf{and \ number \ of \ 20 \ rupee \ notes \ be \ y.}$

$\sf{According \ to \ the \ first \ condition.}$

$\sf{10x+20y=800}$

$\sf{\therefore{10(x+2y)=800}}$

$\sf{\therefore{x+2y=\frac{800}{10}}}$

$\sf{\therefore{x+2y=80...(1)}}$

$\sf{According \ to \ the \ second \ condition.}$

$\sf{x+y=50....(2)}$

$\sf{Subtract \ equation (2) \ from \ equation (1), \ we \ get}$

$\sf{x+2y=80}$

$\sf{-}$

$\sf{x+y=50}$

________________

$\boxed{\sf{\therefore{y=30}}}$

$\sf{Substitute \ y=30 \ in \ equation (2), \ we \ get}$

$\sf{x+30=50}$

$\sf{\therefore{x=50-30}}$

$\boxed{\sf{\therefore{x=20}}}$

$\sf\purple{\tt{\therefore{Number \ of \ 10 \ rupee \ notes \ is \ 20 \ and}}}$

$\sf\purple{\tt{number \ of \ 20 \ rupee \ notes \ is \ 30.}}$

Answer 2

$\huge\underline\mathfrak\color{red}Given$

• A sum of rupees 800 is in the form of 10 rupee notes and 20 notes.
• The total numbers of notes is 50 .

$\huge\underline\mathfrak\color{red}ToFind$

• The total numbers of notes is 50 .

$\huge\underline\mathfrak\color{red}Solution$

Suppose,

the number of 10 rupee notes be x.

and the sum of 20 rupee notes be y.

According to the first condition,we get,

$\sf{10x + 20y) = 800}$

$\sf{\implies 10(x + 2y) = 800}$

$\sf{\implies(x + 2y) = \cancel \frac{800}{10} }$

$\sf{\implies (x +2y) = 80}$-----(1)

Now,by second condition,we get,

$\sf{\implies (x + y) = 50}$--------(2)

Now by subtracting eq (2) from (1) we get,

$\sf{(x + 2y - x - y = 80 - 50}$

$\sf{y = 30}$

Putting the value of y in the eq (2)we get,

$\sf{x + 30 = 50}$

$\sf{\implies x = 50 - 30}$

$\sf{\implies x = 20}$

Hence,the number of 10 rupee notes is 20 and the number of 20 rupee notes is 30.